· 2005-11-21 · 1 September, 2005 Determination of Neutrino Mixing-Angle θ 13 Using The Daya...

1 September, 2005

Determination of Neutrino Mixing-Angle θ13

Using

The Daya Bay Nuclear Power Facilities

Version 2.3

Beijing Normal University, China

Chinese University of Hong Kong, China

Institute of Atomic Energy, China

Institute of High Energy Physics, China

Institute for Scintillation Materials, Ukraine

Institute of Theoretical Physics, China

Iowa State University, U.S.A.

Joint Institute for Nuclear Research at Dubna, Russia

Kurchatov Institute, Russia

Lawrence Berkeley National Laboratory, U.S.A.

Nankai University, China

Shenzhen University, China

Tsing Hua University, China

University of California at Berkeley, U.S.A.

University of California at Los Angeles, U.S.A.

University of Hong Kong, China

University of Houston, U.S.A.

University of Illinois at Urbana-Champaign, U.S.A.

University of Maryland at College Park, U.S.A.

University of Science and Technology of China, China

University of Washington at Seattle, U.S.A.

Contents

1 Introduction 1

2 Physics Motivation 42.1 Current Status of neutrino oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Theoretical expectations of θ13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Expectations of θ13 from global three-neutrino analysis . . . . . . . . . . . . . 92.2.2 Expectations of θ13 from specific neutrino mass models . . . . . . . . . . . . 10

2.3 Measurement of θ13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Long baseline experiments and the measurement θ13 . . . . . . . . . . . . . . 122.3.2 Advantages of measuring θ13 at reactors . . . . . . . . . . . . . . . . . . . . . 14

3 Reactor Antineutrino 233.1 Energy spectrum and flux of reactor antineutrinos . . . . . . . . . . . . . . . . . . . 233.2 Inverse beta decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 Prediction and observed antineutrino flux and spectrum . . . . . . . . . . . . . . . . 273.4 Remarks on very low energy reactor antineutrinos . . . . . . . . . . . . . . . . . . . 28

4 Experimental Site and Laboratory Designs 324.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2 Site geology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.3 Seismic activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Engineering geology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 Hydrogeology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.6 Stability of mountain and cavern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.7 Transportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.8 Design of laboratory facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.8.1 Detector sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.8.2 Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5 Detector 405.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.3 Liquid scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.4 Detector modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.4.1 Module geometry and Energy resolution . . . . . . . . . . . . . . . . . . . . . 46

ii

CONTENTS iii

5.4.2 Gamma catcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.4.3 Oil buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.4.4 Containers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.5 Water buffer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.6 Muon veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.6.1 Water Cherenkov detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.6.2 Resistive Plate Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.6.3 Scintillator-strip muon tracker . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.7 PMT Readout System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.7.1 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.7.2 PMT readout module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.7.3 Muon-veto readout system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.8 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.9 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.9.1 LED system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.9.2 Laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.9.3 Radioactive sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6 Detector Overburden and Backgrounds 646.1 Overburden and muon flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2 Correlated background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2.1 Fast neutrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2.2 Cosmogenic 8He/9Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.2.3 Other correlated backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.3 Uncorrelated background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.4 Summary of backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

7 Systematic Issues 777.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.2 Systematic error estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

7.2.1 Reactor power levels and locations . . . . . . . . . . . . . . . . . . . . . . . . 787.2.2 Detector-related errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.2.3 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.3 χ2 analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.4 Side-by-side calibration and detector swapping . . . . . . . . . . . . . . . . . . . . . 897.5 Baseline optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917.6 Sensitivity results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

8 Other Physics Reaches 958.1 Sterile neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958.2 Supernova Neutrinos and Supernova Watch . . . . . . . . . . . . . . . . . . . . . . . 97

8.2.1 SN neutrino spectra and flux . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.2.2 Detect SN neutrinos in the Daya Bay experiment . . . . . . . . . . . . . . . . 101

8.3 Exotic neutrino properties and nuclear power monitoring . . . . . . . . . . . . . . . 103

iv CONTENTS

A Past Reactor Neutrino Experiments 107A.1 Gosgen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.2 Bugey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108A.3 CHOOZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109A.4 Palo Verde . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111A.5 KamLAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Chapter 1

Introduction

The last decade has seen a tremendous advancement in the understanding of the neutrino sector,unveiling this group of ubiquitous yet elusive fundamental particles. We now know that they havemasses, very likely in the sub-eV region, and they are not the primary component of dark matterthat we once thought they would be. They can transform into one another, reinforcing the idea ofthe standard model’s generation classification of particles of similar properties. We believe that theirspecies belong to ancient relics that have survived eons of the evolution of the universe and carriedwith them the cosmological information older than that of the thermal microwave backgroundradiation. They can interact at very short distances less than a fermi by participating in standardmodel interactions, but can also let their effects be known macroscopically at a distance of manykilometers through the oscillation effect, and play important roles at the cosmic scale throughbig bang nucleosynthesis and the large structure formation of the universe. The fact that theyare massive has provided, to date, the only concrete experimental evidence in the particle physicsrealm that a deeper level of fundamental physics exists beyond the standard model.

Because of their effects as mentioned above, unlike most of the other particles in the standardmodel, our knowledge of neutrinos can come not only from particle physics but also from astro-physics and cosmology, which currently provide the most stringent constraint on the masses ofthe stable neutrinos. Beginning with Ray Davis’ solar neutrino experiment initiated four decadesago, the suitability of neutrino as a cosmic observational tool was reasserted by the SN1987 super-nova event. Relying on the special properties of the neutrino, the new field of Neutrino Astronomypromises to be one of the new observational regimes for fundamental discoveries. This new tool willallow us to view the Cosmos far back in time and to peek into regions hidden from electromagneticradiation and, therefore, complements the traditional optical observations. One can argue that thesolar and atmospheric neutrino detectors are already neutrino telescopes. Pauli’s once desperatephenomenological proposition has truly become a universal essence.

In particle physics the origin of mass is a question which is yet to be answered. Even with thecurrent incomplete information about the neutrino sector, the very small mass and very large or evenmaximal mixing in the lepton sector is at odds with the quark sector, making the Higgs mechanismof the standard model mass generation mechanism even more chaotic. Now the fermion massspectrum of the standard model extends over 11 orders of magnitude: O(≤ 1 eV) − O(1011 eV). Itis clear that for the mass problem the standard model cannot offer any insight other than providingan arbitrary set of parameters, the Higgs couplings, from which the particle mass and mixingmatrices are obtained phenomenologically. One cannot but wonder how the Higgs mechanism can

1

2 CHAPTER 1. INTRODUCTION

be a part of the fundamental structure of a fundamental theory. The very different mass matricesof the quarks and the neutrinos post a challenge which can hopefully lead us to a new insight intothe mass generation mechanism.

Our present knowledge of the neutrino mixing is far from complete. It is necessary to knowprecisely the mixing matrices of both the lepton and quark sectors in order to discriminate thevarious theoretical mass matrix structures proposed in the literature and to know if there are morethan three generations. With the relatively clean experimental environment of neutrino oscillations,not complicated by strong interaction effects as in the quark case, the neutrino mixing matrix hasa better prospect to be precisely determined in the near future.

Although neutrino oscillation experiments do not allow us to measure the complete set ofparameters in the neutrino mass matrix, they are the best approach to obtain the mixing anglesand one of the CP phase angles, which we shall refer to as the Dirac CP-phase. With the existingneutrino oscillation experiments and the new ones to be online in the next few years, we expectthe large mixing angles θ12 and θ23, and the mass square differences ∆m2

21 and ∆m232 to become

more accurately known, but the small mixing angle θ13 is more difficult to obtain because it is asubleading effect in most of the neutrino oscillation phenomena.

To know θ13 is critical not only in its own right, but also for several other important reasons.The lepton CP-violation, which occurs in the mixing matrix element Ue3, is proportional to sin θ13.Hence θ13 is a controlling factor of the measurable lepton CP effects. CP-violation in the leptonsector is important for leptogenesis which is currently considered to be a promising path to baryonasymmetry through the standard model mechanism of baryon number, B, and lepton number, L,violation but the preservation of B−L. As θ13 bridges the solar and atmospheric effects, a global fitof all oscillation data, including solar, atmospheric, reactor and accelerator measurements to obtainaccurately the neutrino mixing parameters can best be done with good information on the value ofθ13. To know all the mixing angles accurately allows us to check the unitarity of the 3-flavor mixingmatrix and therefore the possibility of the existence of sterile neutrinos. There is also a theoreticalreason for the measurement of θ13. Most of the existing neutrino mass matrix models, such asanarchic models and GUT models, tend to predict that the value of sin2 2θ13 is not much below theexisting limit of 0.1. Even if θ13 vanishes for some reason in the GUT model at the GUT energyscale, the renormalization effect estimated through the renormalization group equation indicatesthat sin2 2θ13 will run to a value no less than 0.01 at the neutrino mass of the eV scale. Hencethe value of sin2 2θ13 is a discriminator of theoretical models. If it turns out that sin2 2θ13 is muchsmaller than 0.1, then the present theoretical thinking on the framework of neutrino masses has tobe significantly altered.

With the currently available facilities, the best measurement of θ13 comes from short baselinereactor experiments measuring the surviving probability of νe → νe. The appearance experimentsusing accelerator νµ beams are complicated by parameter degeneracies, low statistics and systematicproblems. The existence of many nuclear power plants world-wide provide ample possibilities fordoing the νe → νe survival experiment, which has several advantages. Since the experiments areperformed at short baselines of the order of kilometers, the vacuum oscillation formula is valid. Theνe → νe survival probability is independent of the CP phase angle and the angle θ23. It is weaklydependent on ∆m2

21 and θ12 under the conditions of the reactor experiment. It has a significantdependence on ∆m2

32, and strongly depends on the experimentally controlled variables of neutrinoenergy and the baseline. With a proper choice of the baseline, the dependence on ∆m2

32 can beminimized. Hence this is a relatively clean environment. Sufficient statistics can be accumulated

3

by large enough detector size and/or long enough running time. The challenge lies in the control ofthe systematic errors and the selection of the baseline. With a multi-detector setup the systematicerrors can be significantly reduced.

In this initiative we propose to measure θ13 using the nuclear reactors of the Daya Bay NuclearPower Plant complex which is located 55 km from Hong Kong. The available thermal power fromthe existing four reactor cores in the Daya Bay and LingAo area is 11.6 GWth. Two more reactorcores east of LingAo, will begin construction soon and is expected to be completed by 2010. Aftertheir completion, the total thermal power will be 17.4 GWth, boosting the Daya Bay facilities tobecome one of the world’s top five most intense νe source. The planned detectors, both near andfar, are of the liquid scintillator type. We have performed a detailed study of the systematics andbelieve that the systematics can be controlled to the 0.5% level. Our bottom line is that we expectto reach a limit of sin2 2θ13 of about 0.01 at 90% confidence level after three years of running.

To conclude this introduction, let us note a delightful historical coincidence. The first obser-vation of the electron neutrino in 1956 which made its existence ”official” by Fred Reines andClyde Cowan was made in a nuclear reactor after the neutrino had been a phantom particle for aquarter of a century. Now we are coming back again to the nuclear reactor for our inquisition intothe detailed properties of the neutrino, as already demonstrated by CHOOZ, Palo Verde, Kam-LAND, and several other reactor experiments. This time the technologies of the nuclear reactorand detector are much improved and we know much more about the neutrino. The intertwining ofscience and technology and their progress in synchronized steps is clearly illustrated in the pursuitof neutrinos.

Chapter 2

Physics Motivation

2.1 Current Status of neutrino oscillations

For N flavors, the neutrino mass matrix consists of N mass eigenvalues, N(N −1)/2 mixing angles,N(N −1)/2 CP phases for Majorana neutrinos or (N −1)(N −2)/2 CP phases for Dirac neutrinos.The mass matrix is diagonalized by the mixing matrix which transforms the mass eigenstatesto the flavor eigenstates. For 3 flavors, the Maki-Nakagawa-Sakata-Pontecorvo [1] mixing matrixwhich transforms the mass eigenstates (ν1, ν2, ν3) to the flavor eigenstates (νe, νµ, ντ ) can beparameterized as 1 0 0

0 cos θ23 sin θ23

0 − sin θ23 cos θ23

cos θ13 0 e−iδCP sin θ13

0 1 0−eiδCP sin θ13 0 cos θ13

cos θ12 sin θ12 0− sin θ12 cos θ12 0

0 0 1

×

eiφ1

eiφ2

1

(2.1)

where the first matrix corresponds to atmospheric neutrino oscillation, the second one involves inreactor neutrino or accelerator neutrino experiment, and the third one responses for solar neutrinooscillation. The fourth matrix which is diagonal gives the two Majorana phases. The neutrinooscillation phenomenology is independent of the Majorana phases φ1 and φ2, which can only bepartially revealed through neutrino-less double β decay experiments, and hence they will not beour concerns here.

For 3 flavors, oscillation experiments can only determine three mixing angles θ12, θ13, θ23, twomass-square differences, ∆m21 ≡ m2

2 −m21, ∆m31 ≡ m2

3 −m21, and one CP phase angle δCP.

There is a series of strong evidence for flavor mixing from solar, atmospheric, reactor and accel-erator experiments.1 The Super-Kamiokande [4] atmospheric µ-like events show increase depletionwith distance while the e-like events agree with the non-oscillation expectation, with the energyand azimuthal angular distributions of both the electron and muon events measured.

1We follow extensively the review article [2]. There are, of course, many excellent reviews on the current statusof neutrino oscillations [3]. Here we can only cite some of them and apologize for missing the rest.

4

2.1. CURRENT STATUS OF NEUTRINO OSCILLATIONS 5

The SNO experiment [5] measures both neutral and charge currents from three different reac-tions:

CC(φCC) : νe + d → p + p + e−

NC(φNC) : νx + d → p + n + νx, x = e, µ, τ (2.2)ES(φES) : νe + e− → νe + e−,

where φCC, φNC, and φES are the neutrino fluxes for charge current, neutral current and elasticscattering, νx is νe, νµ, or ντ . The neutral current reactions measure the total active solar neutrinoflux, independent of the solar model. Furthermore, these reactions measure different types ofneutrino fluxes which are not total independent and hence can serve as a check of the consistenceof the oscillation picture:

φCC = φνe ,

φNC = φνe + φνµ + φντ , (2.3)φES = φνe + 0.15(φνµ + φντ ) ,

= 0.85φCC + 0.15φNC.

These fluxes also agree with the standard solar model 8B neutrino flux. Since only νe is produced inthe sun, the existence of other active neutrino flavors can only be explained by flavor transmutationdue to oscillations.

The KamLAND experiment [25] measures electron antineutrino from reactors and observeda deficit of flux which can only be explained by neutrino oscillation. KamLAND confirms thesolar oscillation with a man-made neutrino source to 99.99996% confidence level. The atmosphericneutrino oscillation is also confirmed by a man-made source, accelerator based experiment K2K[7]. More recently the Super-K atmospheric data provide an even stronger oscillation signature.This is the observation of the dip in the L/E plot [8], which is a characteristics of the data thatmust be observed if oscillation is the physics of the neutrino flavor reduction. The appearance of adip in the L/E plot rules out two alternative explanation of the data that do not require neutrinooscillations. The L/E plot is given in Fig. 2.1.

The solar and atmospheric neutrino oscillations are well established. The oscillation parameterscan be shown in two-flavor mixing approximation as in Fig. 2.2, together with the unconfirmedLSND oscillation [9].

The best fit for 3 flavors from Super-K, SNO, KamLAND and Chooz [24] data are given by:

• Combined with the observed solar fluxes [11], the latest KamLAND results [12] yield:

∆m221 = 7.9+0.6

−0.5 × 10−5, tan2 θ12 = 0.40+0.10−0.07 (2.4)

The νe oscillates into a linear combination of νµ and ντ . Assuming CPT, the final confirmationof the LMA solution of the solar neutrino problem is provided by KamLAND [25] which has anaverage baseline to energy ratio near the second minimum of the survival probability νe → νe

that is optimal for LMA. The KamLAND data exclude no oscillation at the 99.99996% C.L.and confirm the LMA solution by ruling out all other oscillation solutions, nonstandardneutrino interactions, and several other exotic scenarios [3]. Note that θ12 is 6σ away frombeing maximal2.

2This result already satisfies one of the requirements of the satisfactory measurement of the neutrino mixing angleposted by Glashow [13], i.e., to bound θ12 away from π/4 by 5 standard deviations.

6 CHAPTER 2. PHYSICS MOTIVATION

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Dat

a/P

redi

ctio

n (n

ull o

sc.)

Figure 2.1: Oscillation parameters in two-flavor mixing approximation.

• The most recent SNO data obtained with salt added in the detector to improve significantlythe efficiency of neutral current events detection, combined with the current available dataof solar neutrinos from Super-K, SNO, Homestake, Gallex and Sage, lead to [14, 15]:

∆m221 = 6.46× 10−5eV2, tan2 θ12 = 0.398 (2.5)

• Atmospheric [4]: The best fit gives [3]

|∆m232| = 2.1× 10−3, sin2 2θ23 = 1.0. (2.6)

The allowed regions at 90% CL are

∆m232 = (1.5− 3.4)× 10−3eV2 (2.7)

sin2 2θ23 = 0.92− 1.0.

The dominant oscillation of atmospheric neutrinos is νµ → ντ .

• Chooz [24] reactor experiment:The Chooz experiment quoted the following bound for θ13:

sin2 2θ13 < 0.1 (θ13 < 9◦). (2.8)

The bounds extracted from the Chooz data is quite sensitive to the value of ∆m232 used. The

more recent atmospheric oscillation data put a large bound on θ13. For ∆m232 = 2.0 × 10−3

eV2, sin2 2θ13 ≤ 0.2 at the 90% C.L., while for ∆m232 = 1.3 × 10−3 eV2 the corresponding

bound is 0.36 [3, 16].

• K2K long baseline accelerator experiment [17]:The K2K νµ survival measurement, the number of observed events and spectrum combined,is consistent with the atmospheric neutrino data. The SuperK and K2K combined fit gives∆m2

32 = 2.0+0.4−0.3 × 10−3 eV2 [18].

2.1. CURRENT STATUS OF NEUTRINO OSCILLATIONS 7

Figure 2.2: Oscillation parameters in two-flavor mixing approximation.

Since the sign of ∆m232 is not known, there are two possible neutrino mass spectra for 3 flavors:

the normal hierarchy and the inverted hierarchy, as illustrated in Fig. 2.3. The determination ofthe hierarchy is an important program of the future long-baseline oscillation experiments using theEarth-matter effect.

Figure 2.3: Normal and inverted spectra: normal ∆m232 > 0; inverted ∆m2

32 < 0.

There exists another set of neutrino oscillation data from the Los Alamos short baseline beam-stop LSND experiment [9] which found evidence of the oscillation νµ → νe at the significance levelof 3.3σ. The data require a mass square difference ∆m2 ≈ 0.2 − 1 eV2 and a very small mixingangle θLSND, sin2 2θLSND ≈ 0.003 − 0.04. The LSND collaboration also observed the evidence ofνµ → νe at lesser significance [19]. A large region allowed by the LSND data has been ruled outby the KARMEN experiment [2], while remained allowed region will be tested by the MiniBooNE


experiment in progress [21].The LSND data can be interpreted by the existence of a sterile neutrino νs, or an anomalous

muon decay µ+ → e++ νe+ νi, or a CPT violation effect which gives ν and ν different mass spectra.But all are strongly disfavored [22].

As illustrations some of the possible mass spectra of the four-neutrino schemes are shown inFig. 2.4.

∆m2LSND

}

∆m2atm

(a) 2 + 2 spectrum

}

(b) 3 + 1 spectrum

∆m2LSND

}{

(mass)2

∆m2atm∆m2 ∆m2

ν

ν

ν

ν

ν

ν

ν

ν4

3

2

1

s

τ

µ

e

MAS

S

Figure 2.4: Level structures of four neutrinos. The 2+2 scenario is disfavored compared to the 3+1scenario, but neither provides a good fit to the data.

Oscillation experiments do not provide information on the absolute neutrino masses. Whenincorporated with other information there already exist significant constraints on the order ofmagnitude of the neutrino masses. This information comes from two sources. One is the boundof the electron-neutrino mass from the study of the spectrum near the end point of tritium decay.The other is from satellite-born astrophysics experiments.

The most recent Mainz [23] and Troitsk [24] tritium experiments give mνe < 2.2 eV which allowsus to estimate the neutrino masses in two extreme cases in the 3-flavor scheme:

• Small mass scenario:Normal spectrum: m1 ≈ 0, m2 ≈ 0.008 eV, m3 ≈ 0.045 eV.Inverted spectrum: m3 ≈ 0, m1 ≈ 0.044 eV, m2 ≈ 0.045 eV.

• Large (degenerate) mass scenario:√∆m2

atm ≈ 0.045eV � m1 ≈ m2 ≈ m3 < 2.2 eV

There also exists a cosmological bound on the sum of the masses of all stable neutrinos asprovided by the most recent data on galaxy survey of the power spectrum of cosmic microwavebackground radiation from WMAP [25], 2dFGRS [26] and other measurements. The various fitsgive ∑

j

mνj < 0.42 ∼ 1.8 eV. (2.9)

This implies the following limit for the lower bound of the three neutrino scheme:

mν < 0.14 eV. (2.10)

2.2. THEORETICAL EXPECTATIONS OF θ13 9

Massive neutrinos are the first concrete evidence of physics beyond the standard model andexpose an hierarchy problem: the mass spectrum extends no less than 11 orders of magnitude:O(≤ 1 eV) − O(1011 eV). The very small mass and very large or even maximal mixing in thelepton sector, in contrast to the quark sector, seem to make the mass generation mechanism in thestandard model more chaotic. This casts doubts on how the Higgs mechanism can be a part of thefundamental structure of a fundamental theory.

For comparison we give the approximate mixing matrices for neutrino [27] [28]

UPMNS =

Ceiφ1 Seiφ2 S∗13

− Seiφ1/√

2 Ceiφ2/√

2 1/√

2Seiφ1/

√2 − Ceiφ2/

√2 1/

√2

, (2.11)

where C = cos θ�, S = sin θ� and S∗13 = sin θ13e

−iδCP , and for quarks (in the Wolfenstein form)

VCKM =

1− λ2/2 λ Aλ3(ρ− iη)−λ 1− λ2/2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

, (2.12)

where A, ρ, η ∼ O(1) and λ ≈ 0.22. The lack of resemblance between the two mixing matricesis clear. The generational hierarchical structure of the quark mixing is not shown in the leptonicsector. In the lepton sector the first and second generations have large mixing, the second and thirdprobably have maximal mixing. The first and third has small mixing. It is important to know howsmall it is.

The large freedom in the construction of the neutrino mass matrix is subject to diverse physicalinterpretation. The most promising models of mν are the see-saw mechanism and Zee model [29]of radiative masses; the see-saw mechanism requires Majorana neutrinos.

2.2 Theoretical expectations of θ13

Current experimental data, in particular those obtained from the Chooz [24] and Palo Verde [30]reactor neutrino experiments, yield an upper bound for θ13, θ13 < θC, where θC ≈ 13◦ which isthe well-known Cabibbo angle in the quark flavor mixing. The smallness of θ13 requires a goodtheoretical explanation, which might simultaneously account for the largeness of θ12 and θ23. Ifθ13 = 0◦ held, there should exist a new flavor symmetry which forbids the mixing between thefirst and third lepton families. In this special situation, in which the mixing of 3 flavors can beunderstood in terms of 2-flavor mixing, there would be no leptonic CP and T violation to manifestin normal neutrino-neutrino and antineutrino-antineutrino oscillations.

A very challenging question is how small θ13 is, if it is not exactly zero. To answer this questiontheoretically requires the knowledge of the origin of the fermion mass, flavor mixing, and CPviolation. In the absence of a reliable theory which provides the knowledge, we are unable topredict the value of θ13 model-independently. Nevertheless, it is possible to obtain some usefulinformation about the magnitude of θ13 phenomenologically from a global analysis of the knownsolar, atmospheric, reactor and accelerator neutrino oscillation data [31, 32]. Such a “theoretical”expectation of θ13 may serve as a helpful guide to θ13 hunters to design a feasible experiment andmaximize its range of sensitivity. In contrast, the values of θ13 predicted by the existing neutrinomass models depend more or less on some ad hoc phenomenological assumptions [33]. Although


the reliability of such model-dependent predictions should not be overemphasized, some of themcould shed light on the underlying dynamics of lepton flavor mixing once θ13 is measured.

2.2.1 Expectations of θ13 from global three-neutrino analysis

In the scheme of three-flavor neutrino oscillations, a global analysis of the latest solar, atmospheric,reactor (KamLAND and Chooz) and accelerator (K2K) neutrino data has been done independentlyby Bahcall et al. (BGP) [31] and Maltoni et al. (MSTV) [32]. Because of the hierarchy ∆m2

sun �∆m2

atm, it is a good approximation to neglect the effect of ∆m221 in the analysis of atmospheric

and K2K data, and to average out the effect of ∆m231 (or ∆m2

32) in the analysis of solar andKamLAND data. The Dirac-type CP-violating phase is therefore decoupled from the global fit,and the analysis involves totally five parameters: θ12, θ23, θ13, ∆m2

21 and ∆m232). It is possible to

obtain some helpful information about the size or upper limit of θ13 from such a model-independentanalysis. Figure 2.5 shows the ∆χ2 dependence on θ13 obtained by BGP and MSTV. One can seethat the minimum of the ∆χ2 corresponds to sin2 θ13 = 0.009 (BGP) or sin2 θ13 = 0.006 (MSTV),although the latter value is not obvious from the plot.

0

5

10

0 0.02 0.04 0.06

∆χ2 θ13vs

All 2002+ [p-p]ν-e ± 1%

∆χ2

sin2θ13

10-2

10-1

sin2θ

13

0 5 10 15 20

∆χ2

Atm + K2K + Chooz

Solar + KamLAND

Total

Solar

KamLAND

3σ

90% C

L

Figure 2.5: The ∆χ2 behaviors changing with sin2 θ13 obtained respectively by BGP (left) in Ref.[31] and MSTV (right) in Ref. [32].

To be more concrete, we list in Table 1 the best-fits and their 2σ and 3σ intervals of the twomass-squared differences and three mixing angles. It is clear from the table that the BGP andMSTV analysis are basically compatible. We see that the upper limit of θ13 is about θC at the 3σlevel. It is most likely that θ13 ∼ 4◦ or 5◦, according to the BGP and MSTV best-fits. In otherwords, sin2 2θ13 ∼ (2 − 3)% can be expected. This implies that a measurement of θ13 from theνe survival oscillations, νe → νe, may be possible for a reactor neutrino experiment at a baselineappropriate to the ∆m2

32 scale, if its sensitivity can reach the order of 1% or so. Although the moreoptimistic possibility of a larger θ13 that θ13 lies in the range of 6◦ and 12◦ (sin2 2θ13 in the range

2.2. THEORETICAL EXPECTATIONS OF θ13 11

Table 2.1: The best-fit values, 2σ (or 95% C.L.) and 3σ (or 99.7% C.L.) intervals of two mass-squared differences and three flavor mixing angles from the global three-neutrino analysis.

Parameter (BGP [31]) Best fit 2σ interval 3σ interval∆m2

21 (10−5 eV2) 7.1 6.2–8.2 5.5–9.7∆m2

32 (10−3 eV2) 2.6 1.8–3.3 1.4–3.7tan2 θ12 0.42 0.34–0.54 0.30–0.63tan2 θ23 1.0 0.61–1.7 0.45–2.3sin2 θ13 (sin2 2θ13) 0.009 (0.036) ≤ 0.036 ≤ 0.053

Parameter (MSTV [32]) Best fit 2σ interval 3σ interval∆m2

21 (10−5 eV2) 6.9 6.0–8.4 5.4–9.5∆m2

31 (10−3 eV2) 2.6 1.8–3.3 1.4–3.7sin2 θ12 0.30 0.25–0.36 0.23–0.39sin2 θ23 0.52 0.36–0.67 0.31–0.72sin2 θ13 (sin2 2θ13) 0.006 (0.024) ≤ 0.035 ≤ 0.054

of 0.04 and 0.17) can not be excluded, it seems not to be rather likely.

2.2.2 Expectations of θ13 from specific neutrino mass models

At low-energy scales, the phenomenology of lepton masses and flavor mixing can be formulated interms of the charged lepton mass matrix Ml and the (effective) neutrino mass matrix Mν . While Ml

and Mν may stem either from some grand unified theories (GUTs) or from various non-GUT models,their textures are in general unspecified by the theory or model itself. The physical parametersassociated with Ml and Mν include three masses of charged leptons (me,mµ,mτ ), three masses ofneutrinos (m1,m2,m3), three angles of flavor mixing (θ12, θ23, θ13), and three phases of CP violation(δCP, φ1, φ2). Among the parameters, me, mµ and mτ have been precisely measured; and ∆m2

21,∆m2

32, θ12 and θ23 have been determined to an acceptable degree of precision. A successful neutrinotheory should be able to determine the patterns of Ml and Mν with much fewer free parameters, suchthat some testable predictions can be made for some unknown physical quantities. Unfortunately,such a predictive theory has been lacking. Although a number of predictive models have beenproposed in the literature [33], they all have to rely on some extra phenomenological hypotheses.

Regardless of the details of those predictive models, their results for θ13 at low energies canroughly be classified into two different types: (1) θ13 is given in terms of the mass ratios of leptonsor quarks; and (2) θ13 is predicted in terms of other known parameters of neutrino oscillations.Below we provide a few simple examples for illustration to gain some insights of their ball-park,model-dependent predictions for θ13.

Example (A): The so-called “democratic” neutrino mixing model [34], in which the S(3)L×S(3)Rsymmetry of Ml and the S(3) symmetry of Mν are explicitly broken by small perturbations, cannaturally predict

sin θ13 ≈ 2√6

√me

mµ≈ 0.057 (sin2 2θ13 ≈ 0.013). (2.13)


Similar results (i.e., sin θ13 ∼√

me/mµ ) may also be obtained from other nearly bi-maximalneutrino mixing patterns with proper symmetry breaking.

Example (B): A simple SO(10)-inspired fermion mass model [35], in which the four-zero textureof Mν results from the up-quark and right-handed Majorana neutrino mass matrices via the seesawmechanism, may lead to

sin θ13 ≈ 1√2

sin θC ≈ 0.155 (sin2 2θ13 ≈ 0.094), (2.14)

where a sub-leading correction of O(√

mu/mc) has been neglected. Because sin θC ∼√

md/ms

holds approximately, this result illustrates possible relations between lepton and quark mixingparameters in GUTs.

Example (C): In the flavor basis where the charged lepton mass matrix Ml is diagonal, real andpositive, the Majorana neutrino mass matrix Mν with vanishing (1,1) and (1,3) or (3,1) entriesyields [36]

sin θ13 ≈ tan θ12 tan θ23√1− tan4 θ12

√∆m2

21

∆m232

≈ 0.076 (sin2 2θ13 ≈ 0.023), (2.15)

where the best-fit values of ∆m221, ∆m2

32, tan2 θ12 and tan2 θ23 given in Table 1 (BGP) have beenused.

Example (D): Given the Frampton-Glashow-Yanagida ansatz, in which two texture zeros areassumed for the Dirac neutrino Yukawa coupling matrix [37], the minimal seesaw model of neutrinomixing and leptogenesis predicts

sin θ13 ≈ 12

sin 2θ12 tan θ23

√∆m2

21

∆m232

≈ 0.076 (sin2 2θ13 ≈ 0.023), (2.16)

in the leading-order approximation with m1 = 0 (normal mass hierarchy), where the best-fit valuesof ∆m2

21, ∆m232, tan2 θ12 and tan2 θ23 (BGP) have been used.

The above examples illustrate that the value of θ13 is expected to amount to a few degrees inmany viable neutrino models. Such a range of θ13 is certainly consistent with the best-fit resultobtained from a global analysis of current solar, atmospheric, reactor and accelerator neutrinooscillation data [31, 32]. Compared to θ12 and θ23, θ13 is usually more sensitive to the detailedstructure of lepton mass matrices. Hence a precise measurement of θ13 will be crucial to singlingout the most plausible neutrino mass model(s) and rule out the others.

2.3 Measurement of θ13

The oscillatory effect of the mixing angle θ13 is generally subleading or small. The effect showseither in the high energy (order of GeV) νe(νe) → νe(νe) survival processes or the νµ(νµ) → νe(νe)low energy (order of MeV) appearance processes. The latter are performed at accelerator basedlong baseline experiments and the former short distance reactor experiments. Because of thelimited flux intensity of neutrino beams currently available and those planned for the near future,and also because of the inherent complications, the accuracy offered by long baseline acceleratorexperiments in the near future is limited, probing sin2 2θ13 in the region no lower than 0.4, whilereactor experiments have a much better accuracy in the 0.01 range which can be obtained before

2.3. MEASUREMENT OF θ13 13

the end of this decade. We discuss and provide a short overview of the two types of experimentsbelow.

2.3.1 Long baseline experiments and the measurement θ13

In the near term, the first generation accelerator based long-baseline experiments with conventionalνµ beams, K2K, MINOS, and OPERA/ICARUS, should be able to confirm atmospheric neutrinooscillations and improve the precision with which ∆m2

32 and sin2 2θ23 are determined. Experimentsthat measure νµ disappearance will establish the first minimum in the νµ → νµ oscillation. TheK2K experiment from KEK to SuperK [17], a distance of L = 250 km, has begun taking data againfollowing the restoration of the SuperK detector. To date K2K has confirmed neutrino oscillationto the 3.9σ level. The MINOS experiment from Fermilab to the Soudan mine [38], at a distance ofL = 730 km, has been commenced on March 4, 2005 when the first neutrino beam from Fermilabmain injector was provided [39]; it is expected to obtain 10% precision on ∆m2

32 and sin2 2θ23 in3 years running. The CERN to Gran Sasso (CNGS) experiments, ICARUS [40] and OPERA [41],also at a distance L = 730 km but with higher neutrino energy, are expected to be online in mid2006. The appearance of ντ should be observed in the CNGS experiments, which would confirmthat the primary oscillation of atmospheric neutrinos is νµ → ντ . These European programs wouldalso contribute to obtaining a better limit for theta13.

The three parameters that are not determined by the solar, atmospheric, and KamLAND dataare θ13 which is crucial for the Dirac CP effect, the sign of ∆m2

32 which fixes the hierarchy ofneutrino masses, and the Dirac CP phase δCP . The appearance of νe in νµ → νe oscillationsis the most critical measurement, since the probability is proportional to sin2 2θ13 in the leadingoscillation, for which there is currently only an upper bound (0.1 at the 90% C. L., from theChooz [24] and Palo Verde [30] reactor experiments). By combining ICARUS/MINOS/OPERAdata, it may be possible to establish whether sin2 2θ13 > 0.01 at 90% C. L. [42]. With OPERA andICARUS the accuracy of the measurement of sin2 2θ13 is expected to be a lower limit of 0.06-0.04.A summary of the status of the near term programs up to August 2004 can be found in [43].

In the longer term the focus shifts primarily to νµ → νe oscillations performed at acceleratorbased long baseline experiments. A measurement of both νµ → νe and νµ → νe oscillationsallows one to measure θ13 and test for CP violation in the lepton sector, provided that θ13 is largeenough. However, there are difficulties coming from different aspects of such experiments that mustbe overcome, in addition to the fact νµ → νe oscillation is subdominant. One of the difficulties isthe significant background coming from three sources [44]: (a) the νe contamination in the νµ beam;(b) decay of ντ → νe when τ is produced from the dominant oscillation νν → ντ ; (c) backgroundfor the detection of e events in calorimetric detectors.

Another difficulty, which is inherent in the theoretical formulation, is known as parameterdegeneracies that occur when two or more parameter sets are consistent with the same data. Thedegeneracies in general lead to ambiguities in the measured values of θ13 and δCP even if theoscillation probabilities νµ → νe and νµ → νe are precisely known [45, 46]. There are potentiallythree two-fold parameter degeneracies: (i) the (δCP , θ13) ambiguity [45, 47, 48, 49, 50], (ii) theambiguity due to our lack of knowledge of the mass hierarchy (the sign of ∆m2

32 ambiguity) [45, 48,51, 52], and (iii) the (θ23,

π2 − θ23) ambiguity [45, 58], which occurs because only sin2 2θ23, not θ23,

is measured in atmospheric neutrino experiments. Each set of the parameter degeneracies can leadto different inferred values for δCP and θ13, and the three sets can all be present simultaneously,


leading to as much as an eight-fold ambiguities in the determination of θ13 and δCP . In many casesboth CP conserving and CP violating parameter sets are allowed by the same data because of thedegeneracies.

Still another problem is that Earth-matter effects can induce fake CP violation, which must betaken into account in any determination of θ13 and δCP in long baseline experiments. One advantageof matter effects is that they might distinguish between the two possible mass hierarchies.

The future precision measurements will relay on two types of new facilities: the superbeam [53]and the neutrino factory [54]. The high neutrino flux of the superbeam, such as the J-PARC [55]under construction, and other facilities under planning, such as NuMI off-axis NOνA [56] at FNALand the off-axis program of Brookhaven Wide Band Beam [57], will go a long way to pin down fairaccurately most of the oscillation parameters, including the Dirac CP phase. The J-PARC neutrinoprogram will not begin before 2009 and the Fermilab NOνA and BNL Wide Band Beam programsare still in the stage of feasibility study.

The neutrino factory will be the ultimate facility to study neutrino oscillations. With such afacility the very accurate measurement of neutrino oscillation parameters, the study of appearancechannels, and the investigation the CPT invariance can be carried out.

2.3.2 Advantages of measuring θ13 at reactors

In the setting of a nuclear reactor the measured quantity is the survival event νe → νe at a shortbaseline of the order of hundreds of meters to a few kilometers with the νe energy of a few MeV.The matter effect is totally negligible and so the vacuum formula for the survival probability isvalid. In the standard notation of Eq. (2.1), this probability has a simple expression

Psur = 1− C413 sin2 2θ12 sin2 ∆21 − C2

12 sin2 2θ13 sin2 ∆31 − S212 sin2 2θ13 sin2 ∆32, (2.17)

where

∆jk ≡ 1.267∆m2jk(eV

2)× 103 L(km)E(MeV)

, (2.18)

∆m2jk ≡ m2

j −m2k.

L is the baseline in km, E the neutrino energy in MeV, and mj the jth neutrino mass in eV. Theνe → νe survival probability is also given by Eq. (2.17) when CPT is not violated. Equation (2.17)shows that it is independent of the CP phase angle δCP and the mixing angle θ23, and thereforeeliminates the uncertainties introduced by the unknown δCP and the current measurement error inθ23.

To obtain the value of θ13, the depletion of νe has to be extracted from the experimental νe

disappearance probability below the µ production threshold,

Pdis ≡ 1− Psur

= C413 sin2 2θ12 sin2 ∆21 + C2

12 sin2 2θ13 sin2 ∆31 + S212 sin2 2θ13 sin2 ∆32 . (2.19)

Let us define the part of the disappearance probability that is independent of θ13 as

P0 = Pdis|θ13=0 = sin2 2θ12 sin2 ∆21 . (2.20)


Then the part of the disappearance probability directly related to θ13 is given by

Pnet ≡ Pdis − P0

= − sin2 2θ12 sin2 θ13(1 + cos2 θ13) sin2 ∆21

+sin2 2θ13(cos2 θ12 sin2 ∆31 + sin2 θ12 sin2 ∆32). (2.21)

The above discussion shows that in order to obtain θ13 we have to subtract the θ13-independentcontribution P0 from the experimental measurement of Pdis. To see their individual effect, we plotPnet in Fig. 2.6 together with Pdis and P0 as a function of the baseline from 100 m to 100 km.The neutrino energy is taken to be 4 MeV. We also take sin2 2θ13 = 0.05 which will be used forillustration in most of the discussions in this section. The other parameters are given by their bestfit in the atmospheric data and the most recent SNO data given in Eqs. (2.5) and (2.6). Unlessspecified otherwise, we will use

θ12 = 32.5◦, ∆m221 = 7.1× 10−5eV2, ∆m2

31 = 2× 10−3eV2 (2.22)

in the following text.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10-1

1 10

PdisP0Pnet

Baseline (km)

Probability

Figure 2.6: P0: the slowly rising and falling curve, Pdis: the oscillating curve around P0, and Pnet:the low value oscillating curve. The various parameters used are described in the text.

The behavior of the curves in Fig. 2.6 are quite clear from their defining functions, Eqs. (2.19),(2.20) and (2.21). The slowly rising and then falling curve is P0, which is determined solely by∆m2

21 and θ12. The curve oscillating around P0 is Pdis and its rapid oscillation is determined by∆m2

32. The low value oscillating curve just above the horizontal axis is Pnet from which θ13 canbe extracted. The general behavior of the curves can be summarized as follows: Below the firstminimum around a few kilometers P0 is very small, and Pnet and Pdis track each other well. Beyondthe first minimum Pnet and Pdis deviate from each other more and more as L increases when P0

becomes dominant in Pdis.In the range of the first oscillation Pnet is insensitive to ∆m2

21 and sin2 2θ12. At the firstmaximum, Pdis is close to Pnet|Max ' sin2 2θ13. At all the higher maxima Pnet can be significantlysmaller than sin2 2θ13. This suggests that the measurement can be best performed at the firstmaximum of Pnet. Since the maximum of Pnet is determined by ∆2

32, it makes the choice of the


baseline of the far detector Lfar critical. However the choice of Lfar is nontrivial as ∆m232 is not

precisely determined. So for the experimental setup with the detector fixed in position3 we haveto investigate the behavior of Pnet in ∆m2

32 to determine the best possible distance Lfar for the fardetector by taking advantage or the energy spread of the νe beam so as to provide a range of valuesof L/E.

In the case that the incident neutrino energy can be determined event by event, as is the case ofreactor experiments, a range of values of L/E is provided by the neutrino beam energy spectrumwhich will be very helpful in the determination of θ13, although a large amount of statistics isrequired.

The νe interaction rate depends on its flux and the cross section of inverse beta decay νe + p →n + e+ [59]. The quasi elastic cross section is given in [60] and the phenomenological νe flux canbe found in [61]. For the present discussion the shape of the interaction rate which depends on theneutrino energy is needed, while the normalization of the interaction rate which depends on thebaseline is unimportant. Up to a normalization factor, the interaction rate without oscillation canbe approximately expressed as(

dN

dE

)NO

∼ exp(a0 + a1E + a2E2)(E − 1.293MeV)

√(E − 1.293MeV)2 −m2

e , (2.23)

where the energy of neutrino E is in MeV, a0=4.509, a1=-0.2171 MeV−1, a2=-0.08880 MeV−2,(E − 1.293 MeV) is the energy of the positron, and me is the mass of the positron in MeV. Theinteraction rate in the presence of oscillation is(

dN

dE

)OSC

=(

dN

dE

)NO

Psur, (2.24)

where Psur is given by Eq. (2.17). Further discussion on neutrino energy spectrum can be found inthe next chapter.

To demonstrate the critical nature of Lfar, we weight Pnet by interaction rate and integrate overthe whole neutrino energy spectrum. The integrated Pnet is plotted in Fig. 2.7 as a function of Lfar

for three values of ∆m232, i.e., (1.3, 2.0, 3.0) × 10−3 eV2, which cover the ∆m2

32 allowed range inthe 90% CL [3]. sin2 2θ13 is taken to be 0.05. Curves of other values of sin2 2θ13 scale identicallyto those of Fig. 2.7. The curves show that Pnet is sensitive to ∆m2

32 and varies significantly in thepresently allowed range of its value. The maximal probabilities in this range of ∆m2

32 cover a sizableregion of Lfar from 1.5 to 3.5 km. For ∆m2

32 = (1.3, 2.0, 3.0)× 10−3 eV2, the oscillation maximacorrespond to a baseline of 3500m, 2200m, and 1500m, respectively. Furthermore, a maximum for∆m2

32 = 1.3× 10−3 eV2 is near a minimum of ∆m232 = 3.0× 10−3 eV2. These features can create

complications and therefore indicate the challenge in the selection of the baseline of the far detector,Lfar. From this simply study, placing the far detector at 1800 m to 2200 m from the reactor looks tobe a good choice. In addition, statistics must be taken into consideration in the choice of Lfar as theevent rate is proportional to 1/L2

far. Detailed baseline optimization with statistical and systematicerrors, backgrounds, and concrete geographical condition taken into account will be discussed later.

3The design of the Diablo Canyon reactor experiment calls for a movable detector which will be assembled outside of the tunnel and then move into an appropriate spot in the tunnel so that the Lfar can be varied.


0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 2000 4000

sin22θ13=0.05

∆m2=1.3×10-3eV2

Baseline(m)

Pnet

∆m2=2.0×10-3eV2

∆m2=3.0×10-3eV2

Figure 2.7: Integrated Pnet as a function of thebaseline Lfar. The three curves covers the 90%CL range in ∆m2

32 [3].

0

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

0.02

0.0225

0.025

0 1 2 3 4 5

Sin22θ13=0.02, ∆m312=2×10-3eV2

PdisP0PnetP2

Baseline (km)Osc. Probability

Figure 2.8: Size of Pdis, P0, Pnet, and P2, inte-grated over neutrino energy spectrum, versusbaseline for sin2 2θ13 = 0.02.

In the literature, a simplified expression for oscillation probability involving only 2 neutrinoflavors is often used for describing reactor neutrino experiment at short distance:

P2 = sin2 2θ13 sin2 ∆31 . (2.25)

The difference between the two-flavor expression P2 and the three-flavor expression Pdis could belarge, especially for small sin2 2θ13. However, when we are interested in extracting sin2 2θ13, weshould take out the contribution of P0 before fitting sin2 2θ13. The magnitudes of these oscillationprobabilities are shown in Fig. 2.8 for a smaller θ13, sin2 2θ13 = 0.02. Although Pdis is significantlylarger than P2 at the far distance, Pnet is almost the same as the two-flavor expression. Therefore,the two-flavor expression is valid for most physical purposes, e.g. baseline optimization, sensitivityestimation, etc.

Current determinations of θ12 and ∆m221 carry large uncertainties. Pnet itself is insensitive to

∆m221 and sin2 2θ12. However, since we calculate it by Pdis − P0, the error of θ12 and ∆m2

21 willpropagate to Pnet. For the analysis of experimental data, this systematic error must be taken intoaccount and the two-flavor expression is no longer adequate. It is easy to check that for the bestfit value of solar neutrino given in Eq. (2.5), the relative size of P0 to the value of Pnet is about15% to 5% when sin2 2θ13 varies from 0.01 to 0.10. This feature may have impacts on spectrumanalysis of θ13.

Let us summarize with the following remarks:

• The disappearance probability directly related to θ13 is insensitive to θ12 and ∆m221 at short

distance. θ13 can be unambiguously determined by reactor neutrino experiment.


• It is interesting to note that the useful region of the reactor νe energy spectrum is sufficientto cover the 90% C.L. allowed range of ∆m2

32 which is the focus of our discussion. And wedetermine that the optimal choice of Lfar to be 1800m to 2200m.

• The disappearance probability is sensitive to ∆m231. On one side, it creates challenge in the

selection of baseline of the far detector. On the other side, the wide neutrino energy spectrumwill provide information of ∆m2

31.

• The simplified two-flavor oscillation expression is a very good approximation of the three-flavor expression, except that errors of θ12 and ∆m2

21 can not be taken into account in theformer. These systematic errors may have a significant impact on the data analysis.

Finally, we conclude from this theoretical investigation that the choice of Lfar be made so thatit can cover as a large range of ∆m2

32 as possible.

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[39] MINOS Collaboration: See Fermilab news release at:http://www.fnal.gov/pub/presspass/press releases/minos dedication 3-4-05.html. For a mostrecent overview of the status of MINOS, see B. Rebel,talk given in Frontiers in ContemporayPhysics III, May 23-28, 2005, http://www.fcp05.vanderbilt.edu/; K. Grzelak, LBL Experi-ments in the US talk at the it Neutrino Oscillation Workshop 2004 (NOW2004), September11-17, 2004, Otranto, Italy.

[40] ICARUS Collaboration: A. Rubbia, Status Of The Icarus Experiment, talk at Skandina-vian Neutrino Workshop (SNOW), Uppsala, Sweden, February 2001, Phys. Scripta T93, 70(2001); F.Ronga, LBL Experiments in Europe, talk at the Neutrino Oscillation Workshop 2004(NOW2004), September 11-17, 2004, Otranto, Italy.

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[43] Stephane T’Jampens, Current and near future long baseline experiments, talk give at the 6thInternation Workshop on Neurino Factories and Superbeams, July 23-Aug. 1, 2004, OsakaUniversity, Osaka, Japan (http://www-kuno.phys.sci.osaka-u.ac.jp/ nufact04/agenda.html).

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Chapter 3

Reactor Antineutrino

The antineutrino was first discovered in a nuclear reactor experiment by Reines and Cowan in1956 [1]. Nuclear reactors were also first utilized to search for neutrino oscillation by looking fordisappearance of νe’s at various distances from the source. The detectors of the early experiments,for example, ILL [2], Gosgen [3], and Bugey [4], were located very close (as near as 100 m) to thereactor, thus were sensitive to ∆m2

13 of the order of 5 × 10−2 eV2 which is about twenty timeslarger than its current best-fit value at which oscillation related to the mixing angle θ13 is expectedto take place. Although these experiments did not observe neutrino oscillation, the reactor νe fluxand energy spectrum and its time dependence were determined more accurately. The precision wasimproved from 10% to better than 3%. Recently, the Chooz experiment [5] achieved an even betterprecision of 0.7% in the reactor power and 0.6% in the energy released per fission.

In spite of these significant improvements in the knowledge of reactor parameters, the uncer-tainties in the reactor parameters remain the dominant systematic error for θ13 experiments. Asdiscussed in detail in later chapters the near and far detectors scheme allows the cancellation of theuncertainty in the antineutrino flux. The location of the near detector is optimized to further min-imize the adverse effects of the residual flux uncertainty. Assuming a conservative 3% uncertaintyin the absolute neutrino flux from each reactor, the reactor neutrino flux contributes a residualerror of 0.15% to the θ13 measurement.

In the following sections, the energy spectrum and the flux of antineutrinos from reactors andsome features of the inverse beta decay, which are important for detecting low-energy reactor νe’s,are summarized.

3.1 Energy spectrum and flux of reactor antineutrinos

A nuclear power plant derives its power from nuclear fission [18]. Fissionable materials (mainly 238Uenriched in 235U) are packed to form fuel rods which are assembled in the core of the reactor. Thefissile materials are fissioned by thermal neutrons in the core. During fission, unstable radioactivenuclei are formed, producing electron antineutrinos via subsequent beta decays. Typically, eachfission releases about 200 MeV energy and six antineutrinos. The majority of the antineutrinoshave very low energies; about 70% of the antineutrinos have energies below 1.8 MeV. A 3 GWth

reactor emits 6× 1020 antineutrinos per second with antineutrino energies up to 8 MeV.

24

3.1. ENERGY SPECTRUM AND FLUX OF REACTOR ANTINEUTRINOS 25

Up to now, all reactor neutrino experiments have been carried out at pressurized water reactors(PWRs). The reactors at the Daya Bay Nuclear Power Plant are of PWR design. The neutrinoflux and energy spectrum of a PWR depend on several factors: the total thermal power of thereactor, the fraction of each fissile isotope in the fuel, the fission rate of each fissile isotope, and theenergy spectrum of neutrinos of the individual fissile isotopes.

The antineutrino yield is proportional to the thermal power, while other thermal parameterssuch as the temperature, pressure and the flow rate of the cooling water, play negligible role. Thereactor thermal power is measured continuously by the power plant with a typical precision of(1-2)%.

Fissile materials are continuously consumed while other fissile isotopes are bred from fissionablematerials in the fuel (mainly 238U) by fast neutrons. Since the neutrino energy spectra are slightlydifferent for the four main isotopes, the fuel composition and its evolution over time are thereforecritical to the determination of the neutrino flux and energy spectrum. From the average thermalpower and the effective energy released per fission [6], the average number of fissions per secondof each isotope can be calculated as a function of time. Fig. 3.1 shows the results of computersimulation of the Palo Verde reactor cores [7].

Figure 3.1: Fission rate of each isotope as a function of time from a Monte Carlo simulation.

It is common for a nuclear power plant to replace some of the fuel rods in the reactor periodicallyas the fuel is used up. Typically, a reactor core will have 1/3 of its fuel changed every 18 months.At the beginning of each refueling cycle, 69% of the fissions are from 235U, 21% from 239Pu, 7%from 238U, and 3% from 241Pu. During operation the fissile isotopes 239Pu and 241Pu are bredcontinuously from 238U. Toward the end of the fuel cycle, the fission rates from 235U and 239Pu areabout equal. The average (”standard”) fuel composition is 58% of 235U, 30% of 239Pu, 7% of 238U,and 5% 241Pu [8].

The energy spectrum of the νe emitted from the fission reaction depends on the fuel compo-sition. The composite antineutrino spectrum is a function of the time-dependent contributionsof the various fissile isotopes to the fission process. The energy spectra of the antineutrinos for

26 CHAPTER 3. REACTOR ANTINEUTRINO

isotopes 235U, 239Pu, and 241Pu were deduced at ILL [9] by converting the β spectra independentlymeasured with a β spectrometer using 235U, 239Pu, and 241Pu targets. These inferred spectra havea normalization error originating from the uncertainty in calibrating the spectrometer and fromthe error in converting a β spectrum to an antineutrino spectrum. The spectra corresponding tothe two dominant isotopes, 235U and 239Pu, measured at ILL were used by the Gosgen experiment.The antineutrino spectra of the other two isotopes were obtained by theoretical calculation. Bycombining the experimental errors with the uncertainties in the theoretical calculations, a totaluncertainty of 3.0% was obtained for the normalization of the composite neutrino spectrum.

A widely used three-parameter parameterization of the antineutrino spectrum for the four mainisotopes can be found in [10]. Although the parameterization over-estimates antineutrinos above7.5 MeV, in general no serious consequence results by it as the spectrum strength has decreasedby three orders of magnitude there in comparison with that at 2 MeV. A recent update of theparameterization by six-parameter fits is given in [13] which improves the spectrum above 7.5MeV.

The Bugey 3 experiment compared three different models of the antineutrino spectrum with itsmeasurement. Good agreement was observed with the model that made use of the ILL νe spectra[9]. The ILL measured spectra for isotopes 235U, 239Pu, and 241Pu are shown in Fig. 3.2. However,there is no data for 238U; only the theoretical prediction is used. The possible discrepancy betweenthe predicted and the real spectra should not lead to significant errors since the portion of 238U isnever higher than 8%. In Fig. 3.3 we show a theoretical prediction for the spectra of all four mainisotopes. The overall normalization error of the ILL measured spectra is 1.9%. A global shapeuncertainty is also introduced by the conversion procedure.

10-5

10-4

10-3

10-2

10-1

1

10

0 1 2 3 4 5 6 7 8 9 10

235U

239Pu

241Pu

Eν (MeV)

S ν (c

ount

s M

eV-1

fis

s-1)

Figure 3.2: Antineutrino yield per fission ofthe listed isotopes. These are determinedby converting the corresponding measured βspectra [9].

Figure 3.3: Antineutrino energy spectrumfor four isotopes following the parametriza-tion of Vogel and Engel [10].

3.2. INVERSE BETA DECAY 27

3.2 Inverse beta decay

The reaction employed to detect the ν from a reactor is the inverse beta decay νe + p → e+ + n.The total cross section of this reaction, neglecting terms of order Eν/M , is

σ(0)tot = σ0(f2 + 3g2)E(0)

e p(0)e , (3.1)

where E(0)e = Eν − (Mn −Mp) is the positron energy when neutron recoil energy is neglected, and

p(0)e is the positron momentum. The weak coupling constants are f = 1 and g = 1.26, and σ0

is related to the Fermi coupling constant GF , the Cabibbo angle θC , and an energy-independentinner radiative correction. The inverse beta decay has a threshold energy in the laboratory frameEν = (mn +me)2−m2

p)/2mp = 1.806 MeV. The leading-order expression for the total cross sectionis

σ(0)tot = 0.0952× 10−42cm2E(0)

e p(0)e , (3.2)

where E(0)e and p

(0)e are in units of MeV. Vogel and Beacom [11] have recently extended the calcu-

lation of the inverse beta decay total cross section and angular distribution to order 1/M . Fig. 3.4shows the comparison of the total cross sections obtained in the leading order and the next-to-leading order calculations. Noticeable differences are present for high neutrino energies. We adoptthe order 1/M formula for the cross-section calculation in this project. In fact, the calculated crosssection can be related to neutron life time, whose error is only 0.2%.

Figure 3.4: Total cross section of the inverse beta decay calculated in leading order and next-to-leading order.

The expected recoil neutron energy spectrum, weighted by the antineutrino energy spectrumand the νe + p → e+ + n cross section, is shown in Fig. 3.5. Due to the low antineutrino energy


relative to the mass of the nucleon, the recoil neutron has low kinetic energy. While the positronangular distribution is slightly backward peaked in the laboratory frame, the angular distributionof the neutrons is strongly forward peaked, as shown in Fig. 3.6. This feature may provide a usefulcheck for the reactor antineutrino events. If the location where the positron is created and thelocation where the neutron is absorbed are sufficiently well measured, the initial direction of theneutron can be determined. Events originating from reactor antineutrinos are expected to haveneutrons moving preferentially along the antineutrino direction. The observation of such an angularcorrelation was reported by the Chooz experiment [5]. The expected position resolution of the DayaBay neutrino experiment would be sufficiently good to take advantage of this feature.

Figure 3.5: Recoil neutron energy spectrumfrom inverse beta decay weighted by the an-tineutrino energy spectrum.

Figure 3.6: Angular distributions of thepositrons and recoil neutrons in the labora-tory frame.

3.3 Prediction and observed antineutrino flux and spectrum

The expected count rate of antineutrino events can be compared with experimental measurementat short baselines. Based on 300,000 νe + p → n + e+ interactions, with only the neutron detected,collected at 15 m away from the reactor, Bugey measured the cross section of the inverse beta decayprocess per fission to be 5.752 × 10−19 barns/fission with an error of 1.4% [12]. This is in goodagreement with the predicted cross section of 5.824 × 10−19 barns/fission with an uncertainty of2.7% based on the ILL measured νe spectra. Therefore, it is reasonable to adopt the ILL measuredshape of the antineutrino energy spectra, but normalize the total cross section per fission to theBugey measurement.

Fig. 3.7 shows the predicted antineutrino event rate of the Palo Verde experiment as a functionof time with the reactor power, fission rate and the inverse beta decay cross section taken intoaccount. The observed antineutrino spectrum in the liquid scintillator is a product of the reactorneutrino spectrum and the cross section of inverse beta decay. Fig. 3.8 shows the neutrino energy

3.4. REMARKS ON VERY LOW ENERGY REACTOR ANTINEUTRINOS 29

spectrum, the νe + p → e+ + n total cross section, and the expected count rate as a function of theantineutrino energy. The highest count rate occurs at Eν ∼ 4 MeV.

Figure 3.7: Predicted antineutrino event rateof the Palo Verde experiment as a function oftime with the reactor power, fission rate andinverse beta decay cross section taken intoaccount.

Figure 3.8: Antineutrino energy spectrum,total cross section of inverse beta decay, andcount rate as a function of the antineutrinoenergy.

In summary, the expected event rate from reactors has an overall uncertainty of about 3%,including 0.2% from the inverse beta decay cross section, 1% from the thermal power of the reactors,1% from the fuel composition and 2.5% from the energy spectra of neutrinos.

3.4 Remarks on very low energy reactor antineutrinos

Since the inverse beta decay process has a threshold of 1.806 MeV and the cross section favors highantineutrino energy, oscillation experiments use only antineutrinos greater than 2 MeV.

Recently, there is considerable interest in the soft (< 2 MeV) spectrum of antineutrinos. In zero(very short) baseline experiments looking at the νee

− elastic scattering, they offer a search groundfor a range of interesting topics in neutrino physics: the neutrino magnetic moment, new physicsbeyond the standard model, sterile neutrino (using very short baseline and higher energy antineu-trinos), and the measurement of antineutrino spectrum itself. In order to do such experiments verychallenging technical hurdles have to be overcome.

The whole range of antineutrino spectrum has been calculated theoretically by several groups.For energies greater than 2 MeV, good agreement exits among theoretical predictions, and betweentheoretical predictions and experimental measurements.

The spectrum below 2 MeV has not been measured. Theoretical calculations of this soft partof the spectrum, as given in [10], [14], and [15], are generally less precise and can differ as muchas 30%. The results of the more recent calculations, [14] and [15], as shown in Fig. 3.9, are


Figure 3.9: The theoretical low energy reactor antineutrino spectrum. The vertical axis is neutrinoper KeV per fission and horizontal axis in in KeV. The left panel is caculated by [14] and the rightpanel by [15].

similar and much higher than the spectrum of [10] below 1.3 MeV, due to the inclusion of thermalneutron capture by 238U in the two recent calculations. The difference between [10] and [14] forantineutrinos below 1.5 MeV is depicted in Figs. 3.10 [16]. A character of the soft spectrum is thatit is not in equilibrium. A brief review of the situation can be found in [17]. 1

1We would like to thank Dr. V. Kopeikin and Dr. T. Schwetz for helpful communications for the calculationconcerning very low energy reactor antineutrinos below 2 MeV.

3.4. REMARKS ON VERY LOW ENERGY REACTOR ANTINEUTRINOS 31

Figure 3.10: Theoretical results of the soft part of the reactor antineutrino below 1.5 MeV. Theupper curve is given by [16] and the lower curve by [10].

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32

Chapter 4

Experimental Site and LaboratoryDesigns

4.1 Overview

The Daya Bay site is an ideal place for conducting a reactor θ13 experiment. The close-by mountainrange provides sufficient overburden to reduce cosmogenic background at the underground experi-mental halls, making the measurement feasible. Since the Daya Bay nuclear power facility consistsof multiple reactors, there will be two near detectors for monitoring the yields of anti-neutrinosfrom these cores and one far detector to look for disappearance of anti-neutrinos. It is possible toinstall another detector about half way between the near and far detectors to provide independentconsistency checks.

The proposed experimental site is located at the east side of the Dapeng peninsula, on thewest coast of Daya Bay, where the coastline goes from southwest to northeast. It is in the Dapengtownship of the Longgang Administrative District, Shenzhen Municipality, Guangdong Province.There are hills and mountain ranges on the north. The geographic location is east longitudinal114◦33’00” and north latitude 22◦36’00”.

The Daya Bay Nuclear Power Plant (NPP) is situated on the southwest and the Ling Ao NPPto the northeast near the coastline. Each NPP has two reactor cores that are separated by 88 m.The distance between the centers of the two NPPs is about 1100 m. The thermal power, Wth, ofeach core is 2.9 GW. Hence the total thermal power available is Wth = 11.6 GW. A third NPP,called Ling Ao-II NPP, is under construction and scheduled to come online by 2010-2011. ThisNNP is built roughly along the line extended from Daya Bay to Ling Ao, about 400 m northeast ofLing Ao. The core type is the same as that of the Ling Ao NPP but with slightly higher thermalpower. When the Daya Bay-Ling Ao-Ling Ao-II NPP are all in operation, the complex can providea total thermal power of 17.4 GW.

The experimental site is close to two mega cities, Hong Kong and Shenzhen and one mediumcity, Huizhou. The Shenzhen City1 ts 45 km to the west, Hong Kong 55 km to the southwest,and the border of the Huizhou - Daya Bay Economic Development Zone 10 km to the north, all

1Shenzhen is the first Special Economic Zone in China. With a total population of about 7 million, manyinternational corporations have their Asian headquarters there. It is both a key commercial and tourist hot spot inSouth China.

33

34 CHAPTER 4. EXPERIMENTAL SITE AND LABORATORY DESIGNS

Figure 4.1: Daya Bay and the vicinity. The nuclear power plants are located on the south shore ofthe west to east going Minor Daya Peninsula as marked. A town called Dapeng is located in thesouthwest of the peninsula.

measured in direct distance.The site is surrounded in the north by a group of hills which slope upward from southwest to

northeast. The slopes of the hills vary from 10◦ to 45◦. The ridges roll up and down with smoothround hill tops. Within 2 km of the site the elevation is generally 185 m to 400 m. The summit,called Pai Ya Shan, is 707 m PRD2. Due to the construction of the Daya Bay and Ling Ao NPPs,the foothill along the coast from the southwest to the southeast is levelled to a height in the rangeof 6.6 m to 20 m PRD.

4.2 Site geology

Because there is yet no detailed geological survey performed specifically for the experimental site,the present discussion is focused on the sites of the near detectors based on the available informationof the Ling Ao NPP [1]. We will defer the discussion of geology of the far-detector site untilgeological survey is performed.

2PRD is the height measured relative to the mouth of the Zhu Jiang River (Pearl River), the major river in SouthChina.

4.3. SEISMIC ACTIVITIES 35

According to the available geological maps, the near-detector site is located in the southwestportion of the Lianhua Mountain fault, on the south side of Pai Ya Shan. It is on the massifbetween the Wuhua-Shenzhen and Da Pu-Haifeng sub-faults. In the vicinity of the experimentalsite there are very few faults and they are not directly related to the faults mentioned above. Hencethe geological structure of the near site is rather simple.3

Surface exploration and trenching exposure show that the landforms and terrains are in goodcondition. There are no karsts, landslides, collapses, mud slides, empty pockets, ground sinkingasymmetry, or hot springs that would affect the stability of the site. There are only pieces ofweathered granites scattered around.

4.3 Seismic activities

According to the historical record up to December 31, 1994, there were a total of 63 earthquakesabove 4.7 on the Richter scale (RS), including aftershocks, within a radius of 320 km of the site.4

Among the stronger ones, there was one 7.0 RS, one 7.3 RS, and ten 6.0− 6.75 RS. There were 51medium quakes between 4.7 and 5.9 RS. The strongest, 7.3 RS, took place in Nan Ao in 1918. Themost recent one occurred in 1969 in Yang Jiang at 6.4 RS. In addition, there have been earthquakesin the southeast foreland and one 7.3 RS quake occurred in the Taiwan Strait on Sept. 16, 1994.The epicenters of the quake were at a depth of roughly 5 to 25 km. These statistics show that theseismic activities in this region originate from shallow sources which lie in the earth crust. Thestrength of the quake generally decreases from the shelf to inland.

Within a radius of 25 km of the experimental site, there is no record of quakes of Ms ≥ 3.0 (ML ≥3.5),5 and there is no record of even weak quakes within 5 km of the site. The distribution of theweak quakes is isolated in time and separated in space from one another, and without any obviousregularity.

Activity in the seismic belt of the southeast sea has shown a decreasing trend. In the next onehundred years, this region will be in a residual energy-releasing period, followed by a calm period.It is expected that no earthquake greater than 7 RS will likely occur within a radius of 300 kmaround the site; the strongest seismic activity will be no more than 6 RS. In conclusion, 20 yearsof seismic observation indicates that the region surrounding the experimental site is in a state oflow seismic activity, and there has not been any abnormal seismic activity.

4.4 Engineering geology

The following data are based on the geotechnical survey of the Ling Ao NPP. The rock of the nearsite is primarily granite, which is new or lightly effloresced. Some of the physical properties of therock in this area are as follows:

3In more details, the experimental site is about 20 km from the Wuhua-Shenzhen sub-fault, and about the samedistance from the Da Pu-Haifeng sub-fault. It is more than 17 km from the small Daya Bay base fault. The faultscales are generally small. In particular, in the region of the planned near-detector sites, there are only four faultareas, each is no more than 300 m × 2 m.

4The seismic activities quoted here are taken from a Ling Ao NPP report [2]5Ms is the magnitude of the seismic surface wave and ML the seismic local magnitude. Ms is the normal

characteristics of an earthquake. There is a complicated location-dependent relationship between Ms and ML. InDaya Bay Ms ≥ 3.0 is equivalent to ML ≥ 3.5.


• Density6: 26.3 kN/m3.• Pressure resistance strength of a saturated single stalk: 208.4 MPa• Pressure resistance strength of a dry single stalk: 212.1 MPa• Softening coefficient: 0.98• Elastic modulus: 61500 MPa• Poisson ratio: 0.28

These properties indicate that the granite in this region is very strong and intact:The far-detector site is about 400 m underground. It should also be sitting on lightly effloresced

or fresh granites, sandstone or pebble rocks. The rock should have a strength and integrity similarto that of the near site.

4.5 Hydrogeology

Most of the rain fall runs into the ocean directly as surface water, while some permeates into theground to replenish the ground water, especially during the dry season.

Analysis of the water samples from 6 rivers and 3 springs in the region shows that the waterfrom the rivers is slightly acidic with pH value between 6.1 and 6.8. The dissolved chemicals areNa·Ca-HCO3·Cl. The pH value of the water from the springs is lower.

For the bedrock efflorescence belt, the underground crevice water in the upper part of thestrongly effloresced region is acidic, with pH value between 5.89 and 6.23. The water contains alarge amount of organic matter and humic acid. Again, the dissolved chemical is mainly Na·Ca-HCO3·Cl. In the lower part, which is moderately effloresced, the pH of the crevice water is between7.0 and 7.86, which is slightly alkaline. The dissolved chemicals in this case are both Na·Ca-HCO3

and Ca-HCO3. The underground water is thus not corrosive to reinforced concrete.

4.6 Stability of mountain and cavern

The slope of the mountains ranges from 20◦ to 30◦, and the surface consists mostly of lightlyeffloresced granite. The body of the rock is comparatively integrated and the slopes are stable.Although there is copious rainfall and erosion in the coastal area, there is no evidence of large-scalelandslide or collapse. However, there are small-scale isolated collapses due to efflorescence of thegranite, rolling and displacement of effloresced spheroid rocks.

For the near-detector sites, the tunnels and experimental halls will be built in the Late Yan-shanian Granitic Intrusive Mass (Daya near site) and Lower Palaeozoic Group (Ling Ao near site)with about 100 m overburden. During the construction of the Ling Ao NPP, rock samples takenfrom drill holes showed that the depth of the moderately effloresced rocks is less than 30 m. Below30 m, the rock is fresh - it is hard and intact, having good stability. Therefore the undergroundhalls will be stable.

The far-detector site, having about 400 m overburden, will be constructed about 1750 m northof the Daya near site. The rock along the tunnel is lightly effloresced or fresh granite. From a

6In geology the common quoted density is the gravitational force density. In the present case it is about 2.7 g/cm3

which is the density of granite.

4.7. TRANSPORTATION 37

preliminary evaluation, the underground facilities again will be stable. However, it is expected thatreinforcement will be needed at isolated locations where cracks may appear.

4.7 Transportation

There is no railway within a radius of 15 km of the site. The highway from Daya Bay NPPto Dapeng Township (Wang Mu) is second-class grade and 12 m wide. The Dapeng Town isconnected to Shenzhen, Hong Kong, and Guangzhou by highways which are either first-class gradeor expressways.

There are two maritime shipping lines near the site in Daya Bay, one on the east side and theother on the west side of the Central Archipelago. Oil tankers to and from Nanhai Petrochemicaluse the east line. The Huizhou Harbor, which is located on the Quandao peninsula, is 13 kmnorth of the site. Two general-purpose 10,000-ton docks were constructed in 1989. Their functionsinclude transporting passengers, dry goods, construction materials, and petroleum products. Theships using these two docks take the west line. The minimum distance from the west line to thesite is about 6 km. Two restricted docks of 3000-ton and 5000-ton capacity, respectively, have beenconstructed on site during the construction of the Daya Bay NPP.

4.8 Design of laboratory facilities

The laboratory facilities include access tunnels connected to the entrance portals, a levelled maintunnel connecting all the underground detector halls, an assembly hall, control rooms, water andelectricity supplies, air ventilation, and communication. The approximate locations and overburdenof the near, mid, and far detector sites as well as the layout of the tunnels are shown in Fig. 4.2.

4.8.1 Detector sites

Since there are two clusters of twin reactors (will be three groups by 2010-2011) separated inspace at Daya Bay, it will need detectors close to the respective reactor cluster to monitor theanti-neutrinos emitted from the core as precisely as possible. Detailed optimization of the baseline(see the chapter on Systematic for details) indicates that a near detector should be positionedequidistantly from the two cores that it monitors, and should be as close to the cores as possible.This is realized for the Daya Bay NPP. The situation for the Ling Ao and Ling Ao-II NPP’s is alittle bit more complicated since only one near detector is used. It appears that this near detectorshould be equidistant from the centers of the Ling Ao and Ling Ao-II reactors. Taking overburdeninto account, the Daya near detector site is about 500 m from the center of the Daya Bay cores andthe elevation at the top of the site is 117 m (PRD). The Ling Ao near detector hall will be about500 m away from the center of the Ling Ao reactors, and approximately 530 m from the center ofthe Ling Ao-II cores.7 The elevation above the Ling Ao near site is about 115 m PRD.

The far detector site is north of the two near sites. Ideally the far site should be put equidistantlyfrom the two Daya Bay and Ling Ao-Ling Ao-II reactor clusters; however, the overburden wouldbe about 200 m of rocks. At present, the distances from the far detector to the center of the Daya

7The Ling Ao near detector site is about 50 m west from the perpendicular bisector of the Ling Ao-Ling Ao-IIclusters to avoid installing it in a valley which is usually geologically weak, and to gain more overburden.


Figure 4.2: Layout of the Daya Bay-Ling Ao reactor cores, the future Ling Ao-II cores (also knownas Ling Dong), and possible detector sites. The green lines represent access tunnels, and blue linesare main tunnels connecting the underground detector halls.

Bay reactor cluster and to the mid point of the Ling Ao-Ling Ao-II clusters are 2220 m and 1750m, respectively. The overburden is about 430 m of rocks. Optimization showed that the currentlocation of the far detector can still meet the designed sensitivity of sin22θ13.

It is possible to install a mid detector hall between the near and far sites such that it isabout 1100 m from the Daya Bay reactor cluster and 910 m from the Ling Ao-Ling Ao-II cluster.The elevation of mid hall is 205 m PRD. This mid experimental hall could be used to carry outmeasurements for systematic studies and for internal consistency checks.

4.8.2 Tunnels

A sketch of the layout of the tunnels is shown in Fig. 4.2. There are three branches for the horizontalmain tunnel extending from a junction near the mid hall to the near and far underground detectorhalls. There are also an access tunnel and a construction tunnel.

Referring to FIg. 4.2, the entrance portal of the access tunnel is behind the onsite hospital andto the west of the Daya near site. The length of this access tunnel, from the portal to the Dayanear site, is 295 m. Its elevation is 8 m PRD, and has a grade between 8% and 12% [3]. A slopedaccess tunnel will allow the underground facilities to go deeper, providing more overburden. In the

4.8. DESIGN OF LABORATORY FACILITIES 39

case of 8% grade, the elevation of the Daya near site will be -13 m PRD.

Figure 4.3: Cross section of the access and main tunnels.

The access and main tunnels will be able to accommodate vehicles transporting equipment ofdifferent size and weight. A conceptual design of the tunnel is shown in Fig. 4.3. It has an inverse-Ushape. The height, as well as the width, is 7.2 m. The grade of the main tunnel will be at most0.3% to ensure levelled movement of the heavy detectors filled with liquid scintillator inside themain tunnel.

The entrance portal of the construction tunnel is at the lower level of the Daya Bay Quarry at56 m PRD (see Fig. 4.2). The length of this tunnel is 672 m from the entrance to the junction nearthe mid site [3]. During excavation, all the waste rocks and dirt are transfered through this tunnelto the outside. This construction tunnel is also necessary to avoid the interference of excavationactivities from the assembly of detectors in the Daya near and mid sites. The cross section ofthe construction tunnel can be smaller than the access and main tunnel but it is large enough fortramcar transportation. The grade can be as large as 33%.

The total length of the tunnel is 3375 m. The amount of waste to be removed will be 132500m3 [3]. About half of the waste will be stacked up in the Daya Bay Quarry to provide additionaloverburden to the Daya near site which is not far away from the Quarry. The rest of the the wastecan be could be disposed in conjunction with the construction of the Ling Ao-II NPP.

Bibliography

[1] Report of Ling Ao Nuclear Power Plant.

[2] Catalog of Chinese Earthquakes, Quoted in the Preliminary Safety Report on Ling Ao NuclearPower Plant.

[3] Report of Preliminary Feasibility Study of Site Selection for the Daya Bay Neutrino Experi-ment, prepared by Beijing Institute of Nuclear Energy, September, 2004.

40

Chapter 5

Detector

5.1 Overview

Determining sin22θ13 to a value of 0.01 or better implies measuring a small difference in the numberof antineutrino events observed at the far site from the expectation based on the number of detectedevents at the near site after correcting for the inverse-square scaling of distance under the assump-tion of no oscillation. To observe such a small change, the detector must be carefully designedto minimize systematic effects. Based on the experience of the past reactor neutrino experimentsdiscussed in the appendix, the following requirements are established for designing the experiment:

1. The detector should not be too large; otherwise, it would be difficult to move from detectorsite to detector site. In addition, at a certain size depending on the geometry of the detector,the rate of cosmic-ray muons passing through the detector will be unacceptably high and willcompromise the performance of the detector.

2. The detector should be homogeneous to minimize edge effort that could lead to potentialsystematic problems;

3. The mass of the target should be well determined since the number of detected events dependson it;

4. Liquid scintillator, the target material, should be from one batch, and the mixing procedureshould be well controlled. This ensures that the composition of the target is uniform, implyingthe fraction of hydrogen is the same for all detectors.

5. Inefficiency of rejecting cosmic-ray muons should be less than 1% and be known to betterthan 0.25%.

6. Time resolution should be better than 1ns for determining the event time and for studyingbackgrounds;

7. Energy resolution should be better than 15% at 1 MeV. Good energy resolution is desirable forreducing systematic uncertainty should an energy cut is applied. Excellent energy resolutionis also important for studying spectral distortion as a signal of neutrino oscillation.

41

42 CHAPTER 5. DETECTOR

8. The energy threshold of the trigger should be less than 1.0 MeV since the smallest energy ofdetecting the positron comes from electron-positron annihilation at rest.

A Chooz-type detector can in principle fulfill the above requirements although other new con-cepts are not excluded. The energy threshold of a Chooz-type scintillator detector can be reducedby a three-layer structure as shown in Fig. 5.1. The inner-most layer (region I) is the Gd-loadedliquid scintillator as the antineutrino target. The second layer (region II) is filled with normalliquid scintillator which can contain all gamma energies from neutron capture or positron annihi-lation while not acting as the antineutrino target since neutron-capture time is about a factor often longer than that in the Gd-loaded scintillator. The neutron spill-in and spill-out across theboundary between regions I and II during thermalization is a secondary effect and can be correctedfor by calibration process in combination with Monte Carlo simulation. The outer-most layer (re-gion III) is normal mineral oil that shields radiation from the PMT glass from entering the fiducialvolume. This will reduce the singles rate and the threshold can thus be lowered to 1.0 MeV. Allthe three regions are partitioned with UV-transparent acrylic tanks so that the target mass can bewell determined.

Figure 5.1: Cross section of a detector module showing the three-layer structure.

In order to have sufficient target mass at the far site, multiple detector modules, each with atypical target mass of 20 metric tons, is chosen. Identical detector modules, but fewer in number,will be used at the near sites. The scheme of multiple modules offers better scalability, internalconsistency checks at a given location, and statistical reduction of the total systematic errors (seeSec. 7.1 for detailed discussions.) Multiple modules also imply small modules so that it is easier toconstruct and to correct mistakes. In addition, small modules are easy to move so that adjustingthe baseline is possible and less susceptible to cosmic-muon induced backgrounds.

However too many small modules introduce inconvenience for calibration, may introduce othersystematic errors, and are probably not cost-effective due to reduction of fiducial mass. A goodbalance between the number of modules and the size of the module is essential for the success ofthe experiment. Based on the experience of the recent neutrino experiments, we adopt the choiceof 20 ton module. Each module will be viewed with about 200 8” PMTs with low-radioactivity

5.1. OVERVIEW 43

glass.1

At the near site, about 600 to 1400 νe events (500-300m) per day per module can be obtainedat the Daya Bay nuclear power plant, while about 70 events per day per module can be obtainedat the far site (∼ 1800m).2 For the near detector, two modules are necessary in order to have crosscheck. For the far detector, four modules are needed in order to have enough statistics to reach thedesigned sensitivity while keeping the number of modules at a manageable level. To minimize thedifference in systematic uncertainties between the near and far locations, modules can be calibratedat the near site before moving to the far site. With this design, one hundred days of running canreach a statistical error of 0.5%.

A possible setup of the detector system is shown in Fig. 5.2. Each detector module has aradius of about 2.5 m and a height of 5.0 m, with a total mass of about 80 tons. All detectormodules are surrounded by a 2-m-thick water shield with PMTs installed, effectively functioningas Cerenkov counters, and two layers of Resistive Plate Chambers (RPC) on the outside of theshield as active muon-tagging detectors. The RPCs provide redundancy and cross check, hencemeeting our requirements of high efficiency in vetoing cosmic-muons that can induce spallationbackgrounds.

Figure 5.2: An example of the detector setup. The detector modules are enclosed by a 2-m-thickwater buffer which is also used as a Cerenkov muon veto. Muons are tracked with RPC’s on theoutside of the water buffer.

1The detector of Chooz had a mass of 5 tons, Palo Verde 12 tons with fine segmentation, MiniBooNE 800 tons,and KamLAND 1000 tons,

2At a distance of 1 km, the rate is about 1 νe event per GW per ton per day.


5.2 Monte Carlo simulation

A GEANT 3.21 [1] based simulation package has been developed for designing this experiment. Thelayout of the far-site detector consisting of four cylindrical detector modules is shown in Fig. 5.3.The top two plots are the side views and the bottom one is the top view.

Figure 5.3: Layout of the antineutrino detector used in the GEANT3 simulation. The outer-mostlayer is rock around the underground lab. Four detector modules are shielded by 2-m-thick waterbuffer (layer in blue). The three-layer structure of module is shown in white (oil), light blue (gammacatcher), and yellow (target).

To simulate the transportation of neutrons, GCALOR 1.05[2] is employed. In GCALOR, MI-CAP simulates the interactions of neutrons with energies between 10−5 eV and 20 MeV. NMTCis used to transport particles with energies up to 3.5 GeV (proton, neutron) or 2.5 GeV (pion).A scaling model is then used to handle high-energy particles up to 10 GeV. For even higher en-ergy, GEANT-FLUKA is adopted for the simulation. The emitted gamma spectrum after neutroncapture on Gd, shown in Fig. 5.4, is also incorporated in the simulation.

Quenching of scintillator light, important for simulating proton recoil, is included in the simu-lation. The simulated parameters are checked against data taken with an Am-Be neutron sourcein the Palo Verde experiment [3]. The Am-Be source emits neutrons with kinetic energies up to 10MeV, creating proton recoils in the liquid scintillator. The default parameters of the Birk’s law inGEANT yield good agreement between data and Monte Carlo, as shown in Fig. 5.5.

The optical photons originated from scintillation are transported, with attenuation and reflec-tion taken into account, to PMTs using user-written software. The PMT parameters, such asgeometry and quantum efficiency, are taken from the data sheet of Hamamatsu R5912. A recon-struction program is developed using maximum likelihood method and the MINUIT package ofCERN to fit the vertices and energy of an event simultaneously . However, for all simulationsdescribed below, only the total charge collected by PMTs is used for energy reconstruction. Thisleads to a slightly worse spatial resolution but reduces systematic bias due to correlation of thefour parameters in the fit.

5.3. LIQUID SCINTILLATOR 45

generated Eg

96/09/25 09.55

MC

DATA

0

25

50

75

100

125

150

175

200

225

0 1 2 3 4 5 6 7 8

Figure 5.4: The emitted gamma spectrum ofGd after neutron capture.

Figure 5.5: Effect of scintillation lightquenching in proton-recoil events from theAm-Be source. Accurate simulation of pro-ton recoil is useful for understanding the an-tineutrino backgrounds resulting from fastneutrons.

5.3 Liquid scintillator

Gd-loaded liquid scintillator is rich in proton. Hence, it is an ideal antineutrino target. Gd is knownto have a very large neutron-capture cross section. Furthermore, neutron-capture on Gd will leadto emission of gamma-rays with a total energy of about 8 MeV, much higher than the energiesof the gamma-rays from natural radioactivity that are normally below 3.5 MeV. Both Chooz [5]and Palo Verde [4] used 0.1% Gd-doping that yielded a capture time of 28 µs, about a factor ofseven shorter than that by proton in an undoped liquid scintillator. Backgrounds from randomcoincidence will thus be reduced by a factor of seven.

Extreme precaution must be exercised in preparing and using Gd-loaded liquid scintillator. Forinstance, radioactivity cleanliness of the Gd compound, light yield of the scintillator and agingof the scintillator should be taken into account at the beginning of the experiment. Experienceindicates that these issues can be solved if proper methods for synthesizing the Gd-loaded liquidscintillator are applied.

In order to keep the random coincidence below 50 Hz, the scintillator should have contaminationof 238U, 232Th and 40K less than 10−13 g/g. Although it is achievable for normal liquid scintillatormade of pseudocumene and mineral oil [6], special care is required for the Gd compound since itusually contains 232Th at a level of about 0.1 ppm. For a loading level of 0.1% by weight, the Gdcompound has to be purified to a level of better than 10−10 g/g.

Chooz and Palo Verde used two different methods to produce the Gd-doped liquid scintillator.The Chooz experiment, by dissolving Gd(NO3)3, prepared the resulting scintillator that aged at a


rate of 0.4% per day (that is, the attenuation length of the Gd-loaded liquid scintillator decreasedwith time). The Palo Verde experiment used Gd(CH3(CH2)3CH(C2H5)CO2)3 yielding a scintillatorthat aged at 0.03% per day [4]. Fig. 5.6 shows the variation of the attenuation length of the Gd-doped liquid scintillator for three years of operation in Palo Verde.

Figure 5.6: Variation of attenuation length of one cell (top) and all cells(bottom) for three years ofoperation.

Based on the experience of the Palo Verde experiment, the concentrated liquid scintillator mustbe mixed with the mineral oil and pseudocumene at the experimental site to avoid aging effectspossibly caused by motion during transportation. The mixing equipment, consists of a tank andstainless steel pipes, needs to be cleaned very carefully. The mixed liquid scintillator will be filteredto remove particles which will scatter light, making the attenuation length shorter. A delicatemixing procedure must be followed to avoid local build-up of the Gd compound. The Palo Verdeexperiment has shown that the Gd compound will not be removed by the filter and its exact amountin the doped liquid scintillator can be measured by weighting during the synthesis process or byX-ray scattering [7].

The Palo Verde scintillator, now known as Bicron BC521, uses the following formula: 4% 2-ethoxyethanole, 36% pseudocumene, 60% mineral oil plus some amount of PPO, Bis-MSB, BHT,and Gd compounds. Its light yield is measured to be about 55% of anthracene as shown in Fig. 5.7. The chemical ingredient of the Gd-doped liquid scintillator that we plan to use in this experimentis similar to that of Bicron BC521, which yields about 7000 optical photons per MeV energydeposition. Although R&D for a more stable Gd-loaded liquid scintillator will continue, BC521 isa good candidate to start with and it fulfills our requirements.

5.4. DETECTOR MODULES 47

Figure 5.7: Light yield of all batches of BC521.

5.4 Detector modules

5.4.1 Module geometry and Energy resolution

Detector modules with different shape have been considered: cubical, cylindrical, and spherical.From the point of view of easy construction, cubical and cylindrical shape are particularly interest-ing. Monte Carlo simulation shows that cylindrical shape can provide better energy and positionresolution for the same number of PMTs. Fig. 5.8 shows the structure of a cylindrical module.PMTs are arranged only in the radial direction. The surfaces at the top and the bottom of theouter-most cylinder are coated with white reflective paint or other reflective means to provide dif-fused reflection. Such an arrangement is feasible since 1) the event vertex is determined only withthe center of gravity of the charge, not relying on the time-of-flight approach, 3 2) the fiducialvolume is well defined with a three-layer structure, thus no accurate vertex information is required.Based on a detailed Monte Carlo simulation, the neutrino target in the inner-most region of themodule is about 3.2 m high and with a radius of 1.6 m, the middle section is 0.45 m thick and theouter-most mineral oil buffer is also 0.45 m thick. For the entire module, the diameter will be 5.0 mand the height will be 5.0 m. With reflection at the top and the bottom, the effective coverage with200 PMTs is 12%. The energy resolution is expected to be 5.9% at 8 MeV using the total-chargemethod or 5.5% using a fit method.

5.4.2 Gamma catcher

Gamma rays deposit energy in the scintillator by means of Compton scattering. Based on asimulation done with GEANT3, the average track length is 47 cm with a RMS of 35cm for the

3Although time information may not be used in reconstructing the event vertex, it will be used in backgroundstudies. A time resolution of 1 ns is realized in the current design of the readout electronics.


Figure 5.8: Cross section of a detector module showing the acrylic vessels holding the Gd-dopedliquid scintillator at the center, and liquid scintillator between the acrylic containers. PMT’s aremounted inside the outer-most stainless steel tank.

gamma rays emitted from the neutron-capture-by-Gd process. However, some of these gammasproduced in the target can escape, yielding an amount of visible energy below 6 MeV. As a result,requiring the visible energy to be greater than 6 MeV for identifying the neutron will introducean inefficiency. The uncertainty of this inefficiency is an important systematic error for a reactorneutrino experiment for determining θ13 precisely. This inefficiency can be reduced by enclosingthe target with a layer of normal liquid scintillator, called the gamma catcher, that absorbs theescaped gamma rays.

Fig. 5.9 shows the relation between the efficiency of detecting antineutrino events and thethickness of the gamma catcher for the Daya Bay detector module. The efficiency are 87.80%,91.04%, and 95.23% for a gamma catcher with a thickness of 40 cm, 50 cm and 70 cm respectively.For comparison, Chooz obtained an average efficiency of (94.6±0.4)%[5] with a 70-cm thick gammacatcher. Since this inefficiency is almost independent of the neutron path length, we can rely onthe calibration data to evaluate it and use Monte Carlo to cross check. To optimize the modulesize and the neutron efficiency, the thickness of the gamma catcher is chosen to be 45 cm, with anefficiency of 90% for detecting neutrons.

5.4.3 Oil buffer

The oil buffer is used to separate the PMTs submerging in the mineral oil from the scintillator.It prevents natural radiation from the PMT glass from entering the fiducial volume. The mainconcern is the energetic gamma ray that passes through the oil buffer and has more than 1 MeVof energy (positron signal threshold) deposited in the liquid scintillator. Based on Monte Carlosimulation, the estimated rate of detected background neutrons with energies between 6 and 12MeV in a detector module at the near site is 65/day, which is much larger than that at the far

5.4. DETECTOR MODULES 49

Figure 5.9: Efficiency of the 6-MeV-energy cut as a function of the gamma-catcher thickness.

site. To require the ratio of uncorrelated background to signal to be less than 0.1%, the naturalradiation background should be less than 50 Hz. In this case, the rate of random coincidence ofthe background gamma ray and neutron forming a fake signal in 100 µs (should it be 200?) will beRγRnτ < 0.3/day/module.

A potential PMT candidate is the 25-cm-tall Hamamatsu R5912, of which the photocathode is20 cm in diameter. The concentration of 238U and 232Th is less than 40 ppb, and 40K is 25 ppb.Based on these values, the amount of background due to the natural radiation from the PMT glasscan be estimated for the Daya Bay experiment. The results are summarized in Table 5.1. With a20 cm oil buffer, the radiation from the PMT glass detected by the liquid scintillator is 7.7 Hz.

isotopes Concentration (ppb) 20 cm (Hz) 25 cm (Hz) 30 cm (Hz) 40 cm (Hz)238U (>1 MeV) 40 2.2 1.6 1.1 0.6

232Th (>1 MeV) 40 1.0 0.7 0.6 0.340K (>1 MeV) 25 4.5 3.2 2.2 1.3

Total 7.7 5.5 3.9 2.2

Table 5.1: Radiation of the PMT glass detected in the scintillator as a function of the oil-bufferthickness.

The oil buffer also desensitizes interactions occurring in the vicinity of the PMT where themeasured energy will have large bias. Fig. 5.10 is a distribution of the total number of observedphotoelectrons for 1 MeV gamma rays as a function of the vertex position in equal-volume binsfor a tank containing scintillator only. The center of the tank is at 0 whereas the wall is at 40000.In this calculation, the cylindrical tank is 112 cm in radius. When the gamma vertex is near the


wall, the resolution is significantly worse. A cut at 30000 corresponding to 15 cm away from thePMT surface is necessary to ensure uniform efficiency. In Chooz, the vertex distance from thegeode boundary was required to be greater than 30 cm [5]. After taking the size of the PMT intoaccount, our result is comparable to Chooz. To avoid any systematic uncertainties caused by sucha cut, a separation of more than 15 cm between the PMTs and the scintillator is highly preferred.

Figure 5.10: Total number of observed photoelectrons (chqtot) versus vertex position in equal-volume bin (eqvcyl) for 1-MeV gamma rays. The center of the detector is at eqvcyl = 0, and thewall of the container is at eqvcyl = 40000.

In addition, the oil buffer augmenting the 2 m water buffer will further reduce the radiation fromthe surrounding rock and radon in air. The natural radioactivity of a rock sample collected at thepotential detector site at Daya Bay has been measured. The concentration of 238U is determined tobe 560 ppm, 1000 ppm for 232Th, and 2.3 ppm for 40K. The rate of gamma rays that can penetratethrough the 2 m water shield, 45 cm of oil buffer, and deposit more than 1 MeV of energy in thescintillator is 5.4 Hz for 238U, 20.4 Hz for 232Th, and 1.8 Hz for 40K.

Combining the rates of radiation from the PMT glass and the rock, the total rate is 33 Hz. Radonradioactivity can be controlled by ventilation, which will be discussed later. We conclude that a45-cm-thick oil buffer will be sufficient to reduce the uncorrelated backgrounds to an acceptablelevel.

5.4.4 Containers

The outer most tank can be made of steel or polyethylene (PE) by the method of rotomolding. Theinner tank can be made of UV-transparent acrylic whose compatibility with the Gd-doped liquidscintillator will be studied. The selected acrylic used in the Palo Verde and Chooz experiments wascompatible with a liquid scintillator with 40% pseudocumene.

5.5. WATER BUFFER 51

In summary, the dimensions of the target volume, gamma catcher, and the oil buffer are tabu-lated in Table 5.2.

Table 5.2: Dimensions of a detector module.

Inner Outer Inner Outerradius (m) radius (m) half-height (m) half-height (m)

Target volume 0.00 1.60 0.00 1.60Gamma catcher 1.60 2.05 1.60 2.05

Oil buffer 2.05 2.50 2.05 2.50

5.5 Water buffer

The antineutrino detector modules need to be shielded from external background events such asgamma-rays and cosmic-ray-induced-neutrons originated from the surrounding rock. The simplestand cheapest shielding material is water, which has been employed by many of the previous reactorneutrino experiments. The thickness of the water buffer, determined from Monte Carlo simulation,should be sufficient to attenuate the backgrounds to an acceptable level. A 2-m-thick water shieldingbuffer, similar to that of the Palo Verde experiment, appears to meet the goal. The water shieldswill be self-supporting and the end wall should also be movable so that the detector modules canbe accessed. In addition, a purification system is required for purifying the water to the desiredtransparency. At present, there are two conceptual designs of the water buffer, shown in Fig. 5.11and Fig. 5.12, that can be realized.

5.6 Muon veto

Since most of the background come from the interactions of cosmic-ray muons with nearby mate-rials, it is thus desirable to have a very efficient active veto coupled with a tracker for tagging thecosmic-ray muons. This will provide a means for studying and rejecting the cosmogenic backgroundevents. The three types of detectors that are being considered are water Cherenkov counter, resis-tive plate chamber, and plastic scintillator strip. When the water Cherenkov counter is combinedwith a tracker, the veto efficiency can be close to 100 %. Furthermore, these two independent de-tectors can cross check each other. Their inefficiencies and the associated errors can be determinedwell by cross calibration during data taking. We expect the inefficiency will be lower than 0.4%and the uncertainty of the inefficiency lower than 0.2%.

5.6.1 Water Cherenkov detector

Besides being a shield, the water buffer can also be utilized as a water Cherenkov counter of themuon system by installing PMTs in the water. This is a viable option since a total of 800 8” PMTsfrom the Macro experiment have been obtained at no cost. Water Cherenkov detector is based onproven technology, and known to be very reliable. With proper PMT coverage and diffuse reflectionon the inner wall of the detector, the efficiency of detecting muons should be around 95%. However,


Figure 5.11: Conceptual design of the water buffer using water modules. The water modules ontop are moved aside to show the detector modules in yellow.

with only a water Cerenkov detector, it is difficult to meet the requirement of 1% veto inefficiencywith 0.25% uncertainty.

5.6.2 Resistive Plate Chamber

Among all the tracking detectors, Resistive Plate Chamber (RPC) is a potential candidate sinceit is very economical for instrumenting a large area. Furthermore, RPC is simple to fabricate.The manufacturing technique for both bakelite and glass type of RPC, developed by IHEP for theBESIII detector and the long-baseline neutrino-oscillation experiment, is well established [8].

An RPC is composed of two resistive plates with gas flowing between them. Its structure isshown in Fig. 5.13. High voltage is applied on the plates to produce a strong electric field. Whencosmic rays pass through the gas between the two plates, an avalanche or a streamer signal isproduced. The signal is then picked up by a pickup strip and sent to the data acquisition system.In our case, the RPCs will work in the streamer mode.

The efficiency and noise rate of the BESIII RPC have been measured. In Fig. 5.14, the effi-ciencies versus high voltage are shown for threshold settings between 50 and 250 mV. The shownefficiency does not include the dead area along the edge of the detector but includes the dead regioncaused by the insulation gasket. This kind of dead area covers 1.25% of the total detection area.The efficiency of the RPC reaches plateau at 6.8 kV and rise slightly to 98% at 7.2 kV. There is noobvious difference in efficiency above 7,0 kV for thresholds below 250 mV. The singles rate of theRPC is shown in Fig. 5.15. When the threshold is 150 mV or higher, the singles rate is less than0.1 Hz/cm2. The noise rate increases significantly when the high voltage is higher than 8 kV.

The above measurements were made with some one dimensional read-out RPCs. For theDaya Bay experiment, we shall probably use two dimensional read-out RPC to get the x- andy-coordinates of the cosmic muon. Time coincidence of the two dimensional read-out can alsoreduce the noise rate significantly. The efficiency of the two dimensional read-out RPCs has been

5.6. MUON VETO 53

Figure 5.12: A conceptual design of the water buffer using a pool. The top covers are pulled opento show the detector modules submerged in water. Muon tracking detectors are mounted on theoutside and the top of the pool.

determined to be higher than 96%, in good agreement with the expectation based on the measuredefficiency of the one-dimension RPC. To further suppress noise and improve position determination,two layers of two dimensional read-out RPCs will be used in this experiment. For each through-going muon, we shall have four hits at the entrance point and another four hits at the exit point.If we require four hits at a point to identify a cosmic-ray muon, then the tracking efficiency will be92%.

5.6.3 Scintillator-strip muon tracker

Besides RPC detector, scintillator-strip detector is another promising candidate for tracking cosmic-ray muons over a large surface area. This detector is known to have excellent long term stabilityand reliability as well as cost-effective. The strips used in the OPERA experiment are 6.86 m long,10.6 mm thick, 26.3 mm wide. These dimensions can be optimized for the Daya Bay experiment.Each strip is read out using Wave-Length-Shifting (WLS) fibers with photo-detectors placed atboth ends of the fibers. The scintillator strips are extruded by AMCRYS-H (Kharkov, Ukraine) ofpolystyrene, 2% p-Terphenyl (primary fluor) and 0.02% POPOP (secondary fluor) produced by thesame company, with a TiO2 co-extruded reflective coating for better light collection (a technologysimilar to the one developed for MINOS). A 6.86 m long groove, 2.0 mm deep, 1.6 mm wide, in thecenter of the scintillator strip, houses the WLS fiber (Kuraray Y11 (175) of 1 mm diameter) whichis glued in the groove using a high transparency glue.

A basic unit of the plastic-scintillator module is constituted of 64 scintillator strips glued to-gether by means of double-sided adhesive tape between two aluminum sheets (see Fig. 5.16). Amodule has end-caps at each end where the WLS fibers are coupled to two 64-pixel photo-detectors


Figure 5.13: Sketch of a Resistive Plate Counter.

Figure 5.14: Efficiency of the BESIII RPC versushigh voltage for different thresholds.

Figure 5.15: Noise rate of the BESIII RPC versushigh voltage for different thresholds.

(Hamamatsu H7546) through polished opto-couplers (cookies). The mechanical strength is given bythe strips themselves and the aluminum sheets enveloping them. The end-caps host the PM tubesas well as the monitoring light injection system, the front-end electronic cards and data acquisitioncards (Control Cards) . The end-caps also provide the mechanical structure by which the moduleswill be suspended. More details on the module can be found in [9].

Given the low data rate the DAQ system has been designed to sort the data through Ethernetat the earliest stage of each sub-detector. The global DAQ is build like a standard Ethernetnetwork whose nodes are Controller Boards (CB) placed on both side of each plastic-scintillatormodule. Their task is to interface and control front-end (FE) electronics, to sort the data tothe Event Building Workstation (a commercial PC running under Linux), to handle monitoringand slow control from the Global Manager through the same Ethernet processor. The distributedclient/server software is based on CORBA standard. The electronics is divided into 2 boardsconnected by small flat cables: FE board which includes a pair of FE chips and a digital board (theCB). These two boards are enclosed in the endcaps of the modules at the output of the PMTs.

5.6. MUON VETO 55

Figure 5.16: A plastic-scintillator module of scintillator strips during assembly.

The FE board is a 8-layer PCB, which is directly plugged to the PMT, as shown in Fig. 5.17.The FE board contains two read-out chips (ROCs), buffer amplifiers for the differential chargeoutput signals of the ROCs and logic level translators for the digital signals. The ADCs are locatedon the CB, in order to minimize the length of the data bus. Each CB board has 3 cables connectedto it: Ethernet cable for data transfer, clock distribution cable, low voltage power supply. Thesecables run along the plastic-scintillator modules inside the endcaps.

The readout electronics of the module is based on a 32-channel ASIC (ROC) with individualinput, trigger capability and charge measurement, that returns to the ADC a multiplexed outputof all channels. Two ROCs are used to readout each multi-anode PMT, with a total amount of1984 chips for the whole detector. Single channel architecture comprises a low noise variable gainpreamplifier that feeds both a trigger and a charge measurement arms. The autotrigger stage hasbeen designed to be a low noise to provide very high efficiency in the detection of a minimumionizing particle (MIP). These characteristics require a 100% trigger efficiency for a signal as lowas 1/3 of a photoelectron (p.e.), which corresponds to 50 fC at the anode for a PMT gain of 106.After amplification, two copies of the input current are made available to feed both the trigger andthe charge measurement arms. For the corresponding (slow and fast shaper) timings, the noiseRMS is found at or below 1% of p.e.

The auto-trigger includes a fast shaper followed by a comparator. The trigger decision isprovided by the logical ”OR” of all 32 comparator outputs, with a threshold set at once externally.A mask register allows at this stage to disable externally any noisy or malfunctioning channel.Further details about the DAQ architecture can be found in [10].

After the assembly the module is irradiated by electrons with energy corresponding to energydeposition of the minimum ionizing particle (MIP). This way, the response of each strip to MIPsin several points is measured. Figure 5.18 is the response of a strip used in OPERA. On average,a signal equivalent to more than 6 photoelectrons is measured by each sides PMT when a MIPcrosses a strip in the middle point . Given the high quality of the plastic scintillator, an increase of


Figure 5.17: Layout of the electronics in the endcap of the module. A Front-End Card plugged tothe Hamamatsu H7546 PMT as well as the DAQ card is shown.

Figure 5.18: Response to minimum ionizing particles measured by left PMT (red points) and right(green points) for a scintillator strip used in OPERA.

the strip width seems to be very promising. With 4 cm pitch (a la MINOS) the detector cost willbe less than US$500/m2. The required position resolution will be calculated and the dependenceof the strip performance on the strip‘s width will be measured. A single-end readout, which canreduce the cost significantly, may be considered. The variation of the efficiency along the striplength in this case has to be measured. This R&D can be carried out in Dubna and Kharkov.

5.7 PMT Readout System

The PMT readout system is designed to process the output signals from the photomultiplier tubes.The main tasks of the readout electronics are:

• to determine the charge of the PMT signal that is necessary for measuring the photon energycollected by each PMT, from which the total energy of an antineutrino interaction can be

5.7. PMT READOUT SYSTEM 57

deduced.

• to measure the arrival time of the signal to the PMTs so that the event time can be determined.This piece of information can also allow us to reconstruct the location of the antineutrinointeraction in the detector to study and reject potential background events.

• to provide the energy sum of the adjacent 16 channels in real time for the trigger system toestimate the total energy of an event. The energy sum is the key component of the Level-1trigger.

5.7.1 Specifications

• Charge measurement

When a reactor antineutrino interacts in the target, its energy is eventually converted intoultra-violet or visible-light photons that some of them are transformed into photo-electronsat the photo-cathodes of the PMTs. For a given PMT, the minimum number of photo-electron (pe) is one and, based on Monte Carlo simulation, the maximum number is 50 pewhen an antineutrino interaction occurs in the vicinity of the interface of the Gd-doped liquidscintillator and the gamma catcher. For a through-going cosmic-ray muon, typically 500 pewill be recorded by each PMT. Hence the dynamic range of the PMT is up to about 500 pe.

Based on the pulse height distribution given in the Hamamatsu data sheet of R5912, theintrinsic energy resolution for a single photo-electron is about 40% when a 410 nm photon isincident on a PMT operating at 1500 V and at 25 ◦C. This intrinsic resolution varies fromPMT to PMT as well as the operating conditions of the PMT. The energy threshold of eachPMT will set at about 1/4 pe and the noise contribution from the electronics is required tobe less than 1/10 pe.

The charge measurement determined by the charge gravity method will yield the total energydeposited by a signal antineutrino or a background event. This method will also reconstructthe event vertex with a precision of several cm based on the past experience of Chooz andKamLAND.

• Time measurement

The arrival time of the signal from the PMT will be measured relative to a common stopsignal, for example, the Level-1 trigger.

The rise time of the PMT signal is about 2-3 ns and the time walk of the inherent rising edgeof the PMT signal is about 1 ns. Due to the dispersion of the signal cable, the rising edge ofthe signal at the input of the readout module will be smeared depending on the quality andthe length of the coaxial cable. The design goal for the time resolution of a single channel isabout 0.5 ns or better.

The dynamic range of the time measurement depends on the latency of the level-1 trigger andthe maximum time difference between the earliest and the latest arrival of light for a givenPMT. The range is chosen to be from 0 to 500 ns.

Since the antineutrino event is a coincidence of a prompt and a delayed sub-event, the sub-event time is a crucial parameter to be determined. This time is a weighted average of the


individual PMT time after corrections. A precision of 0.5 ns is reasonable given the factthat the coincidence window is about 100 µs. The time measurement of the individual PMTtime can also be used to determine the event vertex. Such a method is particularly suitablefor large detectors similar to KamLAND. However, for small detectors with diameters of afew meters, this measurement only provides an independent measurement in addition to thecharge-gravity method. Thus it offers a cross check of systematic errors and an additionalhandle for studying background.

5.7.2 PMT readout module

A simplied circuit diagram of the PMT readout system, showing the functionality, is given inFig. 5.19. The readout module will be 6U-VME-based. Each module will process 16 PMT signals,and each crate can handle up to 256 PMT signals, just about right for one detector module. Insuch an arrangement, movable modules can be easily realized and correlation among modules canbe minimized.

Figure 5.19: Block diagram of a readout module for processing PMT signals

The analog signal from the PMT is amplified with a fast, low noise (FET input stage) videoamplifier (AD8021). The output of the amplifier is split into two branches, one for charge measure-ment, and the other one for time measurement.

The signal for the time measurement is sent to a fast discriminator at a given threshold togenerate an output, a timing pulse, of which the leading edge defines the arrival time of the signal.A stable threshold is needed for the discrimination in order to achieve the required time resolution.A 12-bit DAC (AD7245) is selected to provide this threshold which can be set via the VMEcontroller. The TDC is realized using resources of a high-performance FPGA. The timing pulse is

5.7. PMT READOUT SYSTEM 59

sent to the TDC as the start signal. An L1 signal derived from the accepted Level 1 trigger is usedas the stop signal for the TDC.

To measure the amount of charge of the PMT signal, a ultra low-noise FET input amplifier(AD8065) is selected for the charge integrator. A passive RC differentiator is used after the inte-grator to narrow the signal for the following charge summing circuitry for all the 16 channels on thesame VME readout module. Since the singles rate of a typical channel is about 5 KHz includingnoise, a 300 ns shaping time constant is chosen. The width of the output signal of the RC2 circuitis around 1 µs. After the baseline is recovered, the analog signal is accurately digitized by FlashADCs. According to our design specification, two 10-bit FADC, one for the high gain and one forlow gain, is sufficient to cover a dynamic range of 1 to 500 PE. A low-cost 10-bit 40-MSPS FADC(AD9215) is selected. The data-processing circuitry of the FADC output is also implemented inthe same FPGA chip.

The digitized information of all the events fulfilling the trigger requirements for each channel isstored in a large buffer and is readout through the VME bus by the data acquisition system.

5.7.3 Muon-veto readout system

We plan to use the identical readout system of the central detector for processing the signals fromthe PMTs of the water Cherenkov counter.

The block diagram of the front-end readout system (FEC) for the BESIII RPC is shown inFig. 5.20. The signal from a RPC strip is digitized with a discriminator on the FEC which islocated close to the RPC. Each FEC card can process 16 RPC strips, yielding a 16-bit word whichis stored in a 16 bit shift register inside the FPGA chip. Every sixteen FEC cards form a FECDaisy Chain. When a trigger is formed, a read-enable command is generated. The data of eachdaisy chain corresponding to the trigger are transferred bit by bit through an I/O module usingdifferential LVDS signal to a readout module in a nearby VME crate. Other events without atrigger will be cleared. One VME readout module can handle 40 FEC Daisy Chains. Besidesreading and suppressing data from the FEC, the readout module also builds data fragments thatare then stored in an on-board buffer until they are readout by the DAQ computer. If the bufferis full, the readout module will issue a FULL command to the FEC’s to halt data transfer, and anRERR signal to the trigger system to inhibit further triggering.

The FEC can be tested remotely. On each FEC card there is a DAC chip which is used togenerate the test signal. When a test command goes to the test-signal generator on the systemcontrol module in the VME crate, the generator converts the command into a series of time pulsesfor controlling the DAC. In turn, the DAC sends the time pulses to the FEC through the locateI/O module. The pulse train sets the DAC chip which then delivers a signal to the input of eachdiscriminator for testing the FEC. The threshold of the discriminator is also programmable, usinga circuit identical to that for the test function.

In addition to the FEC modules and the readout boards, the readout system of the RPC includesa system control module, several I/O modules and JTAG control modules.


Figure 5.20: Block diagram of a front-end readout module for processing the RPC signals.

5.8 Trigger system

When a genuine interaction takes place inside the detector module, essentially a calorimeter, acertain amount of energy will be converted to optical photons that are detected by a good numberof PMTs. Hence, two different types of triggers can be derived to observe this interaction: en-ergy trigger and multiplicity trigger. These two triggers are complimentary, and therefore provideflexibility and redundancy. Fig. 5.21 shows a simplified possible trigger scheme.

The total-energy trigger formed on the trigger module is simply the sum of the charges from allPMT’s obtained from the front-end readout boards. The multiplicity trigger is implemented with aField Programmable Gate Arrays (FPGA) [11] which can perform complicated pattern recognitionin a very short time. The advantage of using a FPGA chip to handle trigger formation is itsflexibility. Any change of the trigger condition is only a matter of modifying the software thatcan be downloaded to the FPGA on board easily. Based on our previous experience at the PaloVerde [12] and the KamLAND experiments, this technology can provide satisfactory performancein terms of speed, reliability and complexity.

The 200 MHz FADC on the trigger module has the following functionality:

• provides a cross check of the trigger performance of the FPGA;

• measures the trigger threshold continuously without the need of taking special runs;

• measures the pulse shape that provides an additional handle for rejecting background;

• measures virtually an infinite number of hits during the DAQ dead-time providing an excellentmonitor against the multi-neutron background.

We plan to have our trigger threshold of energy less than 0.7 MeV in order to reach the off-linethreshold for physics of 0.9 MeV. At such a low energy threshold, this trigger will be dominated

5.8. TRIGGER SYSTEM 61

Figure 5.21: A simplified trigger scheme

by background originated from natural radioactivity in the environment, which is less than 50 Hzbased on Monte Carlo simulation, and the dark current of the PMT’s, each runs at about 4 kHzat 25◦C typically. Using a multiplicity threshold of about 16, the total trigger rate would be lessthan 100 Hz with a 100 ns window.

The time-correlation between simple events, such as electron antineutrino events will be recon-structed off-line. In this way we can easily measure the random correlated background and it isalways possible to have a correlated-event trigger if it is necessary due to physics interest or toohigh a background rate.

The muon veto system will have its own trigger. The presence of a muon going through theexperimental hall can be tagged with a multiplicity trigger based on the hit PMTs of the waterCherenov counter. Similarly, if scintillator strips are used to track muons, the strips can also beutilized to form a muon trigger. The muon triggers can either serve as a tag or launch a delaytrigger looking for activities inside the central detector after the passing of a muon, allowing us tostudy muon-induced background in detail. Information of the muon system along with the centraldetector will be digitized when a muon-related trigger is satisfied. The time difference between thecentral detector and the muon trigger will be recorded,

Each experimental hall will be equipped with an independent DAQ system controlled by alocal clock which is synchronized to a master clock for the entire experiment. The local clock willdetermine the event time for both the veto and the central detector. Furthermore, to minimizecorrelation among the detector modules, each central detector module will have its own triggerboard and VME crate for data acquisition.


5.9 Calibration

To determine θ13 to high precision, it is essential to understanding the performance of the an-tineutrino detector, which is a complicated system, very well. This will require employing manydifferent means to establish the gain and relative timing of the photomultiplier tubes, the energyresponse and the energy scale of each detector module. Furthermore, the stability of the detectorperformance must be monitored regularly through out the entire data-collection period.

It is a common practice to utilize three different types of calibration systems to calibrate andmonitor the behavior the detector:

1. LED system for calibrating and monitoring the stability of gain of photomultiplier tubes;

2. Laser system for timing calibration.

3. Encapsulated radioactive sources for calibrating the absolute energy scale, and the position-dependent energy response of the detector

5.9.1 LED system

The photomultiplier tubes require calibration using a stable uniform light source to establish thegain. The gain stability can also be monitored frequently using the same light source. In addi-tion, the dynamical response of the photomultiplier tubes generally necessitates an extrapolationover two orders of magnitude in light intensity, usually achieved by light injection using powerfullaser. Recently, generic ultra bright LEDs with small size are readily available. This is a cheaperalternative to the laser system.

The emission spectrum of the LED should be compatible to that of the liquid scintillator. Theintensity of the LED is controlled by driving the LED with a nominal square pulse that has anadjustable width and voltage amplitude. Light from the LED can be inject to each photomultipliertube by routing an optical fiber from a distribution system. Alternatively, light can be guided downa thin light-insulated fiber to a small translucent sphere positioned at the center of the detector.Light will then uniformly illuminate the fiducial volume of the detector.

5.9.2 Laser system

The propagation time of the photomultiplier tubes in general varies from tube to tube. Thedifference in the propagation time can be due to different cable length, or transit time. It isessential to obtain accurate relative timing of the PMT signals for precise reconstruction of thevertex position.

A laser flasher with a mixer ball is used to adjust timing and to measure charge dependence.Light pulses from the laser are injected into the light mixer ball at the detector center throughan optical fiber and the isotropic light are emitted by the mixer ball. The light is detected by allthe photomultiplier tubes. The time difference between each PMT and the reference PMT is thenmeasured. The intensity of the laser can be changed by a trigger and is monitored with a 2-inchPMT.

5.9. CALIBRATION 63

5.9.3 Radioactive sources

The absolute energy scale of the experiment can be established by calibrating the modules by aset of radioactive sources along with detailed Monte Carlo simulation. In addition, the linearityof the energy scale in the region of interest can be investigated as well. The non-linearity iscaused by Cherenkov threshold effect, quenching effect, noise hit, and inefficiency of detectingsingle photoelectrons. A combined radioactive source emitting a gamma ray and a neutron can beemployed to estimate the efficiency of detecting reactor antineutrinos since the signal topology ofthe artificial source is similar to the inverse beta decay.

The radioactive sources Ge68, Zn65 , Co60, and Am-Be will be used for energy calibration. Twogamma-rays, each with 0.511 MeV of energy, are emitted from the positron annihilation in the Ge68source. One gamma-ray of 1.116 MeV is emitted from the Zn65 source. A 1.173 MeV gamma-rayand a 1.332 MeV gamma-ray are emitted at same time from the Co60 source. The energy scaleat 7.652 MeV is calibrated by the gamma-ray emitted by the Am-Be source. The monochromaticgamma-ray with energy of 2.22 MeV coming from the muon-induced neutron captured by hydrogenin the liquid scintillator can be utilized for calibration as well. Furthermore, the 4.947 MeV gamma-ray originating from muon-induced neutron captured by carbon in the liquid scintillator will alsobe used.

The absolute efficiency of detecting a neutron can be determined by radioactive sources withtagging capability. For instance, with ≈50% branching fraction of the α+9Be reaction where the α isemitted from Am decay, the neutron emitted by an Am-Be source can be tagged by the accompany4.43 MeV gamma-ray. Another possible candidate is Cf252 which emits on average 3.77 neutronsper fission. A deadtimeless readout system will be needed to perform such calibration; however,the required precision may not be achievable.

Each radioactive source is encapsulated in a small container to prevent any potential contami-nation of the ultra-pure liquid scintillator. The assembly is kept in an extremely clean environmentthat is sealed off from radon penetration. The radioactive source will be deployed to the targetvolume and the gamma catcher in turn along different vertical axes of the detector by attaching itto a string which is lowered into the detector via a controlled motor. The position of the sourceinside detector is determined by the length of the string in the detector.

Bibliography

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[3] L. H. Miller, Ph.D thesis (unpublished), Stanford University (2000).

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[6] K. Eguchi et al. (KamLAND collaboration), Phys. Rev. Lett. 90, 021802 (2003).

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[8] J.W. Zhang et al, High Energy Phys. and Nucl. Phys., 27, 615 (2003).

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64

Chapter 6

Detector Overburden andBackgrounds

For a reactor-based θ13 experiment, minimizing background will be an important consideration insite selection and detector design. In the Daya Bay experiment, the signal events (inverse beta decayreactions) have a distinct signature of two time-ordered signals: A prompt positron signal (prompttrigger) followed by a neutron-capture signal (delayed trigger). Backgrounds can be classified intotwo categories: Correlated backgrounds and uncorrelated backgrounds. If a background eventis triggered by two signals that come from the same source, for example induced by the samecosmic muon, it is a correlated background event. On the other hand, if the two signals comefrom different sources but satisfy the trigger requirements by chance coincidence, the event is anuncorrelated background.

There are three important sources contributing backgrounds to the Daya Bay experiment: Fastneutrons, 8He/9Li, and natural radioactivity. A fast neutron produced by cosmic muons in thesurrounding rock and the detector can produce a signal mimicking the inverse beta decay reactionin the detector; the recoil proton generates the prompt signal and the capture of the thermalizedneutron provides the delayed signal. The 8He/9Li isotopes produced by cosmic muons have sub-stantial beta-neutron decay branching fractions, 16% for 8He and 49.5% for 9Li. The beta energyof the beta-neutron cascade overlaps the positron signal of neutrino events, simulating the promptsignal, and the neutron emission forms the delayed signal. Fast neutrons and 8He/9Li isotopescreate correlated backgrounds since both the prompt and delayed signals are from the same singleparent muon. Some neutrons produced by cosmic muons are captured in the detector without pro-ton recoil energy. A single neutron capture signal has some probability to fall accidentally withinthe time window of a preceding signal due to natural radioactivity in the detector, producing anaccidental background. In this case, the prompt and delayed signals are from different sources,forming an uncorrelated background.

All the three major backgrounds are related to cosmic muons whose flux cannot be easilysuppressed by detector shielding. Locating the detectors at sites with adequate overburden isthe only way to reduce the muon flux and the associated background to a tolerable level. Theoverburden requirements for the near and far sites are quite different because the signal rates differby more than a factor of 10. Supplemented with a good muon identifier outside the detector, we cantag the muons going through the detector, allowing us to study some of the backgrounds in-situ.

In this chapter, we describe our background studies and our strategies for background man-

65

66 CHAPTER 6. DETECTOR OVERBURDEN AND BACKGROUNDS

agement. We conclude that the background is known with sufficient precision such that, afterbackground subtraction, the residual error contributes to less than 0.2% of the overall error.

6.1 Overburden and muon flux

The most effective and reliable approach to minimize the backgrounds to the Daya Bay experimentis to have sufficient amount of overburden over the detectors. The Daya Bay site is particularlyattractive because it is right next to a 700-m high mountain. The overburden, which determinesthe background level, is a major factor in determining the optimal detector sites. The locationof detector sites has been optimized by using the full χ2 analysis described in Chapter 7, takinginto account the oscillation probability of different baselines, statistical errors, detector systematicerrors, reactor residual errors, and errors from background subtraction. Together with civil engi-neering considerations, the optimal far site is located at ∼ 1800 m away from the reactors and boththe Daya Bay and Ling Ao near sites are placed 500 m away from their closest reactor.

Detailed simulation of the cosmogenic background requires accurate information of the mountainprofile and rock composition. Fig. 6.1 shows the mountain profile converted from a digitized 1:5000topographic map. The 6 reactor cores, 4 running and 2 under construction, and the proposeddetector sites are shown on the plot (KL:I cannot see them). The horizontal tunnel and detectorsites are designed to be about 10 m below the sea level. Several rock samples at different locationsof the Daya Bay site were analyzed by two independent groups. The measured rock density rangesfrom 2.58 to 2.68 g/cm3. We assume a uniform rock density of 2.60 g/cm3 in the present backgroundsimulation. We are in the process of obtaining more detailed information on rock composition andterrain.

Figure 6.1: Three dimensional profile of Pei Ya Shan generated from a 1:5000 topographic map ofthe Daya Bay site.

6.1. OVERBURDEN AND MUON FLUX 67

The muon flux at sea level is well described by the Gaisser formula [2],

dIµ

dEµd cos θ= A

(Eµ

GeV

)−γ[(

1 +1.1Eµ cos θ

115GeV

)−1

+ 0.054×(

1 +1.1Eµ cos θ

850GeV

)−1]

, (6.1)

where the standard parameterization A = 0.14 and γ = 2.7 are used. Eµ is the muon energy inGeV, and θ is the zenith angle of the muon (KL: is my interpretation of theta correct?). Usingthe mountain profile data, the cosmic muons are transported from atmosphere to the undergrounddetector sites using the MUSIC package [1]. Some of the simulation results are shown in Table 6.1.In particular, the muon flux and mean energy at the near and far sites are 0.85 Hz/m2 and 55 GeV,and 0.023 Hz/m2 and 150 GeV, respectively.

Daya Bay site Ling Ao site Far siteBaseline (m) 500 500 1800Elevation (m) 116 115 462

Muon Flux (Hz/m2) 0.85 0.85 0.023Muon Mean Energy (GeV) 57.0 54.7 150.8

Table 6.1: Overburden of detector sites and corresponding muon flux and mean energy.

The muon energy spectra at the detector sites are shown in Fig. 6.2. The upper curve in red(KL: need to consider the scenario colored lines are not distinguishable in black and white copies)corresponds to near sites and the lower curve in black is for the far site.

10-7

10-6

10-5

10-4

10-3

10-2

1 10 102

103

Muon Energy (GeV)

Muo

n F

lux

(Hz/

m2 /G

eV)

Figure 6.2: Muon flux as a function of the energy of the surviving muons. The upper curve is themuon flux for the near sites and the lower curve is for the far site.


6.2 Correlated background

For the Daya Bay experiment, the most important correlated backgrounds are caused by fastneutrons induced by cosmic muons in the surrounding rock and cosmogenic radioactive isotopes8He/9Li produced in the scintillator.

6.2.1 Fast neutrons

Besides the cosmic muon flux and average energy at the site, the fast neutron background dependsalso heavily on detector shielding. Two active veto detectors are designed to tag the muons thatenter the detector modules. A 2 meter thick water buffer surrounds the main detector modules,and is viewed by PMTs to reject muons by detecting their Cherenkov light. The muon detectionefficiency of the instrumented water buffer system is expected to be greater than 95%. Outsidethe water buffer, another veto detector, constructed either with Resistive Plate Chambers (RPCs)or plastic scintillator strips, will be installed. Both the RPC and plastic scintillator systems havebetter than 90% muon detection efficiency. Combining the two veto systems, the inefficiency oftagging muons is smaller than 0.5%. Knowing the veto inefficiency is very important to estimatingthe residual background after veto rejection. These two independent active veto detectors will crosscheck each other. Thus, the veto inefficiency will be well determined. At the same time the waterbuffer serves as a passive shield to absorb neutrons induced by muons and natural radiation fromthe surrounding rock. Further passive shielding includes a 45-cm thick oil buffer to protect thescintillator from natural radiation in the PMT glass envelope and other construction materials inthe detector. The 45-cm thick gamma catcher layer of the detector, which is filled with normal(without Gadolinium) scintillator, provides additional shielding against neutrons since only neutroncapture on Gadolinium will be accepted as a valid delayed signal for a neutrino event.

With the detailed muon flux and mean energy at each detector site, the neutron yield and itsenergy spectrum can be estimated with an empirical formula [3] which has been tested againstexperimental data whenever available. Reasonable agreement has been achieved, as shown inFig. 6.3. The neutron yield as a function of the muon mean energy can be expressed as:

Nn = 4.14× 10−6E0.74µ /(muon · g/cm2). (6.2)

A full Monte Carlo simulation has been carried out to propagate the primary neutrons producedby muons in the surrounding rock and the water buffer to the detector. The primary neutrons areassociated with their parent muons in the simulation so that we know if they can be tagged by theveto detector. All neutrons produced in the water buffer will be tagged by the muon veto witha combined efficiency of 99.5%, since their parent muons must pass through the muon systems.About 30% of the neutrons produced in the surrounding rock cannot be tagged. The neutronsproduced in the rock, however, have to survive at least 2 meters of water. The background afterveto rejection is the sum of the untagged events and 0.5% of the tagged events.

Some energetic neutrons will produce tertiary particles, including neutrons. For those eventsthat have energy deposited in the liquid scintillator, quite a lot of them have a complex timestructure due to multiple neutron captures on Gd. These events are split into sub-events in 50 nstime bins. We are interested in two kinds of events. The first kind has a sub-event with thedeposited energy in the range of 1 to 8 MeV, followed by a sub-event with deposited energy in therange of 6 to 12 MeV in a time window of 1 to 200µs. These events, called fast neutron events,

6.2. CORRELATED BACKGROUND 69

Figure 6.3: Neutron yield as a function of mean muon energy. The stars indicate FLUKA simulationresults. The solid line is a fit of the simulation results to a power law. The crosses are data pointstaken from underground experiments at various depths.

can mimic the antineutrino signal as correlated backgrounds. The energy spectrum of the promptsignal of the fast neutron events at the far site is shown in Fig. 6.4 up to 50 MeV. The other kindof events has only one sub-event with deposited energy in range of 6 to 12 MeV. These events canprovide delayed signals for the uncorrelated backgrounds. We call them single neutron events. Thesimulation results are listed in Table 6.2.

near site far sitefast neutron vetoed 41.3 2.4

(/day/module) not vetoed 0.59 0.05single neutron vetoed 975 59.2(/day/module) not vetoed 19.4 1.32

Table 6.2: Neutron rates in a 20-ton module at the Daya Bay sites. The rows labeled ”vetoed”refer to the case where the parent muon track traversed the veto detectors, thus could be taggedwith 99.5% efficiency. Rows labeled ”not vetoed” refer to the case where the muon track did nottraverse the veto detectors.

6.2.2 Cosmogenic 8He/9Li

Cosmic muons, even if they are tagged by the muon identifier, can produce radioactive isotopes inthe detector scintillator which decay by emitting both a beta and a neutron (β-neutron emissionisotopes). Some of these so-called cosmogneic radioactive isotopes live long enough such that their


Figure 6.4: The prompt energy spectrum of fast neutron backgrounds at the Daya Bay far detector.The inset is an expanded view of the spectrum from 1 to 10 MeV

decay cannot be reliably associated with the last vetoed muon. Among them, 8He and 9Li withlifetimes of 0.12 s and 0.18 s, respectively, constitute the most serious correlated background sources.The production cross section of these two isotopes has been measured with muons at an energy of190 GeV at CERN [7]. Their combined cross section is σ(9Li +8 He) = (2.12 ± 0.35)µbarn. Sincetheir lifetimes are so close, it is hard to get their individual cross section. About 16% of 8He and49.5% of 9Li will decay by β-neutron emission. Using the muon flux and mean energy given in lastsection at the sites and an energy dependence of the cross section, σtot(Eµ) ∝ Eα

µ , with α = 0.73,the background-to-signal ratio (B/S) is estimated to be around 0.5% for the near sites and 0.2%the far site.

From the decay time and β-energy spectra, the contribution of 8He relative to that of 9Li wasdetermined to be less than 15% at 90% confidence level. Furthermore, the 8He contribution can beidentified by tagging the double cascade 8He →8 Li →8 Be [10]. In the following we assume thatall isotope backgrounds are from 9Li.

In the Daya Bay experiment, the isotope background can be measured in-situ, even though theaverage time interval between successive muons may be of the same order as the isotope decaytime constant. The arrival times of the muons are uniformly distributed in time. The time intervalbetween two successive muons t obeys the exponential distribution law

fµ(t) =1T

exp(−t/T ), (6.3)

where the time constant T is the mean time interval between successive muons. T = 1/Rµ,where Rµ is the muon rate. The neutrino events are also uniformly distributed in time, and areindependent of the muons. The time interval between a neutrino event and the last muon alsoobeys an exponential distribution law, with a time constant T ′ = 1/(Rµ + Rν), where Rν is theneutrino rate. Since the neutrino rate is 2 ∼ 3 orders of magnitude lower than the muon rate fora typical Daya Bay site, the difference between T ′ and T can be ignored. The production timesof 9Li are correlated with the arrival times of the muons. (KL: did I get this right?) If the muonrate is high, a 9Li is not necessarily produced by the last muon. When summed over all preceding

6.2. CORRELATED BACKGROUND 71

muons, the probability density function of the time since the last muon t is

fLi(t) =1λ

exp(−t/λ),1λ

=1τ

+1T

, (6.4)

where τ is the time constant of 9Li decay. The isotope backgrounds can be measured by fitting theobserved distribution to two exponentials, one for neutrino and the other for 9Li. Since the 9Li andthe neutrino rates are much lower than the muon rate, the probability of two neutrino-like eventsfalling into the fitting time window is negligible. It is therefore not necessary to restrict the fittingtime window to the interval between two muons. The fitting is feasible if the mean time interval oftwo neutrino-like events is much longer than the decay time constant of 9Li. However, if the muonrate is high so that T is of the order or shorter than τ , the fit will be of poor quality or even fail.

In χ2 fitting, contributions of all preceding muons are averaged and combined into the lastmuon. Maximum likelihood fitting can make use of the timing information of preceding muons,instead of using the average value. It will be useful for lower muon rate, such as at the far site. Foreach neutrino-like event, assuming it has probability B to be a 9Li or 1− B to be a neutrino, thelikelihood function can be written as

log L =∑

i

log

B

∑j

1τe−tij/τ

e−ti1/T + (1−B)1T

e−ti1/T

, (6.5)

where i sums over all neutrino-like events and j sums over all preceding muons of the i-th neutrino-like event. ti1 is the time since last muon and tij is the time since the j-th preceding muon. Inpractice, only muons in a 2-second window are summed. This cut-off results in a difference ofprobability smaller than 10−4.

To explore the fitting algorithm and its precision, we simulated the event sample of the DayaBay experiment for 3 years of running, with neutrinos, muons, and 9Li taken into account. Ata given site, the neutrino events are generated with uniform random numbers in time. The totalevent number depends on the baseline of the site and the target mass of the detector. The numberof muons are calculated according to the muon rate Rµ at the site. Muons are also generatedwith uniform random numbers in time. The number of 9Li produced by each muon is calculatedwith Poisson statistics. The 9Li yield is of the order of 10−5 per muon. If a 9Li is produced by amuon, its decay time is sampled by the exponential decay law with a time constant of 0.178 s. Thetwo independent data sets, one containing neutrino events and the other containing muon eventsand the followed(?) 9Li, are combined and sorted by time for the analysis. In the data samplegeneration, only time information is stored. The energy (of what?) is not taken into account,neither is the muon-energy dependence of the yield of 9Li.

The data sample generation and fitting were performed 100 times for each site to explore fittingbiases and precision. The fitting results of the χ2 and maximum likelihood (ML) methods areshown in Table 6.3 and Fig. 6.5. No apparent bias is found. The fitting precision is around 75%for a single 20-ton module for the near sites and 50% for the far site.

The precision of the maximum likelihood fitting can also be estimated analytically. The varianceV (= σ2

est) of a fitting parameter θ is given by [11]

V −1(θ) =

[E

(−∂2 log l(~X|θ)

∂θ2

)]θ=θ

, (6.6)


Near FarInput B/S (%) 0.5 0.2

B/S using χ2 fitting(%) 0.61±0.41 0.22±0.14B/S using ML fitting(%) 0.53±0.40 0.20±0.10

Table 6.3: Fitting results of χ2 method and maximum likelihood method.

0.2

0.4

0.6

0.8

1

1.2

10-1

1 10

ML fitting

χ2 fitting

True value

Muon rate (Hz)

B/S (%)

Far site

Near site

Figure 6.5: Fitting results for the near, mid, and far sites with 3 years of data for a single 20-tondetector module. The χ2 fitting uses the same muon rate as ML fitting but shown on the right ofit.

where l is the likelihood function of a single event, θ is the expectation of the fitting parameter θ, ~Xis the sample space, and E stands for the mathematical expectation in the sample space. Applyingthis formula to 9Li fitting, the variance of B can be written as

V −1(B) = N

∫ (1λe−t/λ − 1

T e−t/T)2

Bλ e−t/λ + 1−B

T e−t/Tdt, (6.7)

where N is total number of neutrino-like events. The theoretical estimation σest is compared withthe simulation results in Table 6.4.

Near FarN 6× 105 6.6× 104

V −1 16.2 N 0.11 Nσest 0.39 0.098σfit 0.40 0.10

Table 6.4: Comparison of theoretical estimation and simulation results.

The maximum likelihood fitting results of the Monte Carlo samples are in excellent agreementwith the analytical estimation. From Eq. 6.7, we conclude that

6.3. UNCORRELATED BACKGROUND 73

• the fitting precision is proportional to 1/√

N ,

• the fitting precision becomes worse when the average muon interval T approaches the 9Lidecay time constant τ (i.e., the muon rate is getting higher).

In conclusion, the background-to-signal ratio of isotope background can be measured to 50%precision with two 20-ton modules at the near sites of the Daya Bay experiment and 25% at thefar site with four 20-ton modules. Inclusion of energy and vertex information may further improvethe precision.

6.2.3 Other correlated backgrounds

Cosmogenic nucleons

Cosmic-ray protons and neutrons are produced from secondary interactions in the atmosphere.The flux of these particles is estimated to be 10−4m−2d−1 at 30 mwe [12, 13]. For the Daya Bayexperiment, this type of background can be safely ignored.

Stopped-muon decay and muon capture

Stopped muons contribute to the correlated backgrounds in two ways: (1) prompt muon ionizationsignal followed by muon decay, and (2) muon capture by 12C to produce 12B. The rate of untaggedmuons that decay in the detector is given by:

R = (1− ε)RµfdecayfE exp(−tv/τ), (6.8)

where Rµ is the muon rate, ε is the efficiency of the muon veto, fdecay is the fraction of muons thatstopped and decayed, fE is the fraction of the decay electrons in the range of the neutron-captureenergy (10%), τ is the muon lifetime and tv is the time window of the veto after any event. With aveto efficiency of 99.5% and 200 mwe of overburden, muon decay will contribute 0.3 events per dayfor the near detector. For the far detector the rate is reduced to <0.001 events per day. In cosmicrays 44% are muons, and 7.9% of them will be captured by 12C. About 80% of the capture willend up in unstable states that typically result in neutron emission. The background due to muoncapture is smaller than that from muon decay. While it is a non-trivial background for a detectorwith shallow overburden, backgrounds coming from stopped-muon decay and muon capture can besafely ignored in the Daya Bay experiment.

6.3 Uncorrelated background

Natural radioactivity and slow neutrons induced by cosmic muons may occur within a given timewindow accidentally to form an uncorrelated background. The coincidence rate is given by

R = RγRnτ, (6.9)

where Rγ is the rate of natural radiation, Rn is the rate of spallation neutron, and τ is the length ofthe time window. Since the geological environment and rock composition are very similar betweenHong Kong and Daya Bay, the natural radioactivity in the Daya Bay sites can be studied in HongKong. The group at Hong Kong University operates an underground lab in the Aberdeen Tunnel


Figure 6.6: Spectrum of natural radioactivity measured with a Ge crystal in the Hong KongAberdeen Tunnel.

in Hong Kong. The spectrum of the natural radioactivity of rock surrounding the lab is shown inFig. 6.6.

Past experiments suppressed uncorrelated backgrounds with a combination of using carefullyselected construction materials, self-shielding, and using absorbers that have large neutron capturecross section. However, attention still needs to be paid to lowering the detector energy thresholdto under 1 MeV, the minimum visible energy of positron annihilation. A higher threshold willintroduce a systematic error in the efficiency of detecting the positron, which is 0.8% in Chooz.Uncorrelated background can be measured by swapping detectors [14]. The precision will be

√B/S.

To achieve a background-to-signal ratio of 0.1%, the rate of natural radioactivity above the 1 MeVthreshold should be smaller than 50 Hz.

Radioactive background can come from a variety of sources:

• U/Th/K in the PMT glass.

• U/Th/K in rock around the detector hall.

• U/Th/K in the scintillator.

• U/Th/K in materials used in the detector.

• Radon in air.

• Cosmic ray.

The natural radioactivity of the glass specially made for the Hamamatsu R5912 PMT wassimulated. The singles rate of radiation from the PMT glass is 7.7 Hz with a 20 cm oil buffer (see

6.4. SUMMARY OF BACKGROUNDS 75

section 5.4.3). The radioactivity of rock at the Daya Bay site contributes 27.5 Hz to the singles rate(see also Section 5.4.3), based on the measured radioactivity of the rock sample and a full MonteCarlo simulation.

Following the design experience of Borexino and Chooz, backgrounds from impurities in thedetector materials can be reduced to the required levels. A 238U concentration of 10−12g/g willcontribute only 0.8 Hz of background in a 20 ton module.

Radon is one of the radioactive daughters of 238U, which can increase the background rate ofthe experiment. Radon concentration in the air can be kept to an acceptable level by ventilation.Based on the measured concentration of 238U in the Daya Bay rock, we can keep the concentrationof radon in the detector hall to around 200 atoms/cm3 by flushing the air twice per hour, whichcorresponds to a background rate of 15 Hz.

The β decay of long lived radioactive isotopes produced by cosmic muons in the scintillator willcontribute a couple of Hz at the near detector, and less than 0.1 Hz at the far detector. The rateof accidental coincidence induced by muon decay or muon capture is less than the muon rate. Sothey can be ignored too.

6.4 Summary of backgrounds

Assuming a 99.5% muon veto efficiency, the three major backgrounds are summarized below whilethe other sources are negligible. In our sensitivity study, the errors were taken as 100% for theaccidental and fast neutron backgrounds and 50% and 25% for the isotope backgrounds at the nearand far sites, respectively.

near site far siteNeutrino rate (/day) 560 80

Natural radiation (Hz) 45 45Single neutron (/day) 24 2

Accidental/Signal 0.04% 0.02%Fast neutron/Signal 0.14% 0.08%

8He9Li/Signal 0.5% 0.2%

Table 6.5: Summary of backgrounds.

The energy spectra of backgrounds are shown in figure 6.4. The background-to-signal ratios aretaken at far site. The oscillation signal is the difference of the energy spectra between the near siteand the far site.


0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9 10Evis (MeV)

Arbitary Units

(b)(c)

(c) Fast Neutrons (0.08%)

(d)

(d) Accidentals (0.1%)

(a)

Figure 6.7: Spectra of three major backgrounds for Daya Bay experiment and their size relative tothe oscillation signal.

Bibliography

[1] P. Antonioli et al., Astro. Phys. 7, 357 (1997).

[2] T. Gaisser, ”Cosmic Rays and Particle Physics”, Cambridge University Press, 1991.

[3] Y.F. Wang et al., Phys. Rev. D 64, 013012 (2001).

[4] M. Apollonio et al., Phys. Lett. 420B, 397 (1998); Phys. Lett. 466B, 415 (1999); Euro. Phys.J. C 27, 331 (2003).

[5] M. Ambrosio et al., (The MACRO Collaboration) Phys. Rev. D 52, 3793 (1995); M. Agli-etta et al., (LVD Collaboration) Phys. Rev. D 60, 112001 (1999); Ch. Berger et al., (FrejusCollaboration) Phys. Rev. D 40, 2163 (1989).

[6] Atomic Data and Nuclear Data Tables, Vol 78, No. 2 (July, 2001).

[7] T. Hagner et al., Astro. Phys. 14, 33 (2000).

[8] (KamLAND Collaboration) T. Araki et al.,, Phys. Rev. Lett. 94, 081801 (2005).

[9] K. S. McKinny, Ph.D thesis, Univer....

[10] Double Chooz LOI: hep-ex/0405032.

[11] John A. Rice, Mathematical Statistics and Data Analysis, second edition, Wadsworth Publish-ing Co., Inc., 1993.

[12] F. Ashton, H.J. Edwards, and G.N. Kelly, J. Physics. A 4, 352 (1971).

[13] White paper report on using nuclear reactors to search for a value of θ13, hep-ex/0402041.

[14] Y.F. Wang et al., Phys. Rev. D 62, 013012.

[15] A. Piepke et al., Nucl. Instr. and Meth. 432A, 392 (1999); F. Boehm et al., Phys. Rev. D 62,072002 (2000).

77

Chapter 7

Systematic Issues

7.1 Overview

The control of systematic errors is critical to achieving the sin2 2θ13 sensitivity goal of this ex-periment. The most relevant previous experience is the Chooz experiment [1] which obtainedsin2 2θ13 < 0.17 for ∆m2

31 = 2.0× 10−3eV2, the best limit to date, with a systematic uncertainty of2.7% and statistical uncertainty of 2.8%. In order to achieve a sin2 2θ13 sensitivity below 0.01, boththe statistical and systematic uncertainties have to be an order of magnitude smaller. The pro-jected statistical error of the Daya Bay far detector is 0.2%. In this section we discuss our strategyfor achieving the level of systematic error comparable to that of the statisitical error. Achievingthis very ambitious goal will require extreme care and substantial effort that can only be realizedby incorporating rigid constraints in the design of the experiment.

There are three main sources of systematic uncertainties: Reactor, background, and detector.Each source of error can be further classified into correlated and uncorrelated errors.

For the Chooz experiment, the systematic errors were due mostly to reactor uncertainties (2%),detector efficiency (1.5%), and the normalization of detector response which is dominated by theuncertainty in the number of free protons calculated from the hydrogen-to-carbon (H/C) ratio ofthe liquid scintillator (0.8%). The systematic uncertainties for the Chooz experiment are presentedin Table 7.2 for comparison. We will use them as reference for estimating the effects of variousimprovements in detector technique and design.

Palo Verde [2] had systematic uncertainties similar to Chooz in detection efficiency and neutrinoflux calculation. Palo Verde had additional errors related to background variations (the overburdenwas much less for Palo Verde) and trigger efficiency (due to the higher energy threshold).

In KamLAND [3], uncertainties related to the reactors and fluxes are similar but a bit largerthan those of Chooz and Palo Verde. Other major sources of uncertainty for KamLAND includethe total mass of liquid scintillator (2.1%), the fraction of liquid scintillator within the fiducialvolume (3.5%), and the level of background (1.8%). The KamLAND detector systematic errors arelisted in Table 7.2 as well.

The reduction in the systematic errors for Daya Bay relative to those of the Chooz experimentrequires special detector techniques and design features. The primary considerations that led tothe improved performance are listed below.

• The use of identical detectors at the near and far sites, a technique first proposed by Mikaelyan

78

7.2. SYSTEMATIC ERROR ESTIMATES 79

et al. for the Kr2Det experiment in 1999 [4]. The event rate in the near detector will be usedto normalize the yield in the far detector. In this approach, all correlated errors essentiallycancel in the ratio of the near and far signal rates. Uncorrelated errors related to reactorscan also be reduced to negligible level by carefully choosing the locations of the near and farsites.

• Employ detector modules with three coaxial regions to reduce detector-related errors bylowering the trigger threshold. The target volume is physically well defined by a centralregion of Gd-loaded scintillator, surrounded by an intermediate region filled with normalscintillator to catch the gammas leaking out of the central region. In this design, no positioncut is needed to determine the target volume, and the remaining errors are dominated by thephysical properties of the scintillator in the central volume. The third outer-most oil bufferregion surrounding the gamma catcher separates the PMTs from the scintillator, reducingnatural radioactivity background from the PMTs. Thus, the energy threshold of the detectorscan be lowered to < 1.0 MeV, producing essentially 100% detection efficiency for the promptpositron.

• Detector components will be measured in advance of assembly, and divided among detectormodules to equalize the properties of the modules. Differences will be distributed amongmodules between the near and far sites to help cancel residual errors.

• Ensure sufficient overburden and shielding at all detector sites to reduce cosmic muon inducedbackgrounds to a manageable level so they can be measured and subtracted out reliably.

• The use of multiple identical modules in each site enables the demonstration of systematicerror control at the limit of statistics. The detectors are movable such that each module willbe calibrated at the near site before it is moved to the far site, providing additional confidenceand reduction of some of the detector-related errors.

With these improvements, the total detector-related systematic error is expected to be 0.1 - 0.3%per detector site which is comparable to the statistical uncertainty of ∼ 0.2% at the far site.[KL:somwhere somehow we need to connect 0.3% per site with 0.5% per module if I understand thesenumbers correctly] Using a global χ2 analysis, incorporating all known systematic and statisticalerrors, we find that sin2 2θ13 can be determined to better than 0.01 precision with 90% confidence.

7.2 Systematic error estimates

7.2.1 Reactor power levels and locations

For a reactor with only one core, all errors from the reactor, correlated or uncorrelated, can becancelled precisely by using one far detector and one near detector (assuming the average distancesare precisely known) [4]. In reality, the Daya Bay Power Plant has four cores in two groups,the Daya Bay Plant and the LingAo Plant [KL: LingAo or Ling Ao? Either way, we need to beconsistent.], and another two cores installed adjacent to LingAo, called LingAo II. The two cores ofLingAo II will start to generate electricity in 2010 and 2011, respectively. Fig. 7.1 [KL: the legend”Day” in this figure should be ”Daya”. Comment applies to Figure 7.7 as well] shows the locationsof the Daya Bay cores, LingAo cores, and the future LingAo II cores. Superimposed on the figure

80 CHAPTER 7. SYSTEMATIC ISSUES

are the tunneling scheme and the proposed detector sites. The distance between the two cores ineach reactor, called a pair here, is about 88 m. The Daya Bay pair is 1100 m from the LingAo pair,and the maximum span of cores will reach 1600 m when LingAo II starts operation.

Figure 7.1: Layout of the Daya Bay experiment.

Reactor systematic errors are associated with uncertainties in the power levels of the differentcores and the effective locations of the cores relative to the detectors. Typically, the reactor cores willhave a correlated error of the order of 2% and an uncorrelated error of similar size. Optimistically,we may be able to achieve uncorrelated errors of 1%, but we conservatively assume that each reactorhas 2% uncorrelated error in the following. If the distances are precisely known, the correlated errorswill cancel in the near/far ratio. In the multiple-reactor (> 2) case one cannot cleanly measure theevent rate from each reactor. We measure the ratio in the event rates of the far and near detectors,

ρ =∑r

φr

L2rf

/∑r

φr

L2rn

, (7.1)

where Lrf and Lrn are the distances from reactor r to the far and near detectors, respectively, andφr is the antineutrino flux at unit distance from core r. The correlated errors of the reactors arecommon to both the numerator and denominator of the ratio ρ, and therefore will be cancelled.The uncorrelated errors of the reactors will partially cancel. Following the approach in [5], theresidual error in the ratio is

σρ =δρrms

ρ=

√√√√∑r

[1ρ

∂ρ

∂φrδφr

]2= σφ

√∑r

[ωr

f − ωrn

]2, (7.2)


where ωrn,f are the fractions of events from reactor r in the near and far detectors, respectively.

δρrms is the rms uncertainties in ρ, and σφ is the uncorrelated reactor error. Thus, the reduction ofthe uncorrelated errors depends on the difference in the fraction of the event rate that each reactorcontributes to the near and far detectors. If there are only two cores and for a fixed far detectorsite, there exists a line of near detector sites where the fractions of the event rate from each reactorto the near and far detectors are equal, ωr

n = ωrf . The uncorrelated errors of the reactors in this

case will cancel exactly (again assuming the distances are precisely known).A similar analysis holds for the three-detector configuration. Again, the correlated errors will

cancel exactly, whereas the uncorrelated errors will partially cancel. The reduction of the reactorsystematic error depends on the event rate fractions ωr

n,f .Assume a detector configuration shown in Fig. 7.1, with two near sites at ∼ 500 m baselines to

sample the reactor cores and the far site at an average baseline of ∼ 2000 m. For an uncorrelatederror of 2% for each core, Table 7.1 shows the estimated errors for the two detector locations forthe two cases of 4 reactor cores and 6 reactor cores.

Baseline (m) Number of cores Uncertaintynear far Power Location Total500 2000 4 0.04% 0.08% 0.07%500 2000 6 0.04% 0.06% 0.09%1000 2000 4 0.04% 0.03% 0.05%1000 2000 6 0.17% 0.03% 0.17%

Table 7.1: Reactor-related systematic errors for different reactor and detector configurations. Theuncorrelated error of a single core is assumed to be 2%.

We have also considered another two-detector configuration with the near detector site at about1000 m from the reactor cores, labeled Mid Hall in Fig. 7.1, and a far detector site at about 2000 m.By forming the ratio again as in Eq. 7.1, we find that the error in the ratio is 0.04% for 4 cores and0.17% for 6 cores, after optimizing the location of the mid detector.

The location of the reactor cores will be determined to a precision of about 30 cm. We assumethat the location errors are uncorrelated, and so their combined effect will be reduced by ∼

√Nr

where Nr is the number of reactor cores. The resulting error in the far/near event ratio is estimatedto be 0.08% for the near baseline of ∼ 500 m and 0.03% for the ∼ 1000 m near baseline.

The power level of a reactor core depends on the time after last refueling. At any given time, thereactor cores operate at different phases of their fuel cycle, as refueling is scheduled at alternatingtimes (typically 4 ∼ 6 weeks every 12 months for each core) to maintain high power output. Thus,for 4 or 6 cores, we are sampling various phases of the fuel cycle at all times so that the resultingerror from this time-dependence effect is actually negligible. The residual error in the ratio will bevery small and less significant than other errors considered here. [KL: the argument is not obviousto me.]

7.2.2 Detector-related errors

For detector-related errors, we use the Chooz and KamLAND results as benchmarks, and estimatethe corresponding values for the Daya Bay case. Some of the errors, not directly inferable from


Chooz or KamLAND, are estimated with our Monte Carlo simulation of the detector response.The results, which are discussed in detail in the rest of this section, are summarized in Table 7.2.

Source of error Chooz KamLAND Daya BayTarget H/C ratio 0.8 1.7 0.2

Mass - 2.1 0.2Positron energy 0.8 0.26 0.05Neutron energy 0.4 0.2Position cuts 0.3 3.5 0.0

Detector Time cuts 0.4 0. 0.2Efficiency H/Gd ratio 1.0 - 0.1

Neutron multiplicity 0.5 - < 0.1Trigger - 0. < 0.1Live time - 0.2 0.03

Total detector-related uncertainty 1.7% ∼ 4.4% ∼ 0.5%

Table 7.2: Comparison of detector-related systematic uncertainties of the Chooz experiment andprojections for the Daya Bay experiment. All errors are in percent per detector module.

Target Mass and H/C Ratio

The antineutrino targets are the free protons in the Gd-loaded scintillator, so the event rate inthe detector is proportional to the total mass of free protons. The systematic error in this quantityis controlled by knowing precisely the relative total mass of the central volumes of the detectormodules, as well as by filling the modules from a common batch of scintillator liquid so that theH/C ratio is the same for all modules. The uncertainty on H/C ratio will cancel out between thenear and far detectors.

The mass of the central detector will be accurately determined in several ways. First thedetector modules will be built to specified tolerance so that the volume is known to ∼ 0.1%. (Theindustrial technique we know has no problem in achieving <3 mm precision out of 4 - 5 meters.[KL:need to use consistent notation for range, a - b or a ∼ b. I chose simply ”a - b”.]) We will makemeasurements of these volumes after construction to characterize them to a precision better than0.1%. We plan to fill each module from a common stainless steel tank maintained at constanttemperature. We will measure the fluid volume using premium grade precision flowmeters witha repeatability of 0.02%. Several flowmeters will be connected in series for redundancy. Residualtopping off of the detector module to a specified level (only about 20 kg since the volume is knownand measured) is measured with the flowmeters as well. We conservatively assign an error of 0.2%on the target mass based on the absolute calibration of the flowmeters.

The absolute H/C ratio in Chooz was determined by using scintillator combustion and analysisto 0.8% precision based on results from several laboratories. We will only require that the relativemeasurement on different samples be known, so an improved precision of 0.2% or better is expected.

Energy Cut Efficiency


To reject uncorrelated backgrounds, Chooz employed a positron energy threshold of 1.3 MeV.This cut resulted in an estimated error of 0.8%. The three-zone design of the Daya Bay detectorand shielding makes it possible to lower this threshold to below 1 MeV while keeping uncorrelatedbackgrounds as low as 0.1%. The theorectical threshold of the visible energy of the neutrino eventsis 1.022 MeV, the annihilation energy of a positron at threshold with an electron at rest. Due tofinite energy resolution, the reconstructed energy will have a tail below 1 MeV. The systematicerror associated with the inefficiency of this cut was studied by Monte Carlo simulation. The tailof the simulated energy spectrum is shown in Fig. 7.2 with the full spectrum shown in the inset.For this simulation, 200 PMTs are used to measure the energy deposited in a 20-ton module. [KL:I think we are using 20 metric tons in which case we should use ”20-tonne”] The energy resolutionis ∼ 15% at 1 MeV. The inefficiencies are 0.32%, 0.37%, and 0.43% for cuts at 0.98 MeV, 1.0 MeV,and 1.02 MeV, respectively. Assuming the energy scale error is 2% at 1 MeV, this inefficiencyvariation will produce a 0.05% error in the detected antineutrino rate.

0.2 0.4 0.6 0.8 1 1.2 1.4

Arb

itra

ry U

nit

s

0

50

100

150

200

250

300

350

400

True Energy

Geant Energy

Reconstructed Energy

0 1 2 3 4 5 6 7 8 9 100

500

1000

1500

2000

2500

3000

3500

4000

Positron Energy Spectrum (MeV)

Figure 7.2: Spectra of prompt energy for true energy, simulated energy (Geant Energy), andreconstructed energy at around 1 MeV. The full spectrum is shown in the inset, where the red linecorresponds to the true energy and the black one corresponds to the reconstructed energy.

Another more important related issue is the neutron detection efficiency associated with thecapture of neutrons on Gd in the central detector volume. The capture releases several gammaswith 8 MeV total energy. Some gammas may escape from the active volume [KL: Is ”active” volumesame as ”central” volume?] of the detector, resulting in a long tail in visible energy. An energythreshold of about 6 MeV will be employed to select these delayed events, and the efficiency of thiscriterion will vary among detector modules depending upon the detailed response of the modules.The detector response can be calibrated by radioactive sources. The KamLAND detector gain isroutinely (every 2 weeks) monitored with radioactive sources, and a relative long-term gain drift of∼ 1% is readily monitored with a precision of 0.05%. According to our Monte Carlo simulations,


1% energy uncertainty at 6 MeV results in 0.2% uncertainty in the neutron detection efficiency.

Position and Time Cuts

The Daya Bay detector modules are designed such that the event rate is measured without resortto the reconstruction of the event vertex. We do not anticipate employing cuts on reconstructedposition to select events. Therefore, the error in the event rate is related to the physical propertiesof the central volume.

However, the time correlation of the prompt (positron) event and the delayed (neutron) eventis a critical aspect of the event signature. Matching the time delays of the start and stop times ofthis time window among detector modules is crucial to reducing systematic errors associated withthis aspect of the antineutrino signal.

The neutron capture time depends on the Gd content in the liquid scintillator. The Choozexperiment calibrates this with an Am-Be source at the detector center and at the bottom edge ofthe acrylic vessel. Since the neutron from the Am-Be source has slightly different kinetic energyfrom that of the neutrino signal, the efficiency related to the neutron delay cut has to rely on MonteCarlo for correction, especially for events at the edge of the vessel. Chooz employed a delay timecut 2 µs < ∆t < 100 µs; the estimated loss due to the 2 µs cut amounts to 1.6 ± 0.2%, and thefraction of neutron captures with ∆t > 100 µs is 4.7 ± 0.3%. This agrees well with the observedefficiency of 93.7± 0.4%.

10-2

10-1

50 75 100 125 150 175 200 225 250 275 300

Delay Time (µs)

Inefficiency

Delay Time (µs)

Inefficiency

10-4

10-3

10-2

0.5 1 1.5 2 2.5 3

Figure 7.3: Monte Carlo simulation of neutron capture time with 0.1% Gd concentration in liquidscintillator. The upper plot shows the inefficiency of ending time cut and the lower plot shows thesame for starting time cut.


The Monte Carlo simulation on the loss of efficiency due to cuts at the start and stop timesare shown in Fig. 7.3. With improved electronics and background shielding, a delay time cut1 µs < ∆t < 200 µs will be applied at the Daya Bay experiment. The inefficiency due to the starttime is 0.2% and that for stop time is 1.5%. Using Chooz’s calibration experience and Monte Carloextrapolation as reference, this uncertainty can be reduced to ∼ 0.2%. If all the modules show highconsistency on time constant calibration and data/MC comparison, we anticipate this error cancelout with the near/far relative measurement. Nevertheless, we adopt a conservative 0.2% error here.

H/Gd Ratio

The fraction of neutron captures on Gadolinium depends on the H/Gd ratio in the liquidscintillator. Chooz measured the time constant of neutron capture with a normal and a specialtagged 252Cf source [KL: two different souces here?]. Again, due to the different kinetic energyof neutrons from calibration sources and neutrino signal, the calibration data has to be coupledwith Monte Carlo to predict the capture efficiency which was measured to be 84.6 ± 0.85%. Thecalibration yields an error as large as 1%.

Unlike other one-detector experiments such as Chooz, the absolute neutron capture efficiencyis not important for Daya Bay experiment since we use near-far relative measurement. Only thedifference of neutron capture efficiencies between the near and far detectors will be involved in theanalysis. In principle, this error will cancel out if we use the same batch of scintillator to ensure thesame Gd concentration, and use identical modules to ensure the same edge effects. In practice, theGd concentration may not be exactly the same for different modules. Monte Carlo studies showthat 1% difference in Gd concentration (around 0.1%) will result in 0.12% difference in capturefraction. The Gd concentration can be measured to 0.5% during the liquid scintillator mixing.While other effects such as data/MC discrepancy are similar for all modules, the relative error ofneutron capture efficiency can be determined to better than 0.1% for the Daya Bay experiment.

Neutron Multiplicity

Chooz imposed a cut on the neutron multiplicity to eliminate events where it appeared thatthere were 2 neutron captures following the positron signal. These multiple-neutron events aremost likely due to muon-induced spallation neutrons, which will be reduced to a much lower levelby the increased overburden at the Daya Bay sites. For the near site at 500 m baseline, themuon rate relative to the signal rate is more than a factor of 9 lower than that of the Choozsite. Therefore, events with multiple neutron signals will be reduced by the same factor relativeto Chooz, and should present a much smaller problem for the Daya Bay near sites. For the farsite, the extra overburden reduces the rate by about an additional order of magnitude, making thiseffect negligible.

Trigger

The trigger efficiency will be measured using pulsed light sources in the detector. KamLANDused this method to achieve 0.02% absolute trigger efficiency [3]. We expect to be able to measurethe trigger efficiency of each detector system to the same precision.


Live Time

With a detailed background simulation, the muon rate is predicted to be ∼ 280 Hz at the nearsites and ∼ 7 Hz at the far site. The muon rate here includes muons passing water shielding, and isthus much higher than that passing only the main detector modules. Neutrons produced by cosmicmuons in rocks, water, and the main detector modules will be vetoed for 200 µs, which correspondsto 5.6% dead time and 0.1% neutron veto inefficiency at the near detector. The pulse shaping andtrigger decision electronics will take 0.5 ∼ 1 µs for an event. The uncertainty on event time will bearound 1 µs, corresponding to 0.028% live time uncertainty.

7.2.3 Background

Backgrounds can be classified into two categories: Correlated and uncorrelated backgrounds. Areactor neutrino signal consists of two characteristic sub-events, the prompt positron signal and thedelayed neutron-capture signal. If the prompt and delayed signals of a background event come fromthe same source, it is a correlated background event. On the other hand, if the two signals comefrom different sources but fall into the time window accidentally, it is an uncorrelated backgroundevent. In general, the correlated backgrounds are induced by cosmic muons. The most importantcontributions are from fast neutrons and 8He/9Li isotopes. The major uncorrelated backgroundcomes from the coincidence of natural radiation gammas and single capture of neutrons induced bycosmic muons. The backgrounds are discussed in detail in the previous chapter. The three majorbackgrounds are summarized below while the other sources are negligible.

near site far siteNeutrino rate (/day) 560 80

Natural Radiation (Hz) 45.3 45.3Single neutron (/day) 24 2

Accidental/Signal 0.04% 0.02%Fast neutron/Signal 0.14% 0.08%

8He9Li/Signal 0.5% 0.2%

Table 7.3: Summary of backgrounds.

All these three backgrounds are related to cosmic muons. While the rate and energy spectrumof surviving muons at the detector sites can be simulated and measured at high precision, theirinteractions with rocks, water, and detector materials are not as well understood as neutrino re-actions in the detector. To be conservative, we assume that the above estimation carries 100%uncertainty in the absence of further constraints from on-site measurement.

The background is dominated by cosmogenic 8He/9Li isotopes produced by muons in the de-tector. At the near site with around 300 mwe overburden, the muon rate in the detector will be∼ 9 Hz. It is hard to measure the 9Li/8He spallation product background because the half-lives ofthese nuclei are 0.178 s and 0.122 s, respectively, comparable to the average time between successivemuons. Thus, we assign a 100% uncertainty in the calculated rate of producing these nuclei at thenear site, or 0.5% in terms of the relative error of the neutrino signal. For the deeper mid site at ∼1000 m baseline, the ∼ 600 mwe overburden is sufficient to reduce the muon rates to < 1 Hz, and

7.3. χ2 ANALYSIS 87

one can study the time distribution of candidate events relative to the time of the most recent muon.This study will reveal the lifetime of the spallation product, and allow a better determination ofthis background. A Monte Carlo simulation shows that we can measure the isotope contribution toa precision of 25%. We thus obtained a smaller uncertainty (relative to the reactor signal) of lessthan 0.1%. For the far site with an overburden of 1200 mwe, the muon rate is reduced to ∼ 0.2 Hzin the detector. The relative error of the isotope backgrounds can also be determined to < 0.1%.

Accidental coincidences of neutron captures (neutrons due to cosmic ray interactions in thesurrounding rock) with radioactivity signals (from PMT’s, stainless steel, surrounding rock, etc.)will occur at a rate < 0.1% of the reactor signal at each site. This uncorrelated backgroundwill be well determined by combining singles events in windows of various delay. We estimateda fractional error relative to the reactor signal of less than 0.04% for the determination of theaccidental background.

In addition to the rate, the knowledge on the energy spectra of various backgrounds will helpimprove the physics sensitivity of the experiment. The prompt signal of the isotope backgroundcomes from the electron of the beta-neutron cascade in the 8He/9Li decay. Its energy spectrumcan be calculated accurately. With two independent veto systems, the muon tagging efficiencywill be as high as 99.5%. Most fast neutron events can be identified with a muon tag, and theirenergy spectrum will be well measured. Based on our Monte Carlo simulation, the statistics ofthe tagged fast neutron events is 50 times higher than that of untagged fast neutrons. Althoughthe energy spectrum of untagged fast neutrons may be different from that of tagged ones, wewill be able to determine it to very good precision with the help of Monte Carlo extrapolation.The energy spectrum of natural radiations can be measured by sampling singles events as well.As a consequence, the energy spectra of all three major backgrounds can be either calculated ormeasured to high precision. The uncertainties of the spectra are negligible, compared with thestatistical error of the neutrino signal.

7.3 χ2 analysis

If θ13 is non-zero, a rate deficit will be present at the far detector due to oscillation. At the sametime, the energy spectra of neutrino events at the near and far detectors will be different becauseneutrinos of different energies oscillate at different frequencies. Both rate deficit and spectraldistortion of neutrino signal will be explored in the final analysis to obtain maximum sensitivity.When the neutrino event statistics is low, say < 400 ton·GW·y, the sensitivity is dominated by ratedeficit. For luminosities higher than 8000 ton·GW·y, the sensitivity is dominated by the spectraldistortion [11]. The Daya Bay experiment will have ∼ 3000 ton·GW·y exposure in three years,where both rate deficit and shape distortion will be important to the analysis.

The neutrino rate and energy spectrum without oscillation effect can be predicted with realtime reactor power data and burn-up calculations [1, 6, 7, 8]. Present uncertainty on the neutrinoflux includes ∼ 2% correlated error and ∼ 2% uncorrelated error. The predicted neutrino energyspectra also carry a 2% shape error. The near-far relative measurement will eliminate the bulkof these errors. The near detector which has large statistics will provide more accurate neutrinoflux and spectrum data than calculations from reactor power. In other words, a combined fit ofcalculations from reactor, measurement at near detector(s), and measurement at far detector willover-constrain the neutrino flux and spectrum.


Ignoring all systematic errors, the standard χ2 function can be written as

χ2 =3∑

A=1

Nbins∑i=1

[MA

i − TAi

]2(σA

i )2=

3∑A=1

Nbins∑i=1

[MA

i − TAi

]2TA

i

, (7.3)

where A sums over three detectors (two near and one far), and i sums over energy bins of theneutrino energy spectrum. MA

i is data in the i−th energy bin at detector A, and TAi is the

corresponding value predicted from reactor running information. The standard deviation (SD) ofthe statistical fluctuations in each bin is

σAi =

√TA

i . (7.4)

The χ2 function is minimized to find the best values for ∆m231 and sin2 2θ13 whose effects are

included in the fit via expected values TAi . The best fit χ2 is labeled χ2

best. The 90% confidenceregion can be obtained by finding the area in the sensitivity plane with ∆χ2 = χ2 − χ2

best < 4.61.If only sin2 2θ13 is of interest, a 90% confidence region can be constructed by finding the area with∆χ2 < 2.71 for any given ∆m2. We will adopt the single parameter fit in the following text. [KL:I don’t understand the origin of the numbers: 4.61 and 2.71. Also, how come they don’t dependon the degrees of freedom in the chisq function. Unless the number of bins is fixed, in which caseit should be specified in the text.]

Tens of systematic errors contribute to the final sensitivity of the Daya Bay experiment. Cor-relations of the errors are complicated and must be taken into account. A rigorous analysis onsystematic errors can be done by constructing a χ2 function with error correlations introducednaturally [9, 10, 11, 12]:

χ2 = minγ

3∑A=1

Nbins∑i=1

[MA

i − TAi

(1 + αc +

∑r ωA

r αr + βi + εD + εAd

)− ηA

f FAi − ηA

n NAi − ηA

s SAi

]2TA

i

+α2

c

σ2c

+∑r

α2r

σ2r

+Nbins∑i=1

β2i

σ2shp

+ε2D

σ2D

+3∑

A=1

(εAd

σd

)2

+

(ηA

f

σAf

)2

+

(ηA

n

σAn

)2

+

(ηA

s

σAs

)2 , (7.5)

where γ denotes the set of parameters {αc, αr, βi, εD, εAd , ηA

f , ηAn , ηA

s } whose systematic errors areincorporated. The SDs of the corresponding parameters are {σc, σr, σshp, σD, σd, σ

Af , σA

n , σAs }. For

each point in the oscillation space, the χ2 function has to be minimized with respect to the param-eters γ. [KL: there are a lot of undefined symbols. For example: σu is not defined. σu = σr??, theη are never defined; I am sure they are the background fractions. Neither is β which are bin-by-binentries,.... I think it is better to use a different symbol instead of the over-used α to denote all thevariable. I used γ . Again, the number of degrees of freedom is not shown anywhere- this may notbe important because we are only interested in the point of minimization.]

Assuming each error can be approximated by a Gaussian, this form of χ2 can be proven tobe strictly equivalent to the more familiar covariance matrix form χ2 = (M − T )T V −1(M − T )[9], where V is the covariance matrix of (M − T ) with systematic errors included properly. Thesystematic errors are described one by one in the following.

Reactor-related correlated error: σc

7.3. χ2 ANALYSIS 89

Reactor-related correlated error accounts for normalization errors of the event rate common toall reactor cores, such as energy released per fission and neutrino yield per fission. With near-farrelative measurement, fully correlated error has almost no impact on the sensitivity. Nevertheless,we use σc = 2% in the sensitivity analysis.

Reactor-related uncorrelated error: σr

Reactor-related uncorrelated error is the normalization error of the event rate which variesindependently from core to core, such as reactor power and related burn-up calculation. It isdiscussed in section 7.2.1; this error does not exactly cancel out by near-far relative measurementfor a complex core layout such as Daya Bay. We take the uncorrelated error of a single core to beσr = 2% while we believe 1% could be reached. ωA

r is the event fraction contribution from core r todetector A, with the constraint

∑r ωA

r = 1 for each detector. Error reduction will be automaticallyrealized with the minimization of αr. For well chosen sites, the residual error could be as low as0.04% (see Table 7.1), and thus has very little impact. For poorly chosen sites or one near detectorscenario, the residual error might have large impact.

Shape error: σshp

Shape error is the uncertainty on neutrino energy spectra calculated from reactor information,σshp ∼ 2%. This error is uncorrelated between different energy bins but correlated between differentdetectors. Since we have enough statistics at near detector to measure neutrino energy spectrum tomuch better than 2%, in addition to this calculation, it has little impact for Daya Bay sensitivity.

Detector-related correlated error: σD

Some detection errors are common to all detectors, such as H/Gd ratio, H/C ratio, neutroncapture time on Gd, and edge effect, assuming we use the same batch of liquid scintillator andidentical detectors. Based on Chooz’s experience, σD is 1 to 2%. Like other fully correlated errors,it has almost no impact on sensitivity.

Detector-related uncorrelated error: σd

Detector-related uncorrelated errors include the mass of active volume, live time, etc., whichdo cancel out with near-far measurement. It is described in section 7.2.2, and estimated to beσd = 0.5% for a single detector module.

Background-related error: σAf , σA

n , and σAs

There are three kinds of major backgrounds in the Daya Bay experiment: Fast neutrons FAi ,

isotopes SAi , and accidental backgrounds NA

i . As described above, their spectra can be eithercalculated or measured to a very good precision, compared with the neutrino oscillation signal.As a consequence, the bin-to-bin uncertainties due to background subtraction, which should beuncorrelated between energy bins and different sites, can be ignored. While we know the spectralshape of each individual background, the rate has a large uncertainty. Our Monte Carlo simulation


shows that the rate of fast neutrons FA =∑

i FAi is 0.14% of the neutrino signal (TA =

∑i T

Ai )

at the near sites (A=1,2) and 0.08% of the signal at the far site (A=3). The rate of isotopesSA =

∑i S

Ai is 0.5% of TA at the near sites and 0.2% of TA at the far site. The rate of accidental

backgrounds NA =∑

i NAi is 0.04% of TA at the near sites and 0.02% of TA at the far site. To be

conservative, we assume these estimates carry 100% uncertainty, i.e., σAf = σA

n = σAs = 100%.

Other errors:

The energy resolution of the detector is ∼ 14%/√

E(MeV), which is 5% at 8 MeV or 14% at1 MeV. Due to energy smearing, the spectra are distorted. However, the energy bins used forsensitivity analysis (∼ 30 bins) is 2 ∼ 6 times larger than the energy resolution, and the distortionhappens at all detectors in the same way, energy resolution has almost no impact on the finalsensitivity.

Detector energy scale error has significant impact on detection errors (neutron efficiency andpositron efficiency). It is taken into account in σd. At the same time, an energy scale error willshift the whole spectrum, thus directly impacting the analysis, especially on the best fit values.However, this shift is not a distortion, and cannot mimic oscillation. It is has very little impact onsensitivity computations.

Current knowledge on θ12 and ∆m21 has around 10% errors. Although the net oscillation effectat Daya Bay baseline is related to θ13 only, the deduction(?) of θ12 oscillation effects might bringerrors.

We have studied the above three error sources and found none of them having visible impacton the sensitivity of the Daya Bay experiment. For simplicity, they are ignored in our χ2 analysisof sensitivity.

There may be other unexpected errors at the level of a few per mil since our experience is onlyfrom measurements at the 3% level. For instance, neutrinos from spent fuel, during or near byfuel recycle period, or other man-made neutrino sources such as nuclear-powered submarines mayaffect our results. Unexpected efficiency variation could also occur at the level of 0.1%. Thereforeredundancy is a must for such a precision experiment. This issue will be discussed further in thenext section.

7.4 Side-by-side calibration and detector swapping

[KL: It may be better to do without the chisq equations (equations 7.6 and 7.7) here. The argumentwith the equations is too subtle to follow. It is perhaps better just to state what we plan to dowith swapping and the arguments (verbal) behind it and what the expected outcomes are] Thesensitivity of the Daya Bay experiment largely depends on detector uncorrelated error (relativedetection efficiency error). With improved design, the detector systematic error could be lowered to∼ 0.5%, based on Chooz’s experience. Nevertheless, it is a challenge to the detector fabrication andoperation. Furthermore, the detection error is a combination of many sources. Their correlationsare not easy to work out. How to combine them may be controversial. Side-by-side calibration ofdetectors can clarify this uncertainty.

If we put two detectors at the same site for the same period of time, the backgrounds andneutrino flux will be identical for them. The only difference is their detection efficiency. Nomatter what the origins of the systematic errors are, the detection efficiency can be corrected to

7.4. SIDE-BY-SIDE CALIBRATION AND DETECTOR SWAPPING 91

the same level, up to the precision of statistics. For a 20-ton detector module at 500 m awayfrom two 2.9 GW reactor cores, the statistical error is 0.3% with one year’s data (300 days) and75% detection efficiency. The relative detection efficiency error could then be determined within√

2× 0.3% = 0.42% in a year. That will be a straightforward check of detector systematics.One advantage of the horizontal tunnel of the Daya Bay experiment is the ability to move the

detector modules conveniently. Swapping detectors between the near and far sites will eliminatedetection efficiency errors and greatly improve the physics sensitivity. Suppose a flux deficit isobserved at the far site, it may be attributed to neutrino oscillation, or it may be due to lowerdetection efficiency at the far site compared with the near site. Then we swap the detectors at thenear and far sites. If the deficit is due to detection efficiency, we should observe a flux surplus at thefar site, compared with the near detector which has a lower detection efficiency. If the previouslyobserved flux deficit is due to oscillation, we should again observe deficit at far site.

To understand how detection efficiency error cancels out with detector swapping, we considera scenario with one reactor, one near detector, and one far detector. The χ2 function is simplifiedto having only two errors, the reactor error σr and detector uncorrelated error σd:

χ2 =[OA

n − TAn (1 + εd1 + αA

r )]2

TAn

+[OA

f − TAf (1 + εd2 + αA

r )]2

TAf

+[OB

n − TBn (1 + εd2 + αB

r )]2

TBn

+[OB

f − TBf (1 + εd1 + αB

r )]2

TBf

+(

εd1

σd

)2

+(

εd2

σd

)2

+

(αA

r

σr

)2

+

(αB

r

σr

)2

. (7.6)

The first line in the equation corresponds to data taking period A when detector 1 sits at the nearsite and detector 2 at the far site. Their detection efficiencies are εd1 and εd2, respectively. Thesecond line corresponds to data taking period B, when the two detectors are swapped. The neutrinoflux for the two periods might be different, within σr ∼ 3%. If we take equal volumes of data fortwo time periods, Eq. 7.6 can be rewritten equivalently as

χ2 =

[2On − 2Tn

(1 + εd1+εd2

2 + αAr +αB

r2

)]22Tn

+

[2Of − 2Tf

(1 + εd1+εd2

2 + αAr +αB

r2

)]22Tf

+(

εd1

σd

)2

+(

εd2

σd

)2

+

(αA

r

σr

)2

+

(αB

r

σr

)2

. (7.7)

The combination of the detection efficiency errors (εd1 + εd2)/2 is fully correlated between the nearand far site measurements, thus has almost no impact on sensitivity. Equivalently, the measurementcan be treated as two effective detectors with exactly identical detection efficiencies.

If the data volumes are not equal, then part of the detector error cannot be cancelled out. For apressurized water reactor, the average up-time is around 80% to 85%. The idle time is normally dueto shutdown for refuelling and maintenance which takes 4∼6 weeks every 12 months. The two coresin a cluster will be shutdowned in turn. It is possible that one data taking period has ∼ 10% moredata than another. Although the detector error cannot be cancelled out exactly, the residual errorcaused by different data volume will be an order of magnitude lower than that without swapping.The impact on sensitivity is much smaller.


A prerequisite for successful swapping is that the detection efficiency of a detector is keptunchanged before and after moving. One possible source of efficiency variation is the energy scale.To monitor liquid scintillator aging and other time dependent effects of detectors, the energycalibration is performed from time to time. The energy scale is not necessarily the same aftermoving. The precision of energy calibration can be as accurate as 0.5 to 1%. The correspondingneutron efficiency error will be 0.1 to 0.2% from our detector simulation. So we assume the residualdetection efficiency error is 0.1 to 0.2% with swapping measurement.

Moving a detector of total weight of 100 tonnes for 2 km may cause unknown variations ofdetection efficiency. This could be fatal for such a precision experiment if we cannot discover theproblem early and solve it. Side-by-side calibration enables us to get full control of the systemat-ics by monitoring detectors at the same site continuously. Variation of detection efficiency afterdetector swapping can be identified up to the precision of statistics.

7.5 Baseline optimization

Taking the best fit value of ∆m231 = 2.0 × 10−3 eV2, the maximum of reactor neutrino oscillation

appears at around 2200 m, shown in Fig. 2.7. The oscillation probability is ∼ 0.8× sin2 2θ13, afterintegrating over the observed neutrino energy spectrum. The oscillation probability is the mostimportant parameter on baseline optimization. Considerations based on statistics alone will resultin a shorter baseline, especially when statistical error is larger or comparable to the systematicerror. For the Daya Bay experiment, overburden should also be taken into account since theoverburden varies along the baseline. Fig. 7.4 shows the sin2 2θ13 sensitivity limit versus baselineusing χ2 sensitivity analysis (see Eq. 7.5), for three ∆m2

31 values which cover 90% confidence level(C.L.) of the current best fit value. The statistical error is calculated based on three years of datataking, which is around 0.2%. The best sensitivity for the oscillation signal occurs at 2200 m for∆m2

31 = 2.0 × 10−3 eV2. The sensitivity varies slowly at baselines from 1800 to 2200 m. Tunnellength is another concern. We prefer a shorter tunnel to save civil construction cost while preservingthe best physics sensitivity. Thus, the optimal baseline of far detector ranges from 1800 to 2200 m.

Three major factors are involved in the near site determination. The first one is overburden.The slope of the mountains near the cores is around 30 degrees. When we put the detector site closerto the cores, the overburden will be significantly reduced. A possible solution is to construct thetunnel with downward slope to gain additional overburden. The second concern is oscillation loss.The oscillation probability is appreciable even in the near sites. For example, for near detectorsplaced at around 400 m away from the center of gravity of the cores, the integrated oscillationprobability is 0.12× sin2 2θ13 at the Daya Bay detector and 0.15× sin2 2θ13 at the LingAo detector,both computed with ∆m2

31 = 2.0× 10−3 eV2. The oscillation probability at the Daya Bay detectoris higher because there are more events from another cluster of cores at the far side [KL: thequoted numbers say otherwise]. The third concern is the near-far cancellation of reactor errors. Asshown in the previous section, the cancellation is not exact if detectors are too close to the reactorcomplex. Sensitivity analyses combining all the three factors show that the best sensitivity will beobtained with the near detectors located roughly on the perpendicular bisector of the nearby coresand about 400 ∼ 500 m away from the middle point.

7.6. SENSITIVITY RESULTS 93

0.008

0.01

0.012

0.014

0.016

0.018

0.02

1500 2000 2500 3000

∆m2= 1.3×10-3eV2

∆m2= 2.0×10-3eV2

∆m2= 3.0×10-3eV2

Baseline (m)

sin2 2θ

13 S

ensi

tivi

ty

Figure 7.4: sin2 2θ13 sensitivity limit versus baseline for three ∆m231 values.

7.6 Sensitivity results

Fig. 7.5 shows the sensitivity contours in the sin2 2θ13 versus ∆m231 plane for three years of data,

using combined analysis. The green area covers the 90% confidence region of ∆m231 determined

by solar neutrino experiments. Taking a design with four 20-ton modules at the far site and two20-ton modules at each near site, the statistical error is around 0.2%. The systematic errors usedhere are described in section 7.3, except the detector-related uncorrelated error σd, which is takento be 0.2% with near-far swapping measurement, as described in section 7.4. The sensitivity of theDaya Bay experiment with this design can achieve the challenging goal of 0.01 with 90% confidencelevel in almost the whole range of ∆m2

31.Fig. 7.6 shows the sensitivity versus time of data taking. After one year of data taking, sin2 2θ13

sensitivity will reach 0.014 (1.4%) at 90% confidence level.The tunnel of the Daya Bay experiment will have a total length around 3 km. The tunnelling

will take 1 ∼ 2 years. To accelerate the experiment, the first completed experimental hall, the DayaBay near hall, can be used for detector commissioning. Furthermore, it is possible to conduct a fastexperiment with only two detector sites, the Daya Bay near site and the mid site. The layout ofthe experiment is shown in Fig. 7.7. For this fast experiment, the ”far detector”, which is locatedat the mid hall, is not at the optimal baseline. At the same time, the reactor-related error would be0.7%, very large compared with that of the full experiment. However, the sensitivity is still betterthan the current best limit of sin2 2θ13. It is noteworthy that the improvement comes from betterbackground shielding and improved experiment design. The sensitivity of the fast experiment forone year and three years of data taking is shown in Fig. 7.8. With one year’s data, the sensitivityis around 0.04 (4%) for ∆m2 = 2.0× 10−3 eV2, compared with the current best limit of 0.17 fromthe Chooz experiment.


0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

10-2

10-1

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Chooz

Daya Bay

sin22θ13

∆m2 (×

10-3

eV2 )

Figure 7.5: Expected sin2 2θ13 sensitivity at 90%C.L. with 3 years of data.

0

0.01

0.02

0.03

0.04

0.05

0 1 2 3 4 5

Year si

n2 2θ13

Figure 7.6: Expected sin2 2θ13 sensitivity at 90%C.L. versus year of data taking, with ∆m2 =2.0× 10−3 eV2.

Figure 7.7: Fast measurement layout of theDaya Bay experiment.

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

10-2

10-1

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Chooz

Daya Bay 1y

Daya Bay 3y

sin22θ13

∆m2(

×10-3eV2)

Figure 7.8: Expected sin2 2θ13 sensitivity at 90% C.L.of fast experiment with only two sites.

Bibliography

[1] M. Apollonio et al., Phys. Lett. B420, 397 (1998); Phys. Lett. B466, 415 (1999); Eur. Phys.J. C27, 331 (2003).

[2] F. Boehm et al., Phys. Rev. D 64, 112001 (2001); Phys. Rev. D 62, 072002 (2000); Phys. Rev.D 62, 092005 (2000).

[3] K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003).

[4] L. A. Mikaelyan and V. V. Sinev, Phys. Atom. Nucl. 63, 1002 (2000); L. Mikaelyan, Nucl.Phys. Proc. Suppl. 91, 120 (2001); L. A. Mikaelyan, Phys. Atom. Nucl. 65, 1173 (2002).

[5] F. Suekane, The systematic error induced from the baseline differences in Kashiwazaki-Kariwasin2 2θ13 experiment: A conceptual description (unpublished).

[6] H. Kwon et al.,, Phys. Rev. D 24, 1097 (1981).

[7] Y. Declais et al., Phys. Lett.B338, 383 (1994). B. Ackar et al., Nucl. Phys. B434, 503 (1995);B. Ackar et al., Phys. Lett. B374, 243 (1996).

[8] K. Schreckenbach et al., Phys. Lett. B160, 325 (1985); A. A. Hahn et al., Phys. Lett. B218,365 (1989).

[9] D. Stump et al., Phys. Rev. D 65, 014012 (2001).

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95

Chapter 8

Other Physics Reaches

In addition to the major goal of measuring θ13, the Daya Bay experiments can also contribute toseveral other related topics that are critical to our understanding of the neutrino sector. We discussthem below.

8.1 Sterile neutrinos

Recent short-baseline neutrino data suggests the existence of one or more sterile neutrinos in ad-dition to the three active neutrinos of the standard model. The Liquid Scintillator Neutrino De-tector (LSND) [1] studied νµ coming from the decay µ+ → e+νeνµ of positive muons at rest.LSND reported an excess of νe events above background that indicated a transition probability ofP (νµ → νe) = (2.64±0.67±0.45)×10−3, and requires a ∆m2 = 0.1 ∼ 0.2 eV2 not consistent with thesolar or atmospheric neutrino results. Later the KARMEN experiment [2], at a somewhat shorterbaseline, found no evidence for such a transition. However, a combined analysis of the two experi-ments using a simple two-neutrino oscillation model found allowed regions in ∆m2 − sin2 2θ spaceconsistent with both experiments. Reactor experiments can provide additional information. TheBugey reactor antineutrino experiment [3] measuring P (νe → νe) survival placed limits on sin2 2θfor ∆m2 > 0.01 eV2. Oscillation parameters in the two regions defined by 0.2 ≤ ∆m2 ≤ 1 eV2 and0.003 ≤ sin2 2θ ≤ 0.03, and ∆m2 ' 7 eV2 and sin2 2θ = 0.004, could explain the results of all threeshort-baseline experiments in the two-neutrino (active-sterile) picture. Since the ∆m2 scale of theseoscillations would be much larger than the scale needed for solar and atmospheric oscillations, theaddition of a fourth light neutrino is required; this extra neutrino must be sterile since it does notcontribute to the invisible width of the Z boson. The existence of more than one sterile neutrinosare also possible.

Four neutrino models that can simultaneously explain the solar, atmospheric and LSND datafall into two categories:

(i) 2+2 models, where the two mass eigenstates that provide the solar mass-squared splittingand the two states that provide the atmospheric splitting are separated from each other bythe much larger LSND mass-squared scale, or

(ii) (3+1) models, where the fourth, sterile neutrino is separated from the active neutrinos bythe LSND mass-squared scale and has small mixings with the active neutrinos, and the ac-

96

8.1. STERILE NEUTRINOS 97

tive neutrino mass-squared splittings are approximately those of the standard three-neutrinomodel that describes the solar and atmospheric data.

Originally the 2+2 models were thought to provide a better fit to all neutrino data but limitson oscillations to sterile neutrinos in both the solar and atmospheric sector strongly disfavor 2+2models [4]. The (3+1) models are also disfavored [4] (although less so) because the amplitude ofthe LSND oscillation is 4|Ue4|2|Uµ4|2, where Ue4 and Uµ4 are the mixings of the νe and νµ with thefourth mass eigenstate, and Ue4 and Uµ4 are constrained by the Bugey reactor and CDHSW [5]accelerator experiments, respectively.

Extensions of the four-neutrino models can provide better fits to the short-baseline data. Thetwo currently recognized possibilities are:

(i) 3+2 models, where a second sterile neutrino is added to the (3+1) model. The secondsterile also has a large mass splitting from the active neutrinos. 3+2 models are allowed atapproximately the 1σ level [7].

(ii) Four-neutrino models with CPT violation. If the masses and mixing angles of neutrinosand antineutrinos are different (CPT violation), then some of the bounds on four-neutrinomodels are relaxed. A (3+1) model with CPT violation, or models with (3+1) structure inthe neutrino sector and (2+2) structure in the antineutrino sector, are consistent with theshort-baseline data [8].

Improved short-baseline limits which would place more constraints on the existing models aredesirable.

The Daya Bay reactor experiment measures νe survival, which in a (3+1) model has oscillationprobability in the leading oscillation of

P (νe → νe) ' 1− 4|Ue4|2(1− |Ue4|2) sin2 ∆41 , (8.1)

where ∆41 = 1.27∆m241(eV

2)L(m)/Eν(MeV). This is the same probability constrained by theBugey reactor experiment. For a near detector with L ∼ 300 − 500 m and for Eν ∼ 3.8 MeV(the value at the peak of the spectrum), ∆41 ' 100 − 170 for ∆m2

41 ' 1 eV2. Therefore theoscillations due to the fourth mass eigenstate are very rapid, the oscillating factor sin2 ∆41 will beclose to its average value of 0.5, and the measured probability in the near detectors will not differsubstantially from that in the far detector. Even for ∆m2

41 ' 0.2 eV2 (the low end of the LSNDregion), ∆41 ' 20 − 30 and an energy spread as little as 10% (due to bin width or finite energyresolution) could average away the oscillations of the sin2 ∆41 term.

If the fast oscillations due to ∆m241 cannot be resolved, the oscillations can only be inferred from

the overall suppression of the rate in both the near and far detectors; this requires good knowledgeof the rate normalization. The rate normalization uncertainties can be divided into two categories:correlated between detectors (such as the neutrino cross section and neutrino flux) and uncorrelatedbetween detectors (such as the detector fiducial mass). For the sterile analysis we assume a 2.0%correlated error and a 0.25 uncorrelated error. Representative expected limits on 4|Ue4|2(1− |Ue4|2from Daya Bay are shown in Fig. 8.1, along with the existing limits from Bugey. A null result inDaya Bay would provide a substantial improvement over the Bugey limit for ∆m2

41 < 0.5 eV2 and∆m2

41 > 2 eV2.

98 CHAPTER 8. OTHER PHYSICS REACHES

Figure 8.1: Expected 90% C.L. limit on4|Ue4|2(1 − |U34|2) from the Daya Bay reactorexperiment, shown versus ∆m2

41 (solid curve),for 20 t near detectors at 300 m from each re-actor cluster and a 40 t far detector 2.0 km fromeach reactor cluster. The current bound fromthe Bugey reactor experiment [3] is also shown(dashed curve).

Figure 8.2: The dashed curve shows the com-bined constraint on 4|Ue4|2|Uµ4|2 versus ∆m2

41

in 3+1 models using the 90% C.L. constraintson |Ue4| (from Bugey [3]) and Uµ4| (fromCDHSW [5]). The dotted curves show the re-gions allowed at 90% C.L. in a combined analy-sis of LSND and KARMEN data [6]. The solidcurve shows the expected bound when the ex-pected 90% C.L. sensitivity of the Daya Bay re-actor experiment is combined with the CDHSWbound.

When combined with the CDHSW bound on |Uµ4|, the Daya Bay limit on |Ue4| would tighten thebound on the LSND oscillation amplitude 4|Ue4|2|Uµ4|2, especially for values of ∆m2

41 below 0.5 eV2

and above 2 eV2 (see Fig. 8.2). Improvements over the Bugey bound for 0.5 < ∆m241 < 2 eV2 are

not as dramatic, but could further disfavor the remaining LSND region. A null result at Daya Bay,when combined with the CDHSW constraints on νµ → νµ oscillations, would also strengthen theconstraints on (3+2) models.

8.2 Supernova Neutrinos and Supernova Watch

One of the most spectacular cosmic events is a supernova (SN) explosion that ends the existence ofa giant star. It either gives out a gigantic optical firework display which is a billion times brighterthan the sun as in the case of type I supernovae, or it becomes an intense source of neutrinos fora very brief period of time, followed by intense electromagnetic radiation in the case of type IIsupernovae.

8.2. SUPERNOVA NEUTRINOS AND SUPERNOVA WATCH 99

The type II SN is a star explosion by the mechanism of core collapse. Neutrinos are an integralpart of the paradigm of the explosion process in reviving the stalled shock wave and the subsequentcooling off of the star. A vast quantity of the energy output of the star, about 99% of the total, iscarried by neutrino emission, which happens several hours prior to the intense visible light from theSN, which is only 0.1% of the total energy. Because the SN processes occur in the extremely denseand hot core, they can only be directly studied through neutrino or gravitational wave emission.For recent reviews on the theoretical status of type II SNe we refer to Ref. [9] and for generaldiscussions of SN neutrinos to Refs. [10, 11, 12].

The first observation of a type II SN, called SN1987A, was made on February 23, 1987 [13, 14].It is an extragalactic SN located near the nucleus of the Large Magellanic Cloud, about 55 kpc(180,000 light years) from the sun. In total 24 neutrino events were observed at Kamiokande II[15], IMB [16], and Baksan [17]1. The duration of the events is about 13 seconds. Although thenumber of events due to SN1987A was too small to allow for a quantitative study of SNe, thisfirst observation of a SN as a neutrino source outside the solar system initiated an era of neutrinoastronomy which uses neutrino detectors as neutrino telescopes for astrophysics and particle physicsstudies.

Since the optical emission from type II SNe is hours after the neutrino signal, SN neutrino eventscan serve as an early warning for the subsequent optical emission to be made by conventional tele-scopes. This provides a valuable rare opportunity to make unprecedented observations of the earlyturn-on of the SN light curve, which allows a study of the conditions of the original, progenitor star.An international network of neutrino detectors, involving the currently active neutrino detectorsand to be joint by future neutrino detectors, called Supernova Early Warning System (SNEWS)[18], has been formed. The rarity of an observable SN neutrino event and its timing uncertaintymake SNEWS necessary to coordinate the study of type II SNe.

8.2.1 SN neutrino spectra and flux

The SN neutrino parameters are generally model dependent, relying on the details of the corecollapse mechanism which determines the total energy release and the mode of neutrino productionand transport. Since all of these are based on general physics arguments and well-establishedparticle and nuclear physics reactions, their general validity is expected, unless, of course verydifferent physics would appear in a high temperature and high density environment. We summarizethe spectra of the neutrino produced in a SN:

• Neutrino spectra: Neutrino spectra can be approximately described by Fermi-Dirac distri-butions [19]. For the neutrino of flavor α, the time-integrated spectrum function is givenby

F (0)α (E) =

L(0)α

F3T 4α

E2

exp(E/Tα) + 1(8.2)

where E and Tα are the energy and effective temperature of να, L(0)α is its total luminosity,

and F3 = 7π4/120. The average neutrino energy is E(0)α = 3.15Tα. The neutrino temperatures

are hierarchical: Tνe < Tνe < Tνx , hence are their average energies: E(0)νe < E

(0)νe

< E(0)νx , where

1An analysis of all the 24 events of the SN1987A can be found in this article.


νx denotes νµ, νµ, ντ , or ντ which behave similarly in SN. The total number of neutrino offlavor α is

N (0)α =

L(0)α

E(0)α

. (8.3)

• Neutrino luminosity: The simplest argument of the production of neutrinos in the coolingcore leads to the equipartition of energy among all six species of neutrinos and antineutrinos(although there are other possibilities). So they are produced with the same luminosity whenemerging from the SN. Lνe ≈ Lνe ≈ Lνx

2 [19] [20]. Then

L(0)α =

0.996

E(0)SN, (8.4)

where E(0)SN is the total energy released in the SN explosion. The numbers of neutrinos of

different flavors emitted by SN also satisfy the hierarchical relation: N(0)νe > N

(0)νe

> N(0)νx .

The oscillation effect is important in determining the detailed features of SN neutrinos thatare detected by a terrestrial detector, such as the total number of each flavor and their energydistributions. To do a detailed study requires a large number of events. The SNEWS network canbe useful. Especially some of the SNEWS detectors can provide the directional information of theSN event to determine the extent of the Earth matter effect.

At their production, SN neutrinos are in a very high density environment of ρ ∼ 1011 g/cm3, thematter effect dominates the Hamiltonian of the neutrino system and hence the flavor eigenstatescoincide with the mass eigenstates. Propagating outward from their production point deep insidethe SN, the neutrino and antineutrino experience a continuously decreasing matter density whichgoes to zero at the SN surface. Hence the neutrino and antineutrino will subject to the MSWresonance effect and level crossing [21, 22].

The treatment of the SN matter effect is similar to that of the sun. While there is only one MSWresonance in the sun, the SN have two MSW resonances. It turns out that with the solar LMAsolution, neutrinos and antineutrinos can have at most only one level crossing; for neutrinos, it isthe usual resonance for the solar neutrinos (involving the neutrino parameters ∆m2

21 and sin2 2θ12)and for antineutrinos a resonance only occurs for the inverted mass hierarchy (involving ∆m2

31 andsin2 2θ13). A detailed treatment of the SN matter effect can be found in [10] which we follow in ourcalculation below.

Before a SN neutrino enters a detector it may go through part of the Earth and therefore besubject to the Earth matter regeneration effect. Depending on the direction of the incoming SNneutrinos, the amount of Earth matter traversed varies from the height of the overburden of adetector to the whole Earth diameter. Unlike the SN matter effect, the Earth matter effect cannotbe specified, a priori, before the direction of the SN event is known. The Earth matter effect isgenerally of second order. Details of the treatment of the Earth matter effect can by found inRefs. [10] and [23].

The effect of the oscillation and the level crossing depend on the mixing angles θ12 and θ13. Dueto the smallness of θ13 and the SN model uncertainty, we will ignore the terms depend on θ13. TheSN neutrino fluxes arriving on Earth (not including the Earth matter effect), expressed in terms ofthe neutrino fluxes originally produced in the SN, are summarized below.

2There are other possibilities. It is generally expected to be true that Lνe ≈ Lνe and Lx ≡ Lνµ ≈ Lνµ ≈ Lντ ≈ Lντ .However Lνe and Lx can differ by a factor 2, Lx = (0.5− 2)Lνe .


• SN matter effect for the normal mass hierarchy, ∆m231 > 0,

F (N)νe

≈ PH sin2 θ12F(0)νe

+ (1− PH sin2 θ12)F (0)νx

(8.5)

F(N)νe

≈ cos2 θ12F(0)νe

+ sin2 θ12F(0)νx

2F (N)νx

≈ (1− PH sin2 θ12)F (0)νe

+ (1 + PH sin2 θ12)F (0)νx

2F(N)νx

≈ sin2 θ12F(0)νe

+ (1 + cos2 θ12)F (0)νx

• SN matter effect for the inverted mass hierarchy, ∆m231 < 0

F (I)νe

≈ sin2 θ12F(0)νe

+ cos2 θ12F(0)νx

(8.6)

F(I)νe

≈ PH cos2 θ12F(0)νe

+ (1− PH cos2 θ12)F (0)νx

2F (I)νx

≈ cos2 θ12F(0)νe

+ (1 + sin2 θ12)F (0)νx

2F(I)νx

≈ (1− PH cos2 θ12)F(0)νe

+ (1 + PH cos2 θ12)F (0)νx

An expression of the H-resonance jumping probability PH can be found in [12]. The value of PH

depends on the mixing angle θ13 and is divided into three regions:

• Region I defined by sin2 2θ13 > 10−3 is adiabatic, with PH ≈ 0.

• Region II defined by 10−5 < sin2 2θ13 < 10−3 has a finite jump probability, 0 < PH < 1.

• Region III defined by sin2 2θ13 < 10−5, where a complete transition occurs, with PH ≈ 1.

The mixing angle θ13 is currently bound by sin2 2θ13 < 0.16 [24], so all three regions are allowed.For the value of θ12 we use the most recent best fit given by KamLAND [25], tan2 θ12 = 0.4±0.09

0.07.Ignoring the uncertainties, we take cos2 θ12 ≈ 0.71, sin2 θ12 ≈ 0.29 and sin2 2θ12 ≈ 0.82. We notethat the results are independent of the CP phase.

Dividing the total neutrino flux by the surface area that the SN neutrinos cover when they passEarth, we obtain the flux on Earth,

fα(E) =Fα(E)4πD2

(8.7)

Using the input given in [26] which computes SN neutrinos for the Borexino detector, we take agalactic SN of total energy release E

(0)SN at the distance D,

E(0)SN = 3× 1053 erg = 1.97× 1059 MeV (8.8)D = 10 kpc = 3.09× 1022 cm

The temperatures and averaged energies, all in units of MeV, are taken to be

Tνe = 3.5 Tνe = 5.0 Tνx = 8.0 (8.9)

E(0)νe

= 11 E(0)νe

= 16 E(0)νx

= 25

The numerical results for the total neutrino flux on Earth for each type of neutrino are summarizedin Table 8.1.


να Total no. να flux (1011/cm2) reaching Earthfrom SN without vacuum Oscill. in SN matter(1057) oscill. oscill. Normal hierarchy Inverted hierarch

PH = 0 PH = 1 PH = 0 PH = 1νe 2.80 2.34 1.80 1.02 1.41 1.41 1.41νe 1.96 1.64 1.39 1.46 1.46 1.02 1.462νx 2.45 2.05 2.59 3.37 2.98 2.98 2.982νx 2.45 2.05 2.30 2.23 2.23 2.67 2.23

Table 8.1: Total number of neutrino reaching Earth from a SN located 10 kpc away under theeffects of different conditions. The vacuum oscillation is the case in which the SN matter effect isignored.

8.2.2 Detect SN neutrinos in the Daya Bay experiment

Below we estimate the number of events expected at the Daya Bay detector, ignoring the Earthmatter effect, which is of second order. We follow the treatment for the Borexino detector given in[26], but we take into account of the SN matter effect which can have an important effect on theobserved number and energy distribution of neutrino events. The Borexino scintillation detectorhas 300t of C9H12. For Daya Bay we use 100t target mass.

We first summarize the results for Borexino [26]. The signals are divided into three types:

• ν − e− elastic scattering via charge and neutral currents

να(να) + e− → να(να) + e− (8.10)

The number of target electrons in Borexino is N(e)T = 9.94×1031. The total number of events

from this class of reactions is 4.8 [26].

• Inverse β-decay. This reaction has the most event number,

νe + p → e+ + n (8.11)σ(νeP ) = 9.5× 10−44(Eν − 1.29)2(MeV)cm2

Eth = 1.80 MeV

The number of target proton is N(p)T = 1.82×1031. The expected number of events is 79 [26].

• Neutrino reactions with 12C that have characteristic signatures allowing for tagging: 12C(νe, e−)12N ,

12C(νe, e+)12B, 12C(νe, νe)12C∗, 12C(νe, νe)12C∗, and 12C(νx, νx)12C∗. The total number of

target carbon atoms for Borexino is N(C)T = 1.36× 1031. The total number of events is about

25 [26].

In general the Borexino results can not be used to scale down to the Daya Bay detector dueto oscillation effect. However, in the present case of equipartition of luminosity and for the ν − e−

elastic scattering, neutrino mixing does not modify the no-oscillation results on the number of eventsof any of the reactions in Eq. (8.10). The flavor mixing will still change their energy distributions.


reaction Vacuum SN matter effect onlychannel No oscill. oscill. Normal hierarch Inverted hierarchy

PH = 0 PH = 1 PH = 0 PH = 1∑(να(να) + e− → να(να) + e−) 1.6

νe + p → e+ + n 27 34 32 32 45 32∑(να(να) +12 C) 8 < 8

Table 8.2: Event types and numbers in Daya Bay of 100t target mass under different conditions.Vacuum Oscillation is for the case that the SN matter effect is ignored

To obtain the number of events at Daya Bay we integrate the product of the number of targetNT (hydrogen atom, electron, or 12C nucleus), the cross section, and the flux spectral functionFα(E)/4πD2 over neutrino energy:

Nα(event) = NT

∫dEνσ(Eν)

14πD2

Fα(Eν). (8.12)

Using the various spectral functions obtained above, the cross sections given in [26] and scalingdown the target mass by a factor 3 from BOREXINO, we can calculate the number of eventsexpected at Daya Bay. The results are listed in Table 8.2. For the events involving the carbonnucleus we simply give an estimate.3

We see from Table 8.2 that the total expected number of events is between 40 and 52. Thisestimate is probably valid even if the Earth matter effect is included. The majority of the eventsare from inverse β-decay, numbering from 32 to 45. It should be noted that the flavor mixing andthe matter effect enhance the number of events for the inverse β-decay reaction by 20% to 70%.The same effects, however, will suppress the number of events from the reactions involving thecarbon nucleus, which have Q-values in the range of 15-17 MeV, because the distributions of νx areshifted to lower energies.

We show in Fig. 8.3 the four different flux spectra of the νe and inverse β-decay event distribution: no-oscillation, vacuum oscillation, SN matter effect in the normal mass hierarchy (independentof PH), and the inverted mass hierarchy for PH = 0. The case PH = 1 for the of the inverted masshierarchy is the same as the normal mass hierarchy.

For simplicity we shall assume that the SN neutrinos enter from the top of the detector, so thatthe Earth matter effect can be safely neglected and the above result, which includes only the SNmatter effect, is applicable.

Let us consider the observability of SN neutrinos at Daya Bay. The SN neutrinos are detectedby the inverse β-decay process which is also used for the θ13 measurement. However, the two typesof signals are sufficiently different, they can be separated, ignoring the effect of detection efficiency.

• Time separation: Roughly the θ13 signal is 1.2 events per day per ton of detector mass, perGW of reactor power, and per 1 km baseline. For a 100t far detector, 11.6 GW reactor power,and at a distance of 2 km, the θ13 reactor process has 348 events per day or 0.044 event per10 sec interval. So reactor events are a negligible background for the 32 to 45 SN eventsexpected in a 10 sec interval.

3We reproduced the Borexino number of events given in Eqs. (8.10) and (8.11) by using the no-oscillation spectraldistributions.


Figure 8.3: The left panel is for SN νe flux on Earth multiplied by 10−8. The right panel is theenergy distribution of the number of events of the inverse β-decay in the Daya Bay detector witha 100t target mass. The horizontal axes are the νe energy in units of MeV. The four curves are forSN matter effect in the inverse hierarchy for PH = 0, vacuum oscillation, SN matter effect in thenormal hierarchy, and no-oscillation, in the order of increasing height of the maximum in the leftpanel, and from the right most to the left for the right panel.

• Energy separation: The neutrino energies of the reactor events are mostly below 8 MeV, whilethe SN events are almost all greater than 10 MeV and can be as high as 70 MeV.

• Local SN Watch network: With a far detector and one or two near detector, the Daya Baysetup can form a local SN Watch network. Assuming a near detector (or two near detectors)of 40t at 300 m, we have 0.7 reactor event in a 10 sec interval, while the number of SN inverseβ-deacy event is about 13-18. The burst-coincidence in the far and near different detector(s)can help identify the SN events.

It will be particularly interesting if Daya Bay has a positive signal for θ13; then the level crossingis in region I and the flip probability PH = 0. The normal and inverted mass hierarchies are expectedto have, respectively, 32 and 45 inverse β-decay events in the far detector under the assumption ofthe SN.

8.3 Exotic neutrino properties and nuclear power monitoring

The measurement of θ13 as discussed in the present work initiates an era of precision measurementof neutrino physics and the study of more details of the properties of neutrinos can be expected infuture neutrino programs. Several questions on neutrinos that seems to be exotic are valid inquiriesbased on theoretical expectation. Hence it is important to investigate them when opportunitiesarise. Any positive signal of them would mean a revolutionary discovery which can open completelynew doors for rethinking of the structure of particle physics. These questions include the sterile

8.3. EXOTIC NEUTRINO PROPERTIES AND NUCLEAR POWER MONITORING 105

neutrinos, the neutrino magnetic moment, and exotic interactions of neutrinos of possibly flavorchanging type. To answer these questions requires very high intensity neutrino beam and suitabledetectors. These can be achieved naturally with an extension of the Daya Bay experiment bysuitably designed an experimental hall constructed very closely to one of the reactor cores of thethe Ling Ao II which is currently under construction. The detector which will be made of highpurity germanium crystals can double as a monitor of the reactor power with a accuracy betterthan what is available to the nuclear power industry. Detailed physics simulation and the detectordesign will be made.

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[3] Y. Declais et al., Phys. Lett. B338, 383 (1994); B. Ackar et al., Nucl. Phys. B434, 503 (1995);B. Ackar et al., Phys. Lett. B374, 243 (1996)

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[8] V. Barger, D. Marfatia and K. Whisnant, Phys. Lett. B 576, 303 (2003) [arXiv:hep-ph/0308299].

[9] A. Mezzacappa, The core collapse supernova mechanism: current models, gaps, and the roadahead, arXiv:astro-ph/0410085.

[10] A.S. Dighe and A.Y. Smirnov, Phys. Rev. D62, 033007 (2000) (arXiv:hep-ph/9907423).

[11] A. Dighe, Supernova neutrinos: production, propagation and oscillations, talk given in neutrino2004, arXiv:hep-ph/0409268.

[12] C. Lunardini, Physics of Supernova Neutrinos, Proceedings, International Workshop on As-troparticle and High Energy Physics, Valencia, Spain, 14-18, 2003 (IHEP2003/043).

[13] D. Schramm, Neutrinos from supernova 1987A, Fermilab Report: FERMILAB-pub-87/91-A.

[14] T.K. Kuo and J. Pantaleone, Rev. Mod. Phys. 61, 937 (1989).

[15] [Kamiokande II] K. Hirata et al., Phys. Rev. Lett. 58, 1490 (1987).

[16] [IMB] R.M. Bionta et al., Phys. Rev. Lett. 58, 1494 (1987).

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BIBLIOGRAPHY 107

[17] [Baksan] E.N. Alexevey, et al., Phys. Lett. B205 (1988) 209. An analysis of all the 24 eventsof SN 1987A can be found in this paper.

[18] [SNEWS] P. Antonioli et al., SNEWS: The SuperNova Early Warning System, arXiv:astro-ph/0406214; K. Scholberg, Supernova Neutrino Detection, 19th International Conference onNeutrino Physics (Neutrino 2000), Sudbery Ontario, 2000, arXiv:hep-ex/0008044.

[19] T. Totani, K. Sato, H.E. Dalhed, and J.R. Wilson, Astophys. J. 496, 216 (1998) (arXiv:astro-ph/9710203).

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Appendix A

Past Reactor Neutrino Experiments

The detectors of the early reactor neutrino experiments, for example ILL [1], Gosgen [2], andBugey [3], were located very close to the reactor (up to 100 m), thus sensitive to ∆m2

31 of theorder of 5 × 10−2 eV2 which is about twenty times larger than the current best-fit value whereoscillation related to the mixing angle θ31 is expected to take place. In the nineties, motivatedby the observation of atmospheric neutrino oscillation, two reactor-based neutrino experiments,CHOOZ [4] and Palo Verde [5], were carried out to investigate this surprising phenomenon. Basedon ∆m2

32 = 1.5×10−2 eV2 as reported by Kamiokande [6], the baseline of CHOOZ and Palo Verde,was chosen to be about 1 km, corresponding to the location of the first oscillation maximum ofνe → νµ when probed with low-energy reactor νe. Since the νµ coming from oscillation does nothave enough energy to produce a µ+ through the charged-current process, reactor-based neutrinoexperiments are disappearance experiments. Both CHOOZ and Palo Verde were looking for adeficit in the νe flux at the location of the detector, as compared with the calculated flux assumingno oscillation occurred. With only one detector, both experiments must rely on the operationalinformation of the reactors, in particular, the composition of the nuclear fuel and the amount ofthermal power generated as a function of time, for calculating the rate of νe produced in the fissionprocesses.

CHOOZ and Palo Verde utilized Gd-doped liquid scintillator to detect the reactor νe via theinverse beta-decay νep → ne+ reaction. The ionization loss and subsequent annihilation of thepositron give rise to a fast signal obtained with an array of photo-multiplier tubes. The energyassociated with this signal is termed the prompt energy, Ep. From kinematic consideration, it iseasy to realize that Ep is directly related to the energy of the incident νe. After random walkingfor about 30 µs, the neutron is captured by the Gd nucleus, emitting several gamma-ray photonswith a total energy of about 8 MeV. This signal is called the delayed energy, Ed. The temporaland spatial correlation between the prompt energy and the delayed energy constitutes a powerfultool for identifying the νe and for suppressing backgrounds.

Both CHOOZ and Palo Verde did not observed any rate deficit in νe. This null result is used toset a limit in the neutrino mixing angle θ13. In terms of sin22θ13, CHOOZ obtained the best limitof 0.2 at the 90% confidence level.

KamLAND [7] is the only reactor-based neutrino experiment currently taking data. It is de-signed to address the quest of neutrino oscillation first discovered as a deficit in the solar-neutrinoflux on Earth. Through a series of studies of solar neutrino, there is compelling evidence thatthe mass-square difference, ∆m2

21, should be less than 10−4 eV2. In order to investigate this phe-

108

A.1. GOSGEN 109

nomenon with anti-neutrinos from nuclear reactors, the baseline has to be on the order of a hundredkm and the detector be about a kilo-ton in mass. These are the unique features of KamLAND. Re-cently, KamLAND has observed a reduction in anti-neutrino flux, which strengthened the evidenceof neutrino oscillation and favors the large mixing-angle (LMA) solution.

In the following sections, some of the features of Gosgen, Bugey, CHOOZ, Palo Verde and Kam-LAND that are relevant to the design of the next generation of reactor-based neutrino experimentfor determining θ13 are summarized.

A.1 Gosgen

The Gosgen experiment was conducted at the 2.8 GWth nuclear power reactor at Gosgen (Switzer-land). The energy spectrum of the anti-neutrinos was measured at three distances, 37.9, 45.9, and64.7m, from the reactor core. The experiment was carried out during 3 periods from 1981 to 1985.Roughly 104 anti-neutrinos were registered at each of the three positions.

The detector is approximately one cubic meter in size and consists of two different kinds ofdetector systems sandwiching each other as shown in Fig. A.1. The detector elements record,respectively, the positron and neutron generated in the inverse β-decay reaction νe + p → e+ + n.One system is made of thirty cells filled with a proton-rich liquid scintillator and arranged in fiveplanes served both as the target for the incident anti-neutrinos and as detector for sensing thegenerated positrons. The neutrons emerging with an energy of several keV are thermalized in thescintillator cell within a few µs and diffuse within a mean diffusion time of about 150 µs into one ofthe adjacent wire chambers filled with 3He, where they are detected. An anti-neutrino candidatesatisfies a proper spatial correlation as well as a coincidence within a time window of 20 µs betweena positron in a scintillator cell and a neutron in one of the multiwire proportional chambers.

A.2 Bugey

The Bugey nuclear power plant (France) operates four Pressurized Water Reactors. Each cangenerate 2.8 GWth. The Bugey-3 experiment was carried out at 15 m and 40 m away from one ofthe reactor cores. The detector is a 600 liter stainless steel tank with two acrylic windows on twoopposite faces to collect the scintillation light. The tank is optically segmented into 7×14 cells bywalls made of 150-µm-thick steel foil. Each cell has a volume of 8.5×8.5×85 cm3 and viewed at eachend by a 3” photomultiplier tube.. The steel foil is covered with an aluminium foil and separatedfrom the liquid by a layer of 125-µm-thick transparent thermosealed PEP teflon. A nitrogen gasgap maintained by spacers between the teflon and aluminium foil provides optimal light reflection.The tank is filled with pseudocumene-based liquid scintillator with an H/C ratio of 1.4 loaded with0.15% in mass of 6Li. Neutron capture on 6Li has a Q-value of 4.8MeV and occurs 30 µs on theaverage after the inverse beta-decay reaction induced by the incoming anti-neutrino takes place.Comparison of the pulse heights from the PMT’s at opposite ends determines the location of thelight-emission point at which the anti-neutrino interaction occurs along the cell.

110 APPENDIX A. PAST REACTOR NEUTRINO EXPERIMENTS

Figure A.1: The central anti-neutrino detector of Gosgen. It consists of 30 liquid-scintillator cellsarranged in five planes for detecting positrons and four 3He-filled multiwire proportional chambersfor observing neutrons.

A.3 CHOOZ

The two CHOOZ reactors are located on a flat island by the River Meuse in the Ardennes regionnear the France-Belgium border. The reactors can generate a total of 8.5 GWth. The CHOOZdetector was placed on the other side of the river in a underground hall with an overburden of 300MWE and at a distance of 1115 m and 998 m from the cores. At this depth, the cosmic-ray muonflux was reduced to 0.4 m−2s−1.

Anti-neutrinos were detected with a central detector made up of five tons of Gd-doped liquidscintillator inside a 8 mm-thick cylindrical acrylic vessel, with hemispherical end-caps, immersedin a 70-cm-thick mineral oil contained inside a steel vessel. The concentration of Gd in the liquidscintillator was 0.09% by mass. The transparency of the scintillator was found to degrade overtime, with a decay constant of (4.2 ± 0.4) × 10−3 d−1. A total of 192 eight-inch photomultipliertubes were mounted on this steel container, as shown in Fig. A.2. The photo-cathode coverage was15% and a light-yield of about 130 photoelectrons per MeV was obtained. The central detector wasshielded with 90-ton of liquid scintillator which was at least 80-cm thick, and a passive shieldinglayer made of 75-cm thick low-activity sand. Ambient natural radioactivity and cosmic-ray inducedbackgrounds, mainly neutrons and gamma rays, were detected in the veto scintillator with two ringsof 24-eight-inch photomultiplier tubes. To improve the veto efficiency, the steel tank of the vetodetector was painted with white reflective paint.

The central detector was calibrated daily with radioactive sources 60Co, 252Cf, and Am-Be (aγ-and-neutron emitter to simulate the inverse beta-decay reaction) deployed along the symmetryaxis of the detector through pipes. In addition, six laser flashers were installed in three regions

A.3. CHOOZ 111

veto

acrylicvessel

neutrinotarget

opticalbarrier

low activity gravel shielding

containmentregion

steeltank

Figure A.2: Schematic drawing of the CHOOZ detector.

inside the detector to monitor its stability. The energy resolution of the CHOOZ detector wasσ(E)/E = 5.6% at 8 MeV, whereas the position resolution was σ = 17.5 cm in all direction.

CHOOZ took data between April 1997 and July 1998 with a live time of 8209 hours, about40% of which both reactors were off. The overall efficiency of detecting anti-neutrino events was(69.8±1.5)%. With at least one reactor on, 2704 anti-neutrino candidates were found. In addition,287 events were obtained with both reactors off. Based on the reactor-on sample, the ratio ofmeasured number of events to the expected number without oscillation was determined to beR = 1.01± 2.8% (stat)±2.7% (syst). Systematic errors are listed in table A.1 and Table A.2. Bothrate and spectral analyses yielded no evidence for neutrino oscillation. Fig. A.3 shows the exclusioncontour at 90% confidence level along with the Kamiokande results. At ∆m2

31 = 2.5 × 10−3 eV2,CHOOZ obtained sin2(2θ13) < 0.14, which is the best limit at present.

parameter relative error (%)reaction cross section 1.9number of protons 0.8detection efficiency 1.5reactor power 0.7energy released per fission 0.6combined 2.7

Table A.1: Contributions to the overall systematic uncertainty in the absolute normalization.


10-4

10-3

10-2

10-1

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1sin22Θ

∆m2 (

eV2 )

Kamiokande (90% CL)

Palo Verde (Swap)

Palo Verde (Rate)

Chooz

Figure A.3: Exclusion contours determined by CHOOZ, Palo Verde, and Kamiokande.

selection ε (%) relative error (%)positron energy 97.8 0.8positron-geode distance 99.9 0.1neutron capture 84.6 1.0capture energy containment 94.6 0.4neutron-geode distance 99.5 0.1neutron delay 93.7 0.4positron-neutron distance 98.4 0.3neutron multiplicity 97.4 0.5combined 69.8 1.5

Table A.2: Summary of the anti-neutrino detection efficiency.

A.4 Palo Verde

The Palo Verde experiment utilized the Palo Verde Nuclear Generating Station which is about 70km west of Phoenix, Arizona. The detector was located underground with 32 m of overburden,reducing the cosmic-ray muon flux to 22 m−2 s−1 but about 50 times higher than that at CHOOZ.The detector was 890 m from the outer reactors and 750 m from the core at the center. The threeidentical reactors generated a total of 11.63 GW thermal power. The walls of the hall were madeof crushed marble with low natural radioactivity, reducing the ambient gamma ray by a factor often.

A.4. PALO VERDE 113

Fig. A.4 is a sketch of the Palo Verde detector. The 11.34 tons of Gd-loaded liquid scintillatorwas contained in a 6 by 11 array of acrylic cells. Each cell was 9-m long, 12.7-cm wide and 25.4-cmtall. Between the liquid scintillator and the photomultiplier tube at each end of a cell, a 0.8-mlong region was filled with mineral oil that blocked external gamma ray and neutron backgroundsfrom entering the fiducial region. The array was further shielded at all sides with 1-m thick ofpurified water in steel tanks. Outside the water jacket was an array of muon veto-counters madeof PVC tanks filled with dilute liquid scintillator and viewed with photomultiplier tubes at bothends. Contrary to the CHOOZ detector, signals corresponding to the inverse beta-decay processspread over a few cells in the Palo Verde detector.

Figure A.4: Schematic drawing of the Palo Verde detector.

The stability of the central detector was monitored with two blue LEDs installed in each cell.Light attenuation and absolute energy/position calibration were determined with 22Na, 137Cs, 65Zn,228Th and Am-Be radioactive sources once every two to three months. The light yield was foundto be about 50 photoelectrons per MeV. The Gd-dope liquid scintillator was quite stable over thecourse of the experiment, about one year, with the attenuation length dropped by roughly 1 mmper day.

A undesirable consequence of having insufficient amount of overburden is the reduction of thelive time due to the high trigger rate. Vetoing cosmic muons with a time window of 150 µs afterthe muon signal led to a detector live time of 74.2%. In addition, about 7.5% of the anti-neutrinoevents were interrupted by this veto between the positron and neutron-capture signals. Anothersource of dead time was due to the DAQ.

Palo Verde collected data between July 1998 and September 1999, yielding a total of about4000 anti-neutrino candidates and 8700 background events. Comparing to the expected numberof anti-neutrino events with no oscillation, Palo Verde obtained a ratio of R = 1.04 ± 0.03 (stat)


± 0.08 (syst), consistent with a null result. The systematic errors are listed in table A.3. Theresults from CHOOZ, Palo Verde, and Kamiokande are shown in Fig. A.3. The systematic errorsis listed in Table A.3

Error source on-off (%) swap (%)e+ efficiency 4 4n efficiency 3 3νe flux prediction 3 3νe selection cuts 8 4Bpn estimate - 4Total 10 8

Table A.3: Contributions to the systematic error of the reactor power and swap analysis.

A.5 KamLAND

The KamLAND detector is located underground with about 2700 MWE overburden in the Kamiokamine in Japan. It is surrounded by the Japanese nuclear reactors that provide a flux-weighted-average baseline of about 180 km.

Figure A.5: Schematic drawing of the KamLAND detector.

anti-neutrinos are detected with 1 kton of liquid scintillator composed of 80% dodecane, 20%pseudocumene (1,2,4-trimethyloxazole), and 1.52 g/L of PPO (2,5-diphenyloxazole) as a fluor. Asshown in Fig. A.5, the liquid scintillator is contained in a 13-m-diameter balloon made of 135-µm-thick transparent film (nylon-ethylene vinyl alcohol copolymer composite). External radiation is

A.5. KAMLAND 115

absorbed by a 2.5-m-thick layer of mineral oil (dodecane and isoparaffin) placed inside a sphericalstainless-steel container, outside of which 1325 seventeen-inch-diameter and 554 twenty-in-diameterphotomultiplier tubes are mounted. The total photocathode coverage is 34%. To suppress radonfrom the photomultiplier glass from entering the liquid scintillator, 3-mm-thick acrylic plates areplaced at 16.6 m from the center of the stainless-steel container which is shielded by a cylindricalcolumn of water, 3.2 kton, viewed with 225 twenty-inch photomultiplier tubes.

The energy scale and position resolution are established with 68Ge, 65Zn, 60Co, and Am-Besources. The stability of the detector is monitored with nitrogen laser as well as LED light sources.The light yield is approximately 300 photoelectrons per MeV. Using only the 17” photomultipliertubes the energy and position resolutions are 7.5%/

√E(MeV ) and about 25 cm respectively in

the 5.5-m-diameter fiducial volume, which contains 408 ton of liquid scintillator or 3.46× 1031 freeprotons. The efficiency of identifying an inverse-beta-decay event is about 78%, which is verifiedwith the Am-Be source that provides a 4.4 MeV prompt gamma and a 2.2 MeV gamma fromdelayed neutron captured by proton.

Due to the low contamination of 238U [(3.5± 0.5)× 10−18 g/g], 232Th [(5.2± 0.8)× 10−17 g/g],40K [< 2.7×10−16 g/g], the accidental background in a delayed window of 0.020-20 sec is negligible.The dominant backgrounds are gammas from 208Tl in the rock, and spallation products producedby cosmic-ray muons. At KamLAND, 0.3 Hz of muons in the liquid scintillator is observed, givingrise to about 3000 neutron events/day/kton and roughly 1300 radio-isotope, such as 8He and 9Li,events/day/kton are expected.

The major systematic errors in KamLAND are the uncertainties in the fiducial-mass ratio(4.1%), the anti-neutrino spectra, total liquid-scintillator mass (2.1%), energy threshold (2.1%),efficiency of event selection (2.1%), and reactor power (2.0%). They are listed in table A.4.

Total LS mass 2.1 Reactor power 2.0Fiducial mass ratio 4.1 Fuel composition 1.0Energy threshold 2.1 Time lag 0.28Efficiency of cuts 2.1 ν spectra 2.5Live time 0.07 Cross section 0.2Total systematic error 6.4%

Table A.4: Estimated systematic uncertainties (%) of KamLAND.

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