A Measurement of the Branching Ratio of the 0 -decay in...

Universita degli Studi di Torino

Facolta di Scienze Matematiche, Fisiche e Naturali

DOTTORATO DI RICERCA IN FISICA

XVI Ciclo

A Measurement of theBranching Ratio of the Ξ0

β-decay in the NA48experiment at CERN

Candidate: Marco Clemencic

Supervisor: Ezio Menichetti

Contents

1 The hyperon semileptonic decay 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The current-current phenomenological interaction . . . . . . . 2

1.3 The mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Semileptonic baryon decays and weak form factors . . . . . . . 6

1.5 SU(3) breaking . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 The case of Ξ0 semileptonic decay . . . . . . . . . . . . . . . . 9

1.6.1 Vus extraction . . . . . . . . . . . . . . . . . . . . . . . 10

1.6.2 Form factors extraction . . . . . . . . . . . . . . . . . . 13

2 The NA48 Experiment 15

2.1 The Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 The decay region . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 The detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 The spectrometer . . . . . . . . . . . . . . . . . . . . . 19

2.3.2 The charged hodoscope . . . . . . . . . . . . . . . . . . 24

2.3.3 The electromagnetic calorimeter . . . . . . . . . . . . . 25

2.3.4 The neutral hodoscope . . . . . . . . . . . . . . . . . . 30

2.3.5 The hadronic calorimeter . . . . . . . . . . . . . . . . . 31

2.3.6 The veto system . . . . . . . . . . . . . . . . . . . . . 32

2.3.7 The beam monitor . . . . . . . . . . . . . . . . . . . . 34

2.4 The trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.4.1 The neutral trigger subsystem . . . . . . . . . . . . . . 35

iii

iv CONTENTS

2.4.2 The charged trigger subsystem . . . . . . . . . . . . . . 38

2.4.3 The decisional system . . . . . . . . . . . . . . . . . . 44

2.4.4 The software trigger . . . . . . . . . . . . . . . . . . . 47

2.5 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.6 Data processing and analysis . . . . . . . . . . . . . . . . . . . 49

3 Analysis 53

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.1.1 Signal channel . . . . . . . . . . . . . . . . . . . . . . . 53

3.1.2 Normalization channel . . . . . . . . . . . . . . . . . . 54

3.2 Trigger setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.2.1 Signal channel . . . . . . . . . . . . . . . . . . . . . . . 55


3.3 Data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.1 Signal channel . . . . . . . . . . . . . . . . . . . . . . . 58


3.5 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5.1 Signal channel . . . . . . . . . . . . . . . . . . . . . . . 60


3.6 Measurement procedure . . . . . . . . . . . . . . . . . . . . . 65

4 Montecarlo 67

4.1 NASIM structure . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1.1 Decay simulation . . . . . . . . . . . . . . . . . . . . . 67

4.1.2 Physical simulation . . . . . . . . . . . . . . . . . . . . 69

4.1.3 Data digitization . . . . . . . . . . . . . . . . . . . . . 71

4.2 Hyperon decays implementation . . . . . . . . . . . . . . . . . 72

4.2.1 Simulation of Ξ0 → Λπ0 decay . . . . . . . . . . . . . . 72

4.2.2 Simulation of Ξ0 β-decay . . . . . . . . . . . . . . . . . 74

4.3 Polarization of the Ξ0 . . . . . . . . . . . . . . . . . . . . . . . 76

CONTENTS v

5 Results 83

5.1 Acceptances . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.1.1 Energy of Ξ0 in the β-decay . . . . . . . . . . . . . . . 84

5.1.2 Acceptance computation . . . . . . . . . . . . . . . . . 87

5.2 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.2.1 Level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2.2 Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.3 Level 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.3 Observed events . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.1 Fiducial region . . . . . . . . . . . . . . . . . . . . . . 91

5.3.2 Signal channel . . . . . . . . . . . . . . . . . . . . . . . 92


5.3.4 Background . . . . . . . . . . . . . . . . . . . . . . . . 92

5.4 Branching ratio . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.5 Systematic errors . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.5.1 Acceptance . . . . . . . . . . . . . . . . . . . . . . . . 97

5.5.2 Trigger efficiency . . . . . . . . . . . . . . . . . . . . . 99

5.5.3 Branching ratio of the secondary decays . . . . . . . . 100

5.5.4 Energy scale . . . . . . . . . . . . . . . . . . . . . . . . 100

5.5.5 Distance of the proton track from the beam pipe . . . . 101

5.5.6 Polarization of the Ξ0 . . . . . . . . . . . . . . . . . . . 103

6 Conclusions 107

vi CONTENTS

Introduction

The study of the hyperon β-decays provide important information to im-

prove our understanding of the strong interaction among the the proton con-

stituents, and about the correctness of both the SU(3) model and the quark

mixing model. This information, also provided by the study of semileptonic

meson decays, is richer in the baryon case because of the presence of three

valence quarks, as opposed to a quark-antiquark pair.

In the last few years the interest on the hyperon semileptonic decays has

known a second youth. Historically, the main problem in the study of the

hyperon semileptonic decays was their small branching ratio (. 10−3). The

situation has changed since the first operation of the intense, neutral kaon

beams designed for the study of direct CP violation (NA48 at CERN and

KTeV at FNAL). In fact, as a byproduct, a large amount of neutral hyperons

are produced together with the kaons. After the successful completion of the

study of direct CP violation in the KL decays, NA48 has dedicated the 2002

run to the search of rare KS decays, also collecting a large sample of Ξ0

decays in various modes.

In the first chapter I will briefly recall the standard theoretical picture

of the weak interaction between quarks, namely the Cabibbo-Kobayashi-

Maskawa mixing model. The effective theory describing the semileptonic

meson and baryon decays will be also recalled, and the current situation of

the predictions of effects of SU(3) breaking summarized.

In the second chapter the NA48 experimental setup, from the beam to

the central data recording system, will be described in some detail.

vii

viii CONTENTS

In the third chapter I will describe the selection criteria for the signal and

normalization events, and the procedure followed to obtain the branching

ratio from the data.

The characteristics and the numerous improvements and additions to the

NA48 Montecarlo program will be described in the forth chapter, together

with some comments on the feasibility of measuring the Ξ0 polarization.

In the fifth chapter I present the result obtained for acceptance, trigger

efficiency, background and branching ratio, with an evaluation of the main

systematic errors.

To conclude, in the sixth chapter I will compare this measurement to

the other recently mad available, and to the theoretical prediction made by

Cabibbo back in 1963.

Results obtained in this thesis should be taken as still preliminary, since

further systematics checks are in progress.

Chapter 1

The hyperon semileptonic

decay

1.1 Introduction

The first successful theory of the weak interaction was originated by Fermi

in the ’30s to explain the main features of the nuclear β-decay. Twenty years

later, the discovery of parity violation in the weak decays gave rise to the

generalization of the current-current Fermi theory to all the weak processes,

leading to the formulation of the V-A model of the weak charged current.

The universality of the vector part of the charged weak current was under-

stood in the framework of the Conserved Vector Current (CVC) hypothesis,

allowing to apply the Fermi theory to hadrons. Systematic discrepancies con-

cerning the weak decays of all strange particles were subsequently explained

by the Cabibbo theory (1963)[6], extending in turn the notion of universal-

ity to strange particle decays by introducing the concept of flavor mixing

within the framework of the unitary symmetry SU(3). The quark model

provides a framework which is naturally fit to account for universality of the

weak currents and to describe flavor mixing. The later discovery of neutral

currents, heavy quarks and gauge bosons, while definitely establishing the

Weinberg-Salam-Glashow theory of the electroweak interaction as the Stan-

1

2 CHAPTER 1. THE HYPERON SEMILEPTONIC DECAY

dard Model, still left unanswered many detailed questions on the dynamical

mechanisms of the hadronic weak decays, simply because the strong inter-

action between quarks gives rise to sizeable corrections, difficult to calculate

in a non-perturbative regime. On the other hand, the phenomenological

current-current interaction, extended by the Cabibbo theory to encompass

decays of strange particles, provides detailed predictions of the phenomeno-

logical form factors needed to describe all weak processes involving hadrons.

It still represents the best available tool to describe weak decays of hadrons

containing light quarks.

1.2 The current-current phenomenological in-

teraction

The current-current Lagrangian, including only charged lepton currents and

neglecting higher order terms, is written as:

L = −2√

2GF j†µj

µ (1.1)

where GF is the Fermi constant and

jµ =∑

leptons

ψlγµ

1

2(1 − γ5)ψl (1.2)

is the leptonic part of the charged weak current. The V-A Lorentz structure

of the current entails maximal P and C violations in all charged leptonic

processes, which can be naturally described as arising from weak transitions

within leptonic doublets:

x

y

(

νe

e

)

,

(

νµ

µ

)

,

(

ντ

τ

)

(1.3)

To the extent one neglects the recent experimental hints for a non-zero neu-

trino mass and flavour oscillation, strict conservation of the individual lepton

numbers is predicted and observed.

1.3. THE MIXING 3

In the framework of quark model, it is tempting to extend this description

to all processes involving hadrons, by introducing a charged quark current

term quite similar to the leptonic one. By taking quark doublets

(

u

d

)

,

(

c

s

)

,

(

t

b

)

(1.4)

where the quark states have sharp flavor content, the following expression

could be written for the charged quark current

Jµ =∑

quarks

ψqγµ

1

2(1 − γ5)ψq (1.5)

which is unsatisfactory because it cannot account for observed flavor vio-

lating transitions, like many decays of strange particles. Nevertheless, one

is reluctant to abandon the general picture, which in many respects is well

supported by the data.

The key step to solve the puzzle was taken by Cabibbo by introducing

the concept of flavor mixing.

1.3 The mixing

The central assumption in Cabibbo’s theory is to take the weak current Jµ is

a member of the octet of currents J iµ = V i

µ +Aiµ, where V i

µ and Aiµ are octets

of vector and and axial currents. The relation given is[8]

Jµ = cos θC(J1µ + iJ2

µ) + sin θC(J4µ + iJ5

µ) (1.6)

The assumption that the vector and axial part of the current Jµ are the same

elements of the octet includes the V −A hypothesis. Assuming that the vector

part of the weak current belongs to the same octet as the electromagnetic

current includes also the CVC hypothesis.

If we use the quark description, the equation (1.6) assumes the simple

form

Jµ = cos θCuγα(1 − γ5)d+ sin θCuγα(1 − γ5)s (1.7)


The idea of quark mixing proposed by Cabibbo was soon extended by

Kobayashi and Maskawa[19] with the addition of other 2 quarks and thus

accommodating the CP violation in a natural way, as well.

The mixing can be accomplished via a 3×3 unitary mixing matrix (CKM

matrix)

Jµ =∑

i,j

Vijiγα(1 − γ5)j (1.8)

where i = u, c, t, j = d, s, b. In this picture we have that

tan θC =Vus

Vud

. (1.9)

From the analysis of the decays of baryons and hyperons, we can extract

independent and redundant informations about the elements of the CKM

matrix.

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

0.9734(8)0.2196(23) Ke3

0.2250(27) hyp.[8]0.0036(7)

0.224(16) 0.996(13) 0.0412(20)

0.004 ÷ 0.014∗ 0.037 ÷ 0.044∗ 0.94+0.31−0.24

Figure 1.1: Current measures of the CKM matrix elements[16]. (*) The

limits for Vtd and Vts are obtained using tree-level constraints together with

unitarity and assuming only three generations (90% confidence).

The values currently stated for |Vus| come from two kind of sources: the

β-decays of the K mesons and the β-decays of the strange hyperons (Σ, Λ

and Ξ). The two categories are taken separately because of the theoretical

differences between them. In the mesons we have to take into account only

1.3. THE MIXING 5

decay mode |Vus|Ke3 0.2196(23)

Λ → p e νe 0.2224(34)

Σ− → n e νe 0.2282(49)

Ξ− → Λ e νe 0.2367(99)

Ξ0 → Σ+ e νe 0.209(27)

hyperons combined 0.2250(27)

Table 1.1: Current |Vus| measures[8]

the presence of one extra quark, while the baryon have two extra quarks

inducing strong effects to the matrix element of the decay.

The numbers given by the two kind of experiments (Table 1.1) suggest

that there can be some theoretical aspect not well enough understood, and

they can also rise some doubt on the unitarity of the CKM matrix. Being it

unitary means that the we can take one line (or one column) and the sum of

the squared module of its element will give 1. If we try this simple exercise

on the numbers of Figure 1.1, we obtain1

|Vus| from Ke3 → |Vud|2 + |Vus|2 + |Vub|2 = 0.9957(19)

|Vus| from hyperons → |Vud|2 + |Vus|2 + |Vub|2 = 0.9981(20)

Still, there is room for improvement also from the experimental point

of view, in fact the Ξ0 β-decay was observed the first time only few years

ago[1, 2] and the big uncertainty is mainly due to the statistical error.

1The contribution of |Vub|2 is negligible, thus the unitarity test reduces to the consis-

tency of cos θC determined from nuclear β-decay and sin θC from the strangeness changing

semileptonic decays


1.4 Semileptonic baryon decays and weak form

factors

In order to understand the origin of the weak form factors in the hyperon

decays, it is worthwhile to sketch first the equivalent description of electro-

magnetic transitions. The nucleon electromagnetic current is usually written

as

〈Ψ(p′)|JEMµ |Ψ(p)〉 =

eu(p′) ·

1

2

[

Cn(q2) + Cp(q

2)]

γµ +Kn(q2) +Kp(q

2)

Mp

σµνqν+

[

[

Cp(q2) − Cn(q2)

]

γµ +Kp(q

2) −Kn(q2)

Mp

σµνqν+

]

τ3

u(p) (1.10)

where q = p− p′ is the 4-momentum transfer and τ3 is the third component

of the nucleon isospin operator. Here the C’s and K’s are unknown (i.e.

phenomenological) functions of the square 4-momentum transfer, called the

electromagnetic form factors of the nucleon. They take into account the non-

point-like distribution of charge and magnetic dipole moment of the nucleon,

and are constrained by experimental data to satisfy the boundary conditions

(i.e. static limits):

Cp(0) = 1, Kp(0) =µp − µ0

2µ0

Cn(0) = 0, Kn(0) =µn

2µ0

One can see that the full electromagnetic current contains a isovector as well

as a isoscalar component.

One can model the nucleon charged weak current in tight analogy to the

electromagnetic case as

〈Ψ(p′)|JWµ |Ψ(p)〉 =

GF

2Vudu(p

′) ·

f1(q2)γµ +

f2(q2)

Mp

σµνqν +

f3(q2)

Mp

qµ+

[

g1(q2)γµ +

g2(q2)

Mp

σµνqν +

g3(q2)

Mp

qµ

]

γ5

τ+u(p) (1.11)

1.4. SEMILEPTONIC BARYON DECAYS AND WEAK FORM FACTORS7

Here τ3 has been replaced by τ+ to account for the difference in charge be-

tween initial and final baryons. We also have two extra functions, f3 and g3,

not needed in the parity conserving electromagnetic current, and the CKM

matrix element Vud. The functions fi and gi are called the weak form factors

of the nucleon. It can be shown that for a generic semileptonic baryon tran-

sition, like neutron or hyperon β-decay, the expression above for the baryon

current yields the following matrix element:

M =GFV√

2ub(O

Vµ +OA

µ )uBueγµ(1 + γ5)uν + h.c. (1.12)

where

V : appropriate element of CKM matrix

OVµ = f1(q

2)γµ +f2(q

2)

Mp

σµνqν +

f3(q2)

Mp

qµ

OAµ =

(

g1(q2)γµ +

g2(q2)

Mp

σµνqν +

g3(q2)

Mp

qµ

)

γ5

No information is available a priori on the form factors involved in this ex-

pression, nevertheless general symmetry arguments can be invoked in order

to relate them to their electromagnetic equivalents.

In the standard Model, the unified electroweak interaction naturally em-

bodies the Conserved Vector Current hypothesis, starting that the vector

part of the charged weak current belongs to the same isospin triplet as the

isovector part of the electromagnetic current. As a consequence one obtains

f1(q2) = Cp(q

2) − Cn(q2) = 1

f2(q2) = Kp(q

2) −Kn(q2) = 1.8

f3(q2) = 0

(1.13)

Of course, no such connection exists for the axial form factors, other than

the vanishing value of g3 for decays into electron, due to its proportionality

to m2e.

Neglect of small electromagnetic corrections lead to take into account

only first class currents, whose vector part is odd under G-parity. Since this


necessarily yields g2 = 0, one is left with only one unknown form factor,

namely g1.

The Cabibbo theory can be considered as an extension on the CVC hy-

pothesis to the SU(3)f symmetry, where the spin 12

baryons belongs to the

representation 8. If SU(3)f were unbroken, by use of the Wigner-Eckart the-

orem, any transition operator between octet baryons could be written as[15]

〈Bj|Ok|Bl〉 = ifjklF + djklD (1.14)

where fjkl are the structure constants of SU(3) and djkl are defined by the

relation λj, λkl = 12(δjk + djkl), where λi are the generators of SU(3). It

is easy to show that in this limit the following expressions hold for the form

factors:

fi = CD(B, b)Di + CF (B, b)Fi

gi = CD(B, b)Di+3 + CF (B, b)Fi+3

(1.15)

where CD and CF are related to the well known Clebsch-Gordan coefficients

for SU(3), while Di and Fi depend on each particular form factor. Bay

taking the case of g1,which is the only one undetermined, one can build the

following schematic picture showing how all the octet decays depend on the

two unknown parameters F and D:

SU(3) Baryons

1.5. SU(3) BREAKING 9

Therefore, in this exact symmetry limit, a measurement of two decays with

different Clebsch-Gordan coefficients would fix the form factors for all the

octet transitions.

1.5 SU(3) breaking

One expects some deviation from exact SU(3) due to different quark masses

and charges. Data on form factors can be extracted from rates and angular

distributions of the 12 allowed decays. Four cases, namely Ξ− → Ξ0e−ν,

Σ− → Σ0e−ν, Σ0 → Σ+e−ν and Σ0 → pe−ν , are predicted with branching

ratios less than 10−10, and are not likely to be observed. The remaining 8

decays can be used to make an overall fit to F and D, yielding indeed a bad

χ2 of 62.3/23 d.o.f.. Some modeling of SU(3) breaking is clearly required, at

least in order to improve predictions of f1, the most relevant with respect to

extraction of Vus. By use of the commutation relations of the weak vector

charge, Ademollo and Gatto showed long time ago that the first order cor-

rection to the vector form factor f1 vanishes, allowing for direct combination

of measurement of Vus from different decays. Beyond first order corrections,

recent model building can be traced back either to improved quark models

or to Chiral Perturbation Theory (χPT). Revisited quark models tend to

predict a small reduction of f1, of the order of 1-2%. Calculations based on

χPT yield larger and scattered corrections, ranging from small negative to

large positive, and should be therefore taken with some care.

1.6 The case of Ξ0 semileptonic decay

The interest in the cascade β-decay is due to many reasons. First of all, it

is the last seen of the observable hyperon β-decays and much work can still

be done. Most of all, the statistical significance of the analysis of this decay

can be improved a lot. The only available measurement to now is the one

from KTeV, whose resolution is mainly limited by statistics. A larger sample


obtained by NA48 will be used to extract an improved measurement of Vus.

From the experimental point of view, the Ξ0 β-decay is one of the most

accessible in the family of the hyperon β-decays. The Σ+ is a very clear

signature, because the analogue two body decay (Ξ0 → Σ+π−) is forbidden

by energy conservation. Thus the most dangerous background that can affect

an experiment that aims to collect this kind of events is removed by the nature

itself.

The extraction of the form factors from the Ξ0 β-decay can be quite eased

by the self analyzing power of the Σ+ → pπ0 decay. The large asymmetry

in this secondary decay (98%), imply that the study of the polarization of

the final state Σ+ of the Ξ0 decay can be performed by just observing the

correlations with the proton.

The large production of Ξ0 decays needed to obtain a high number of

β-decays (BR ∼ 2 · 10−4) can be easily achieved in the framework of the

experiments tuned for the precise measurement of the violation of CP in the

K0 decays. The large phase space that this kind of experiments have can

yield to a better collection efficiency than that obtained with the narrow

phase space selection of a usual charged hyperon beam. KTeV and NA48

are, in fact, two beautiful examples of this kind of experiments.

Another interesting point is that the vector form factors of the Ξ0 β-decay

are the same of the well measured neutron β-decay, at least in the exact SU(3)

limit. This allow to investigate in detail the effects of the symmetry breaking.

Table 1.2 contains a summary of the available experimental data on

branching ratio and g1/f1 for the allowed octet decays.

1.6.1 Vus extraction

Assuming that the effects of SU(3) breaking are under control, the extraction

of Vus is simple. Starting from the matrix element for the β-decay (1.12)

applied to the case of the Ξ0, one can obtain the value of the rate as

Γ =BR(Ξ0 → Σ+eνe)

τΞ0

=GF

60π3|Vus|2I (f1, f2, f3, g1, g2, g3) (1.16)

1.6. THE CASE OF Ξ0SEMILEPTONIC DECAY 11

W−Ξ0 = uss

e

νe

Σ+ = usu

W−n = udd

e

νe

p = udu

(a) (b)

Figure 1.2: Feynman diagram for Ξ0 (a) and neutron (b) β-decays

Decay Lifetime Branching Rate

Process (s) Fraction (10−3) (µs−1)

n→ pe−ν 886.7(1.9) 1000 1.2778(24)10−9

Λ → pe−ν 2.632(20)10−10 0.832(14) 3.161(58)

Σ− → ne−ν 1.479(11)10−10 1.017(34) 6.88(24)

Σ− → Λe−ν 1.479(11)10−10 0.0573(27) 0.387(18)

Σ+ → Λe+ν 0.8018(26)10−10 0.020(5) 0.250(63)

Ξ− → Λe−ν 1.639(15)10−10 0.563(31) 3.44(19)

Ξ− → Σ0e−ν 1.639(15)10−10 0.087(17) 0.53(10)

Ξ0 → Σ+e−ν 2.900(90)10−10 0.257(19) 0.876(71)

Table 1.2: Summary of octet baryon beta decay data.


where I is the result of integration over phase space.

The evaluation of the term I can be complex, but essentially depends on

the form factors. As already said in 1.4, some simplifications can be made.

In the case of the Ξ0, the smallness of the momentum transfer allow us to

expand in term of q2 and retain only elements O(q2).

In this expansion the q2 dependence of f2 and g2 can be neglected, because

their contribution is already of the order O(q). Moreover any contribution

from g2 can arise only from radiative corrections which do not conserve G-

parity, but are well understood.

The contribution of f3 and g3 can be safely neglected because is of the

order m2e/MΞ0.

The f1 form factor can be expressed, from (1.15), as

f1(q2) = CF (B, b)F1(q

2) + CD(B, b)D1(q2)

= CF (B, b)[F1(0) + λF q2] + CD(B, b)[D1(0) + λDq

2](1.17)

where F1(q2) and D1(q

2) can are obtained from the β-decay of the neutron,

because the Ademollo-Gatto theorem grants that the SU(3) breaking correc-

tions are of the second order.

The axial form factor g1 can only be related to neutrino reactions, but

the data are not sufficient to determine two separate slopes for the D and F

part. The work of [14] suggest to use a dipole form

g1(q2) =

g1(0)

(1 − q2/M2A)2

(1.18)

where the parameter MA can be obtained from the one measured for the

neutron decay.

Applying all the considerations and factorizing the contribution of f1(0)

one obtains

Γ =BR(Ξ0 → Σ+eνe)

τΞ0

=GF

60π3|Vus|2|f1(0)|2I

(

f2

f1

,g1

f1

,g2

f1

)

(1.19)

where I can be now calculated.

1.6. THE CASE OF Ξ0SEMILEPTONIC DECAY 13

1.6.2 Form factors extraction

Since we cannot detect a neutrino in a hyperon decay experiment, one can-

not reconstruct unambiguously all the kinematical variables of the decay in

the center of mass, but is possible to obtain unambiguous angular variables

transverse to the direction of the Ξ0 momentum.

First we consider the decay sequence[13]

Ξ0 → Q + νe , Q→ Σ+ + e (1.20)

where Q is a fictitious particle introduced for simplification purposes. Quan-

tities expressed in the Q rest frame will be denoted with an asterisk.

Then we can measure the transverse momenta of proton, electron and

neutrino in the Q frame: −→p ∗p⊥, −→p ∗

e⊥ and −→p ∗ν⊥ ' −→p ν⊥

2. The transverse

momenta are needed to calculate the unambiguous kinematic quantities

xeν⊥ =−→p ∗

e⊥ · −→p ν⊥

E∗eE

∗ν

(1.21)

and

xpν⊥ =−→p ∗

p⊥ · −→p ν⊥

|−→p ∗p|E∗

ν

(1.22)

which correspond to the electron-neutrino correlations and the polarization

of the Σ+ along the neutrino direction respectively. We can also measure the

proton-electron correlation xpe, which is the cosine of the angle between the

proton and the electron in the Σ+ rest frame.

The technique to extract the value of the form factor ratios g1/f1 and

g2/f1 is a maximum likelihood fit of the one dimensional distributions of

xeν⊥, xpν⊥, xpe and Ee (the energy of the electron in the Σ+).

2Being the Q and Ξ0 momenta almost parallel, the transverse momentum of the neu-

trino is almost the same in both the frames.

Chapter 2

The NA48 Experiment

The NA48 Experiment is a fixed target experiment performed at the CERN

SPS accelerator. In its early stage, its main goal was to measure the direct

CP violation in the KL-KS system[3].

The second phase of NA48, called NA48/1, sees a slightly modified beam

line and some improvements in the electronics of the detector, to make pos-

sible the search for very rare KS decays and the study of neutral hyperon

decays.

To perform the precise measure of the direct CP violation, the KL and

KS beams were obtained steering a proton beam on a first target (KL target)

and then steer the protons that passed through the first target to a second

target (KS target), 120m downstream the first, after an adjustment of the

intensity.

For NA48/1, the beam line is simplified and coincide essentially with the

configuration used in NA48 to produce an intense KS beam.

2.1 The Beam

The beam used by NA48 is obtained from a primary proton beam produced

by the CERN Super Proton Syncrotron (SPS). The SPS ring (7 km diameter)

is filled with two trains of bunches of about 2000 proton bunches each by the

15

16 CHAPTER 2. THE NA48 EXPERIMENT

PS Booster (PSB). (Fig. 2.1)

The bunches are 2 ns wide and there are 5 ns between two bunches. Few

empty bunches separate the trains. The bunches are accelerated with a

200MHz radio frequency system to 450GeV/c, preserving the 5 ns structure.

At the end of the acceleration, the momentum spread of the bunches

around the nominal momentum (450GeV/c) is . 0.2%. The RF is switched

off when the extraction begins. The extraction consists of a spill (called

burst) of 5.2 s. The time between the end of a burst and the begin of the

next one is 16.2 s.

The proton beam extracted is then collimated and driven to the experi-

ment location in the so called North Area of CERN.

The intensity of the beam is adjusted to about 1010 particles per burst

and sent to a beryllium target. The target is a cylinder with a diameter

of 2mm and long 40 cm. After the target, a photon converter, consisting

in a platinum absorber 24mm thick, and a sweeping magnet are placed to

reduce the photon background mainly due to π0s generated in the target.

A collimator 51 cm thick selects a beam of neutral long-lived particles (KL,

KS, Λ, Ξ0, n and γ) which forms an angle of 4.2mrad with the direction of

incoming protons.

The burst time is divided in slices 25 ns long by a 40MHz clock distributed

to all the detectors. The proton intensity is roughly constant during the whole

spill length, with a mean of 5 × 1010 particles per pulse.

2.2 The decay region

The decay region of NA48 starts at the end of the final collimator and it is

enclosed in a cylindrical steel tank (vacuum tank) evacuated to a pressure of

less than 3 · 10−5 mbar.

The vacuum tank is terminated, 90m downstream the collimator, with a

0.9mm thick Kevlar window (0.003 radiation lengths), which separates the

vacuum volume from the spectrometer region, a tank filled with Helium at

2.2. THE DECAY REGION 17

*

*electronspositronsprotonsantiprotonsPb ions

LEP: Large Electron Positron colliderSPS: Super Proton SynchrotronAAC: Antiproton Accumulator ComplexISOLDE: Isotope Separator OnLine DEvicePSB: Proton Synchrotron BoosterPS: Proton Synchrotron

LPI: Lep Pre-InjectorEPA: Electron Positron AccumulatorLIL: Lep Injector LinacLINAC: LINear ACceleratorLEAR: Low Energy Antiproton Ring

CERN Accelerators

OPALALEPH

L3DELPHI

SPS

LEP

West Area

TT

10 AAC

TT

70

East Area

LPIe-

e-e+

EPA

PS

LEAR

LINAC

2

LIN

AC

3

p Pb ions

E2

South Area

Nor

th A

rea

LIL

TTL2TT2 E0

PSB

ISO

LD

EE1

pbar

Figure 2.1: The accelerators complex at CERN. The NA48 experiment is

located in the North Area.


Figure 2.2: The proton beam and the target

PROTON STEERING MAGNET

72 mm

KS BEAMKS TARGET

AK

S CO

UN

TER

S

PROTON BEAM

21.6 mm 7.2 14.4 7.2 3.6 6.0

KS SWEEPING MAGNET

VACUUM

KS aperture diameters:

FISC 7+8

B6

10 mm

1 m

B7

KS SWEEPING MAGNET/ COLLIMATOR

VACUUM

KLAPERTURE PLUG

Figure 2.3: The Final Collimator

2.3. THE DETECTOR 19

Figure 2.4: Schematic view of the decay region and the detector.

atmospheric pressure (Helium tank).

The particles of the beam that do not decay enter a 16 cm diameter

evacuated aluminum beam pipe that goes from the Kevlar window through

all the detector down to the beam counter and the beam dump. The beam

pipe is needed to avoid interactions of the not decaying part of the neutral

beam with the matter of the detector.

2.3 The detector

2.3.1 The spectrometer

The measure of momenta and directions of the charged particles is performed

with the magnetic spectrometer. It consists of two pairs of drift chambers

(DCH), that track the charged particles before and after a magnetic dipole

that bends their trajectories. The drift chambers are not strong enough to

stand the difference of pressure between the gas mixture inside them and the

vacuum, thus they are immersed in a cylindrical tank (with axis parallel to

the beam direction) filled with Helium. The Helium is used to reduce the


Kevlar window

Drift chamber 1

Anti counter 6Drift chamber 2

Magnet

Drift chamber 3

Helium tank

Anti counter 7Drift chamber 4

Hodoscope

Liquid krypton calorimeterHadron calorimeter

Muon veto sytem

Figure 2.5: The NA48 detector


multiple scattering of the products of the decay. The gas is kept pure at 99%

with a system of filters and the purity is constantly monitored.

The four drift chambers[4] have an octagonal shape, with 2.40m diameter,

oriented orthogonally to the beam direction. Each chamber consists of 8

planes of 256 grounded sense wires oriented in four different ways (views),

X, Y, U and V, as shown in Fig. 2.6. Each sense wire is surrounded by four

potential wires kept at 2300V, Fig. 2.7. The voltage of the potential wires

is controlled by a different power supplies for each plane. The two planes of

Figure 2.6: The drift chambers’ reference system and views.

each view are staggered to resolve left-right ambiguities (Fig. 2.7). To allow

the placement of the beam pipe, the chambers have a hole in the center.

The gas that fills the chambers is a mixture of 50% Argon and 50%

Ethane, with a small addition of water vapour to slow down ageing processes.


mylar foils

12 mm

15 mm

480

mm

6 m

m6

mm

potential wires

sense wires

10 mm5 mm

t

t’

graphite coated

Figure 2.7:

The internal atmosphere of each chamber is separated from the Helium by

two thin mylar foils to reduce multiple scattering and the probability of

conversions of photons.

The fine granularity of the sense wires allows a maximum drift distance

of 5mm which implies a drift time of the order of 100 ns. The efficiency of

each view is as high as 99% with the potential wires kept at 2300V, but the

voltage can be lowered to 2200V without significant reduction of efficiency.

The position resolution for a single chamber is of 90µm.

The integral of the magnetic field of the dipole placed between the second

and the third chamber is 0.883Tm, corresponding to a momentum kick along

the horizontal direction of 265MeV/c. The uniformity of the field in the

active region is better than 10%, allowing a fast online calculation of the

track momentum, and the fringe fields at the two drift chamber closer to the

magnet is smaller than 0.02T. The direction of the magnetic field is reversed

once a week to reduce possible systematic effects due to left-right asymmetry

of the detector system.


Beam

Drift Chambers

Magnet

Beam

Drift Chambers

10 m

2.2

m

XYUV XYUV XYUV XYUV

Figure 2.8: Scheme of the NA48 Spectrometer

The momentum resolution of the system is

σp/p = 0.48% ⊕ 0.009% × p with p in GeV/c (2.1)

where first part is due to the multiple scattering in the Helium and the second

one comes from position resolution of the drift chambers.

The charge collected on the sense wires is amplified and sent to TDCs

of the read-out system. The read-out electronics of the spectrometer was

specifically re-engineered for the 2002 run. The TDCs used are the “TDC-

F1” chips developed by the University of Freiburg and ACAM mess-electronic

for the COMPASS experiment at CERN. Each chip hosts 8 TCDs with an

adjustable resolution that can reach 120 ps. Two boards, a master/slave pair,

with 16 chip per board are is used for each plane, excluding the U and V

views of the third chamber that are not read. The information of which wire

was hit and when is stored in a FIFO queue and then sent to a ring buffer on

one of the four Crate Service Card (CSC), one for each plane, where it can

wait up to 200µs. A Master Service Card (MSC) receives trigger requests

from the trigger system and dispatch them to the CSCs that, depending on

the kind of request, send the data collected for an event to the charged trigger

system or to the data acquisition system.


2.3.2 The charged hodoscope

To measure the time of the tracks with high precision a charged hodoscope

(HOD) is placed downstream the spectrometer, just after the aluminum win-

dow that closes the helium tank. It is used also to provide fast topological

information on the event to be used in the trigger.

Quadrant 4

Beam PipeHole

Second PlaneFirst Plane

Quadrant 1 Quadrant 2

Quadrant 3

Figure 2.9: NA48 Charged Hodoscope

The hodoscope consists of two planes of plastic scintillator (NE-110) 2 cm

thick and separated by 75 cm, the one upstream divided in 64 vertical stripes

and the downstream one in 64 horizontal stripes (Fig. 2.9). The light pro-

duced by the charged particles traversing the strips is collected by Plexiglas

light guides onto the cathodes of Philips XP2262B photomultipliers, one per

each stripe.

The distance between the planes and between the second one and the

calorimeter (80 cm) are chosen to reduce the effect of back scattering from

the calorimeter itself.


The strips of a plane are divided in four quadrants of 16 strips each, with

lengths varying from 60 cm to 121 cm, and widths of 6.5 cm for those closer

to the beam pipe and 9.9 cm for the others.

The readout electronics is housed in pipeline memory boards (PMB)

modules, Fig. 2.10. Inside the modules, the signal arriving from the photo-

multipliers is shaped, digitized, sampled every 25 ns and read out by a 10-bit

FADC card. At the same time the discriminated signal triggers a current

which ramps between two fixed levels and is sampled every 25 ns with a sec-

ond 10-bit FADC card. By fitting the ramp, it is possible to measure the

time with a precision better than 250 ps for a single counter (after offline

corrections).

ShapingAmplifier

10 bit 40 MHzflash ADC

analog inputfrom phototube

RampGenerator

digital inputfrom discriminator 10 bit

40 MHzflash ADC

Pulseheight

Time

Analog Board Digital Board10 + 10 bits

Pipeline

Output buffer

CONT

ROL

LOGI

C

BOARDCONTROLLER

Ctrls

PMChip

PMB Board

VMEinterface

Zero Suppressed DATA

SBCcommands

Sta

rt o

f B

urs

t

Stop

of

Bur

st

40 MHz clock

Tim

e

Sta

mp

Figure 2.10: Functional scheme of the Pipeline Memory Boards.

The high granularity of the hodoscope design minimizes the effects of

accidental activity and maximizes both the efficiency of the detection and

the time measurement resolution.

2.3.3 The electromagnetic calorimeter

Electron and photons are identified by an electromagnetic calorimeter con-

sisting of a liquid krypton quasi-homogeneous ionization chamber with a

volume of 9 m3 with only 0.8 × X0 of material before the sensible region.

The calorimeter (LKR) is located 80 cm downstream the charged hodoscope

and contained in a cryostat, formed by an external aluminum vessel and


an internal steel vessel, which maintains the krypton at the temperature of

121K.

The krypton is used both as absorber and active medium. The charged

particles forming the electromagnetic showers produced in the calorimeter are

collected by Cu-Be-Co ribbon electrodes, 40µm thick, 2 cm wide and as long

as the calorimeter (127 cm). The electrodes are organized in 13248 cells of

Figure 2.11: Scheme of the tails of a CuBe ribbon.

2×2 cm2, formed by two cathodes (grounded) and one anode (5 kV) as shown

in Fig. 2.12. The cells have a projective geometry pointing to the average

decay position in the decay volume, in this way the showers generated by

photons and electrons develop almost parallel to the electrodes. The krypton

physical properties (Tab. 2.1) grant that a typical shower is fully contained

in the 127 cm of depth of the LKR and its transversal development involve

only few cells (cluster). The energy of the particle is reconstructed using the

expected shower profile in the calorimeter.

To measure accurately the energy of a shower, the transversal position

of the cells must be accurately known. To ensure the transverse placement

of the ribbons, they are stretched between five accurately machined placed

spacer plates and the front and back plates of the calorimeter (Fig. 2.13). The

plates give also the electrodes a zig-zag or accordion geometry with an angle


+/- 0.048 rad

cathodes

anodes

2 cm x 2 cm ce l l

DETAIL ON RIBBONSAND SPACER-PLATE

Figure 2.12: LKR calorimeter cell.

Z 36

Density 2.4 g/cm3

Interaction length 60 cm

Radiation length 4.7 cm

Moliere radius 6.1 cm

Boiling point at 1 bar 119.8K

Radioactivity 500 Bq/cm3

Electron drift velocity at 5 kV/cm 0.36 cm/µs

Dielectric constant ∼ 1.7

Table 2.1: Properties of the liquid Krypton.


LKr CALORIMETER ELECTRODE STRUCTURE

CuBe ribbons Beam tube

Back plate

Front plate

Outer rods

Spacer plates

Figure 2.13: Internal structure of one quadrant of the LKR calorimeter.

of 48mrad. The advantage of the accordion geometry is that it reduces the

dependence of the signal on the impact point of the particle. The electrons

of the showers and those produced by the ionization of the krypton atoms,

because of the electric field, drift to the anode, where they induce a current.

The current induced varies non-linearly with the distance of the shower core

from the anode. In particular, the closer the core is to the anode, the lower

is the response. The accordion shape grants that a shower core does not

stay critically close to the anode as the shower develops through the detector

(Fig. 2.14). The residual correction to the energy due to the impact position

of the particle is ±0.5% and is applied offline.

The front-end “cold” electronics is mounted directly on the detector back

plate in order to minimize the noise and optimize the timing of the signal

extraction. This includes preamplifiers and a calibration system.

Outside the cryostat, a transceiver drives the output signals to 246 cus-

tom readout modules, the Calorimeter Pipeline Digitizers (CPD). Each CPD

digitizes the signals in a 40MHz FADC. To allow an accurate read out of large


+_Shower core producedby incoming e or γ

anodes

Non-Accordion Geometry Accordion Geometry

Figure 2.14: The effect of the accordion geometry of the LKR cells.

range of energies (from 3.5GeV up to 100GeV), the FADC has a 4-bit gain

switching algorithm. From the pulse height information the FADC chooses

dynamically the algorithm, or gain, optimized for the specific energy sub-

range. The chosen gain and the digitized signal are stored in a buffer which

is read by the data concentrator. This is a dedicated processor that, when a

trigger is issued, identifies the cells with energies above a predefined thresh-

old, then select which cells to read out with a cluster finding algorithm. For

a typical photon shower about 100 cells are read out.

Summed signals of the calorimeter information are also produced in the

CPDs and used by the neutral trigger system.

The importance of a good resolution of the electromagnetic calorimeter

in the measure of the direct CP violation parameter pushed for the develop-

ment of various method to measure the performance and the response of the

calorimeter. Ke3 decays are used to perform an intercalibration

To permit a precise measure of the energy of photon and electrons, the

response of the calorimeter is studied with the Ke3 decays, where the energy

of the electron is measured by both the spectrometer and the calorimeter, in

order to calibrate the detector.

After calibration factor are applied, the energy resolution is measured as

σE

E=

3.2%√E

⊕ 0.1

E⊕ 0.5% with E in GeV (2.2)


where the first term relates to sampling functions, the second to stochastic

fluctuations (electronic noise) and the third to the uncertainty in the cali-

bration factors.

Energy (GeV)

Res

olut

ion

σ(E)/E

0

0.005

0.01

0.015

0.02

0.025

0.03

0 20 40 60 80 100

Figure 2.15: The LKR energy resolution.

Any residual energy scale correction can be determine fitting the distri-

bution of the decay vertices to find the known position of the final collimator

edge.

The position of the impact point of a photon on the calorimeter can be

determined with a resolution better than 1.3mm in both x and y. For a

single photon of 20GeV, the time resolution is better than 300 ps.

2.3.4 The neutral hodoscope

Inside the active region of the LKR calorimeter an auxiliary detector is

placed, the neutral hodoscope (NHOD).

The neutral hodoscope consists of 256 bundles of scintillating fibers. Each

bundle is enclosed in an epoxy-fiberglass tube with a diameter of 7.7mm, and

contains 20 fibers of BICRON with a diameter of 1mm each. The hodoscope

is positioned at the second spacer plate, as shown in Fig. 2.16, where, in

average, the electromagnetic showers have the maximum. The fiber bundles


Figure 2.16: Mounting scheme of the NHOD fibers inside the LKR calorime-

ter.

are then grouped together and sent to 32 Hamamatsu R1668 photomulipliers

located on the calorimeter front plate, inside the krypton but outside the

active volume of the calorimeter.

For photons of more than 15GeV, the time resolution of the NHOD is

better than 300 ps. This measure is used to cross-check the time measurement

by the calorimeter.

2.3.5 The hadronic calorimeter

A conventional iron-scintillator sandwich hadronic calorimeter (HAC), 6.7

interaction length thick, follows the LKR, to measure its hadronic shower

leakage.

The HAC consists of two modules (front and back), each made of 24

scintillator planes which are divided into 44 half-strips per plane and are

arranged alternately horizontally and vertically oriented. Light guides drive

the light of the scintillators to 176 photomultipliers in such a way that the

signals of the strips in the same position and orientation are sent to the same

photomultiplier, thus that the readout is projective. Four CPDs are used to

digitize the signals.


1 m

Photomultipliers

Scintillators

Light guides

Figure 2.17: Schematic layout of the hadronic calorimeter.

The reconstructed energy resolution achieved offline is

σE

E=

65%√E

(2.3)

with E expressed in GeV.

2.3.6 The veto system

Two detectors provide the vetoing system of NA48: the Muon Veto (MUV)

and the AKL anti-counter.

The MUV

The MUV is located downstream the HAC and consists of three 80 cm of

iron walls, which act as muon filters, each followed by a plane of scintillators

strips.

The first 2 planes have 11 strips of scintillators, 1 cm thick, oriented hor-

izontally and vertically respectively, are used for the actual muon detection.

The third plane has only 6 thinner (6mm) strips oriented vertically and is


used in conjunction with the HAC mainly for monitoring the efficiency of

the other 2 planes. The strips overlap slightly to avoid inefficiencies. The

scintillators are read out at both ends of the strips by photomultipliers.

The efficiency of the MUV is close to 99% for muons above 5GeV, and

its time resolution is 350 ps.

The information of the MUV is used in the offline analysis for vetoing,

but can be also used for muon identification for particular decays both offline

and in the trigger.

The AKL

The AKL veto is used to detect secondary particles, charged ones and pho-

tons, that are going out of the detector acceptance. It consists of seven

octagonal “rings” of iron and scintillators which enclose the decay volume

as shown in Fig. 2.4. The AKL covers an acceptance region of ∼ 10 mrad

(Fig. 2.18), complementary to the main detector one.

0

20

40

60

80

100

120

140

0 20 40 60 80 100

7max

7min

6max

6min

5max

5min

4max

4min

3max

3min

2max

2min

1max

1min

z (m)

q (m

rad

)

1

23

45

67

Figure 2.18: AKL acceptance coverage.

The rings consists of two pockets each. The pocket are made of a 3.5 cm

thick iron layer, acting as a photon converter, followed by plastic scintillator

bars read out on both ends by photomultipliers. There is a total number of

144 channels.


Figure 2.19: Scheme of one of the pockets of the AKL.

The efficiency for photon detection is about 95%.

The AKL is used in the trigger to increase the purity of the data taken,

rejecting part of the accidental activity.

2.3.7 The beam monitor

At the very end of the detector system, directly behind the beam dump, the

beam counter is placed to measure the beam intensity detecting photon and

neutrons produced at the target and that go through the beam pipe to the

beam dump. It consists of one horizontal and one vertical plane each made

of 24 scintillating fiber bundles. The sensible region is preceded by a thin

layer of an absorber material, aimed to convert the photons into electrons to

be detected by the scintillating fibers. The neutrons contributes to the signal

as well, although in much smaller intensity.

The beam counter is not calibrated to give a direct measure of the beam

intensity, but is used to study the accidental activity and to give a random

trigger correlated with the instantaneous beam intensity.

2.4. THE TRIGGER 35

2.4 The trigger

The trigger system of NA48 consists of two branches, one for the identification

of the decay based on charged particles (charged trigger), another that uses

the informations provided by the calorimeters (neutral trigger). The two

branches are feed by the detectors fast logic informations and, on their turn,

feed a final decision system (trigger supervisor) that initiate the read out

of the events to be stored temporarily on disk from the detectors. The

events selected by the trigger supervisor and written on disk are read by a

software trigger used to reduce the amount of data stored definitely on tape,

by rejecting the background events.

In normal running conditions, few millions of signals per burst enter the

trigger system, of which about 50,000 are accepted by the trigger supervisor.

The typical size of the data of a burst are about 700Mb, that means about

4Tb/day. The software trigger can reduce the amount of data written on

tape to 2.8-3Tb/day.

2.4.1 The neutral trigger subsystem

The neutral trigger (L2N) is implemented in a 40MHz dead-time free pipeline.

The total latency of the pipeline is 128 clock cycles, 3, 2µs. Every 25 ns, the

trigger reconstruct online a set of physical quantities, like the total energy,

the center of gravity, the kaon vertex position and the number of peaks in

both horizontal and vertical projections. With the reconstructed quantities,

it performs a selection and send the information to the trigger supervisor and

partially also to the charged trigger chain.

To calculate physical quantities quickly, the informations of the single cells

of the LKR are summed in horizontal and vertical projections in two steps.

In the first step the cells are summed in groups of 16 (2× 8) cells, supercells,

with analog-sum circuits. For the two views (x and y) the supercells are

oriented in the two different directions (Fig. 2.21). The signal of each cell

is used twice in the analog-sum procedure. After the first step the 128 rows


Figure 2.20: Simplified scheme of the trigger system.

2.4. THE TRIGGER 37

-view stripsXNeutral Trigger

Neutral Trigger -view stripsY

X -view

(2 X 8 )x y

Y -view supercellsxy(2 X 8 )

Individual CalorimeterCells

supercells

Figure 2.21: The summing procedure scheme for defining the projections of

the LKR.

and 128 columns are grouped in 64 (128/2) raws and 64 columns with a

maximum of 16 (128/8) supercell each. The signals of the supercells enter

the Vienna Filter Module (VFM), where they are digitized by 10-bit 40MHz

FADCs, filtered to remove supercells below a threshold, then summed up

into 64 vertical and 64 horizontal projections. The SPY system fans out the

projections to PMBs, to be able to monitor the L2N at various check points,

and to the Peak Sum System (PSS). The PSS calculates the total energy

deposed in the LKR (ELKR), the first and second energy momenta, defined

as

M1x =∑6

i=1 4Ex,i(i− 32) M1y =∑6

i=1 4Ey,i(i− 32)

M2x =∑6

i=1 4Ex,i(i− 32)2 M2y =∑6

i=1 4Ey,i(i− 32)2,

and the number of peaks in each projection, with a peak-finding algorithm.

The informations provided by the PSS are sent to PMBs, for monitoring,

and to the Look-Up Table system (LUT), where they are merged to obtain

the needed physical quantities and the trigger cuts are applied. The LUT

calculate also the sum of LKR and HAC energies (ETOT) and send all the


informations to the triggers supervisor and the charged trigger chain. In

Fig. 2.22 is shown the path that the informations follows from the LKR

through the L2N.

Tra

nsce

iver

s

FADC

FILTER

DIGITALSUM

PEAK SUMSYSTEM

LOOK UPTABLES

P M B

128

128 13340

850 X850 Y

64 X64 Y

L2N

SHA

PER

S RINGBUFFER TO

DAQ

TOL2TS

CPD

ANALOGSUM

FM

Figure 2.22: Logical scheme of the neutral trigger.

2.4.2 The charged trigger subsystem

The charged trigger system consists of three layers: the pretrigger (L1C), the

trigger supervisor of level 1 (L1TS) and the Mass Box (MBOX or L2C).

L1C

In the L1C, the discriminated signal coming from the HOD, NHOD, AKL

and MUV are aligned in time and combined with fast logic modules.

From the HOD, a simple information on the topology of the event is

obtained. Coincidences of first and second plane permit to know in which

2.4. THE TRIGGER 39

Fig. 1. The signal flow in the neutral trigger.

K0LP2p0 decays sets the limit on the statistical error.

The high-intensity K0L-beam generates an instan-

taneous particle rate of +1MHz in the detector.

The relevant neutral decays KL,S

P2p0P4c are

detected by a 8m3 quasi-homogeneous electro-

magnetic Liquid-Krypton (LKr) calorimeter with

a longitudinal readout structure. The detector

readout geometry is a matrix of 20]20]1250mm3

tower cells. The active volume length is equivalent

to 27 radiation lengths.

In order to handle the high single rate a fast

readout using the initial current method has been

developed. The data is digitised and stored in ring-

buffers with a length of 200ls to allow a dead-time

in the Data Acquisition (DAQ) system.

The neutral trigger has to produce a decision

every 25 ns. The total latency has to be below

100ls, otherwise the event might be lost. The

trigger should select 2p0 events and suppress the

high background from 3-body decays from K0L.

The loss of events in which accidental activity from

other particles is present in the detector should

be low.

2. The neutral trigger pipeline

The NA48 neutral trigger is implemented in

a 40MHz “dead-time free” pipeline using the in-

formation of the LKr-calorimeter. The total latency

of the trigger pipeline is 128 clock cycles corre-

sponding to 3.2ls.

The trigger reconstructs the total energy, the

Centre Of Gravity (COG), the kaon lifetime and the

number of peaks in the horizontal and vertical

calorimeter projection online every 25 ns and per-

forms a cut on this physical quantities.

In order to calculate these quantities, the calori-

meter single-cell information is reduced to two ortho-

gonal views of projective calorimeter information.

The data flow in the neutral trigger is shown in Fig. 1.

The first step in making the granularity of the

calorimeter coarser is to add the calorimeter signals

from 16 (2]8) single cells with analogue-sum cir-

cuits to form super-cells. The information from

a single calorimeter cell is used twice to get two

orientations (x- and y-view). This is done in the

Calorimeter Pipeline Digitiser (CPD) system [3].

696 G. Fischer et al./Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 695—700

Figure 2.23: Signal flow in the neutral trigger.

quadrant there were charged particles. The signals of the quadrant are com-

bined to divide the events in the three topological classes:

• Q1

at least one charged particle in one of the quadrants, it signs decays

that have any charged particle, but it is quite noisy, taken by itself,

and fires easily on accidentals

• Q2

charged particles hit two quadrants in the same half-plane (up, down,

left or right), it signs decays were there are both neutral and charged

particles, the signal is purer than in the case of Q1, but the efficiency

is lower

• QX

charged particles in two opposite quadrants (up-left and down-right,

or up-right and down-left), it is used to identify two body decays like

KS → π+π−, the signature is quite clean, but almost useless when

dealing with mixed decays


The HNOD gives to the trigger system only the information of the pres-

ence of any kind of shower in the LKR. The signal, called T0N, is useful as

minimum bias trigger for efficiency studies.

The MUV provides informations on the compatibility of the hits in the

scintillator with one or two muons: 1µ, 2µ and looser version of the 2µ, called

2µ-loose.

The coincidences made within each pocket are summed to obtain the

AKL trigger condition, that can be used as a veto.

All the signals are synchronized and combined before going to the L1TS.

DCH multiplicity box

The “DCH multiplicity box” is a part of the CSC of DCH1 that counts the

hits in the drift chamber and issue three signals: 1TRK if the count is not

compatible with the presence of more than one track, 2-4TRK if the hits

are compatible with the presence of two or three tracks, GT4TRK if four or

more tracks seems to be present.

The logic of the multiplicity box is implemented in a FPGA (Field-

Programmable Gate Array) and can be modified if needed.

L1TS

The L1TS is fully pipelined system that works at 40MHz. It can combine a

maximum of 28 signals to obtain a 3-bit trigger code.

The signals coming from the L1C, the L2N and the DCH multiplicity box,

are synchronized and shaped to to fit one cycle of the 40MHz clock (25 ns),

a cycle of the clock is usually referred as timeslice or timeslot. The number

of clock cycles from the beginning of the burst is called Time Stamp and is

used by all the detectors to identify the data of an event in their buffers.

Before entering the L1TS, some signals can enter a prescale module

(downscaler) to reduce (downscale) of a given factor the number of hits per

burst. The downscaled trigger can be used as minimum bias trigger for effi-

ciency studies.

2.4. THE TRIGGER 41

One of the signals is sent to a Fine Time module where its position inside

the 25 ns of cycle is converted in two Fine Time (FT) bits, that will be used

by the L2C. The signal for which the FT is measured must be the base for

all the three trigger conditions sent to the Mass Box.

Even if the signals are carefully aligned, some jitter is still possible for

edge effects. To increase the efficiency of the coincidences, inside the L1TS,

just before the decisional part, some of the signals can be widened to three

timeslices, by replicating them, inside the pipeline, in the preceding and

following timeslices.

The decisional part of the L1TS consists of a system of Look-Up Tables

organized in three levels as shown in Fig. 2.24.

Inputbits

0 to 15

Inputbits

16 to 27

A1.

lA

1.h

A2.

lA

2.h

B2

B1

C

Tri

gger

Wor

d

Level CLevel BLevel A

8

8

8

8

8

8

3+2

Figure 2.24: Logical representation of the decisional LUTs of the L1TS.

L2C

When the L1TS finds a candidate event, it sends the trigger, the Time-Stamp

and the Fine Time to the MSC of the DCH readout. The trigger information

is distributed to the chambers CSCs that send the informations of the times

of the hits in the planes of DCH 1, 2 and 4, for the requested event, to the

Mass Box.

The A&B cards, or Coordinate Builders, receive the data of the hits in the

two planes of a view. There is one A&B card for each view of the chambers


L1 DCH

MSC

TS+FTQx

Etot

2tr

TS TDC

A B

A&B

Coordinates

Event Dispatcher

8 ppc

Event Workers

1 12

1 8MISC

TS+

MB

Xan

swer

TS

SupervisorTS

L1on

L1on

AB

ED

DCH

L2

readout

TRIGGER CHARGED

12 packets

Trigger L1+L2 DCH readout

MBX

MBX

A&Bcards

technical gallery

Figure 2.25: Scheme of the MBOX connections with the DCH readout, the

L1TS and the trigger supervisor.

2.4. THE TRIGGER 43

1, 2 and 4. Putting together the raw data coming from the two planes of

a view, the Coordinate Builder process them through a 40MHz pipelined

algorithm to obtain a pairs indexes that feed a 2D Look-Up Table which

gives the corresponding coordinate value.

The coordinates of the hits in the 12 considered views are sent to the

Event Dispatcher (ED) that route them to the first available Event Worker.

Each of the 8 Event Workers uses the 12 coordinate packets, delivered by

the ED, to build the particle space-points, tracks and magnetic deflections.

With the space-points of the first two drift chambers, the EW find vertices

and fill a list with them, then it loops on the list and, combining them with

the space-points of the fourth chamber, calculate momenta and invariant

masses.

Fig. 1. The charged trigger inside the experiment.

Fig. 2. KPp p decay in the spectrometer elements used by the

L2C (not to scale).

100kHz, and the level 2 trigger (L2C) which redu-

ces that rate down to about 2 kHz. The L1C is a fast

logic trigger, based on several simple criteria, which

achieves a first selection of the charged events data

and injects them into the L2C. The L2C is a parallel

processing system mixing hardware and software

elements; for each event, it computes the coordi-

nates of the particle in the drift chambers, recon-

structs tracks, calculates the kinetics and flags the

event as signal or background. This paper describes

the salient features of the L2C.

2. Basic concepts

2.1. The charged detection principles

The axis of the Kaon beam defines the z-axis of

the coordinate system of the experiment. Each drift

chamber (DCH) has 8 parallel sense wire planes, all

perpendicular to the z-axis. They are grouped by

staggered pairs to form 4 coordinate views —

X,½,º,» VIEW’s — (Fig. 2). Each VIEW is essen-

tially made of 512 parallel wires perpendicular to

the axis of the coordinate it measures. Whenever

a charged particle crosses a VIEW, it necessarily

goes through two neighboring wires, leaving an

electric pulse on each. The coordinate of the cross-

ing point (also called space-point) is computed by

combining the coordinates of the wire pair with an

analysis of the timing difference between the two

pulses.

In principle, two VIEWs (x and y) would be

enough to determine the space-point of a particle

inside a chamber. But since we are interested in

pairs of particles (KPp`p~), a typical event

comprises a pair of x coordinates and a pair of

y coordinates; a third coordinate (u"(x#y)/2)

corresponding to a fixed linear combination of

x and y is then needed to determine which x is

associated to which y. Finally, since each VIEW

has an inefficiency close to 1%, a fourth plane

(v"(y!x)/2) is added to each DCH to improve

the overall trigger efficiency.

The L2C uses all the hits produced in DCH1,

DCH2 and DCH4 to compute the coordinates,

tracks and kinetics of each event it receives.

2.2. The trigger principles

The whole NA48 experiment is synchronized by

a 40MHz clock, that is, time is defined for all

687S. Anvar et al./Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 686—694

XI. ELECTRONICS

Figure 2.26: An example of a decay with two charged particles (K0 → π+π−)

in the spectrometer as it is reconstructed by the Mass Box.

The L2C is an asynchronous queued system. The requests of the L1TS

are first queues in a FIFO queue inside the MSC of the spectrometer readout,

then are fed into the FIFO of the Coordinate Builders, which calculate the


coordinates and push the results in the FIFO of the ED. The filling of the

queues depends on the time elapsed between two requests (Poissonian), and

on the time the Mass Box need to process the events, which varies depending

on the complexity of the event itself. The length of the queues can be, in

principle, increased to be able to handle the worst case, but the limited length

of the detector buffers (200µs) forces the queue to be small (2-3 places) to

avoid that an event waits too long before being read out.

To control the FIFO fillings, an XOff mechanism is implemented within

the L1TS–MSC–L2C chain. In normal working operation, a signal called

L1ON is set to the logical level ON. When a problem, like a FIFO full or the

DCH readout too busy, occurs, the L1ON signal is lowered to prevent that

the L1TS sends any other request to the system. The L1ON is then raised

when the system is again able to handle events.

After all the calculations, the results, in the form of a set of tagging bits

and the time-stamp of the event, are sent to the final stage of the hardware

trigger, the decisional system.

2.4.3 The decisional system

The decisional system of NA48, the L2TS or Trigger Supervisor, collects

the informations from L1TS, Mass Box, L2N and L1C and make the final

decision to write or not the event on disk.

Fig. 1. Block diagram of the NA48 Trigger Supervisor.

private bus and monitored by a single board CPU.2

The TS is hardware controlled by a "nite state

machine during the burst, and by the CPU in the

interburst period. The CPU, running a real-time

Unix-like operating system,3 is the system bus mas-

ter and is used to set up and interface the TS with

the NA48 run control program.

Fig. 1 shows a block diagram of the TS, indicat-

ing the main components.

3.1. Input stage

The TS receives and correlates both synchronous

and asynchronous trigger informations, the latter

occasionally out of time order. The input stage is

structured as four identical subdetector cards, each

dedicated to a di!erent trigger source (L1TS, L2C,

NT and one used for miscellaneous signals). Each

source provides the TS with up to 24 bits of data,

synchronized with the system clock, together with

a strobe used for data validation, at a maximum

rate of 40 MHz. These signals have already been

aligned in time among themselves at the source,

therefore no additional time adjustment is required

in the TS.

2FIC 8234 from Creative Electronic Systems, Geneve, CH.

3OS-9 from Microware Systems Co., Des Moines, IA, USA.

The trigger information is identi"ed by a 30-bit

timestamp indicating its 25 ns time slot within the

burst. Asynchronous trigger sources, like L2C, pro-

vide their own timestamp together with the data,

while for synchronous ones (L1TS, NT) the time-

stamp is derived by 40 MHz counters located on

the TS.

Since the timestamp information is required to

retrieve detector data from the circular bu!ers, it is

very important that di!erent trigger sources pro-

vide the same timestamp for a given event. The

relative time alignement of the synchronous trigger

sources is realized by using di!erent presets for the

40 MHz counters.

Data from each trigger source are continuously

stored into dual-ported, 8K deep, 56-bit wide fast

static RAMs, addressed by the 13 low-order bits of

the timestamp. Simultaneously with the writing, the

memories are read out sequentially via the second

port after a "xed (programmable) delay of &100

ls. This delay is the maximum time budget given to

the L2C for its computations.

The 8K memory space is scanned every 204.8 ls,

being rewritten many thousand of times in a burst.

To recognize and discard data referring to `olda

triggers, without having to clear the memories

themselves, a special technique is adopted. The 17

high-order bits of the timestamp are stored into the

memories together with each trigger word; during

the reading process, these bits are matched with

22 R. Arcidiacono et al. / Nuclear Instruments and Methods in Physics Research A 443 (2000) 2026

Figure 2.27: Scheme of the trigger supervisor.

2.4. THE TRIGGER 45

Subdetector cards

Four identical subdetector cards, collect the information given by the four

subsystems. The informations coming from the L2C, which arrives with an

almost random delay, are synchronized with those coming from the other

sources, which instead have a fixed delay, using the time-stamp associated.

The signals in each card, formed and synchronized with the 40MHz clock,

enter a widening circuit, analogous to that also present in the L1TS, that

enlarges some signals to increase the efficiency of the coincidences.

L2TS Look-Up Table

The signals, synchronized and opportunely widened, are transferred from

the subdetector cards to the Look-Up Table card (LUT) via a private VME

bus. The LUT is the module that actually combines the signals. It consists

of three stages, the first two made with Xilinx FPGAs and the third with

memories. The first stage consists of two Xilinx (Xil1 and Xil3 of Fig. 2.28)

Xil1

Xil3

Xil2

lut1

InputSignals

(96 bits)

TriggerWord

(16 bits)

RoutingStage

Routing& Logic

StageLogicStage

Xil4

lut4

lut3

lut2

72b

96b

96b

72b

12b

12b

12b

12b

4b

4b

4b

4b

Figure 2.28: Data-flow in the L2TS Look-Up Table card.

which receive all the 96 input bits and route part of them to the next stage

chips. The second stage Xilinxes (Xil2 and Xil4) receive 72 bits each and

route them to the four chips of the final stage. To fit in the 48 bits in input

of the final stage, some logic can be performed inside the second stage. The

memories of the third stage (lut1 to lut4) calculate four bits of the final

trigger word each, 16 bits in total.


All the stages can be programmed via software to achieve the maximum

flexibility of the system.

Each of the 16 bits of the trigger word can enter a downscaler circuit, out

of which only a fraction 1/D of the times it is propagated out of the circuit.

The 16 possible downscaling factors D can be independently set via software.

After the downscaling stage, the 16 bits are counted and sent to the

Derandomizer card.

Usually, each bit of the trigger word is used to mark a particular kind

of event, but some, or all, of them can be grouped into a “coded” sub-

triggerword. In this way instead of n independent signatures we can have

2n − 1 signatures1, with the drawback that they are mutually exclusive.

Derandomizer

The time between two triggers has a Poissonian distribution, so it can be

smaller then the time needed by the detectors readout electronics to finish

the extraction of the data (20µs).

To avoid that the trigger requests are sent to the detectors while they are

still extracting data, a Derandomizer card is inserted in the trigger chain.

The Derandomizer consists essentially of a FIFO queue with a fixed serv-

ing time. A trigger can exit the queue only when are elapsed at least 20µs

since when the previous trigger was sent to the detectors, otherwise it waits

inside the queue.

When an event enters the queue, the time-stamp is also inserted in the

queue. The time-stamp will be used to tell the detectors which are, inside

their ring buffers, the data about the event candidate.

TAXI card

The actual duplication and delivery of the triggers request are accomplished

by a dedicated module, the TAXI card.

1The number of configurations obtained from n bits is 2n − 1 instead of 2n because the

case with all the bits set to 0 cannot be considered a signature.

2.4. THE TRIGGER 47

Inside the TAXI card, the event triggerword and time-stamp are sent to a

fan out together with the number of the event inside the burst (Global Event

Number), which must match the count done inside each detector readout

(Local Event Number) to grant consistency.

After the duplication, the words are serialized and sent to the detectors

through pairs of coaxial cables, using a set of AMD TAXI-Chips, that is

where the card take its name.

Control card

All the operation of the seven cards of the L2TS are arbitrated by a eighth

card, the Control Card.

Its role is to get the experiment clock and the signals that indicate the

boundaries of the bursts and fan them out to the other modules. It also start

or stop the acquisition (RUN phase) inhibiting the work of the LUT card.

2.4.4 The software trigger

After that the L2TS has selected the events to be written on disk for each

burst, the Software Trigger (L3) read the burst files from disk and rejects the

events that would have not been used in any analysis.

The triggerword, according to a configuration file, tells the L3 which kind

of action perform on it. The actions can be of various type, like write only a

fraction of the events that enter the action, but the most common is to send

the event to a Filter or a set of Filters.

A filter is a routine that, depending on the characteristics of the event,

decides if write it on tape or reject it. Each filter can be a simple selection

routine or can consist in a set of subfilters, which on their turn check the

event and if it is interesting it is accepted. When an event is accepted, the

bits corresponding to the filters that accepted the event are set. If the event

is accepted by a subfilter, both the bits corresponding to the subfilter and to

its filter container are set.


The work of the L3 is so deeply integrated in the data acquisition that is

usually considered part of it, instead of part of the trigger system.

2.5 Data acquisition

When a trigger is issued by the L2TS, the detector readout systems extract

the data associated to the event and transfer them to a set of subdetector

PCs (one for each subdetector).

At the end of each bursts, during the interburst period, the data are

moved from the subdetector PCs to the Event Builder PCs. In the EB PCs,

the data are stored grouping together the information of all the detectors

on a event by event basis, while in the subdetector PCs, all the events were

grouped together detector by detector. The EB PCs perform also consistency

checks on the data collected, for example all the detector must have the same

number of events with the same triggerwords sequence.

Each EB PC holds only a part of the burst that it sends through a Gbit

Ethernet Link to a pool of dedicated disk servers in the computer center of

the main site of CERN.

A complex of programs, the CDR system (Central Data Recording), put

together the part of a burst (burstlets) and fills a database of the stored

bursts.

When a new burst is inserted into the database, it is also added to the

list of burst to be processed by the L3. A pool of PCs hosts copies of the

L3 programs (L3Trigger) that, as soon as they can process a burst, ask a

common server (ControlPool) for one, either saying that they are ready or

sending a brief status report of the last processed busts. The ControlPool

take a burst from the list of bursts to be processed, and give it to the ready

L3Trigger together with the names of the output disk servers. If the request

of the L3Trigger was associated with the report of a just processed burst, the

ControlPool updates the database, the list of files to be copied on tape and

mark the original burst as removable.

2.6. DATA PROCESSING AND ANALYSIS 49

A daemon program, part of the CDR system, polls the list of file to be

written on tape and, as soon as they are enough, starts a program that

merges them into one superfile and write them to a tape of the Tape Server.

After the copy to tape is finished the database is updated, the entries are

removed from the list of files to be stored on tape and the files on disk are

marked as removable.

Another daemon is used to remove the files from the disk servers to econ-

omize the available disk space.

2.6 Data processing and analysis

The raw-data files, i. e. the files written on disk by the EB PCs, are huge

and the time needed to analyze the data they contain make them impossible

to be used.

To make things easier for the people, two other file formats are available:

COmPACT and SuperCOmPACT[17].

COmPACT files are produced by the L3. After the data taking period,

all the raw data stored on tape are processed again by the L3 (reprocessing)

which is configured to not reject events and to write many COmPACT data

streams. Each stream contains the events useful for some kind of analysis,

for example we have, for the 2002 data, a hyperons stream (hyperon decays

study), a KS → π0ee stream, an autopass stream (L3 efficiency measure)

etc. .

The main advantage of the COmPACT format is that, instead of the low

level informations of the raw data (like the hit times in the drift chambers),

it contains high level human-usable informations, like the momenta of the

reconstructed tracks. In order to save disk space and reduce the time needed

to read from disk, COmPACT files are written to disk compressed with the

zlib library.

Even if the data in the COmPACT format are dense of information and

much smaller then those in the raw-data format, their size is still to big to


Gbit Switch

HIPPI Switch

STK Tape Server

Gbit Switch

ReadoutSubdet

ReadoutSubdet

ReadoutSubdet

ReadoutSubdet

PC PC

ChargedTrigger Trigger

Neutral

Trigger supervisor

ReadoutSubdet

PC PC PC

PC PC PC PC PC PC PC PC

PC

MonitWSAlpha

MonitWSAlpha

MonitWSAlpha

MonitWSAlpha PC PC PC PC

PC PC PC PC PC PCPC

GigaRouter

NA48 Detectors (Charged Spectrometer, Calorimeters, Veto Counters)

Switch for Fast Ethernet

Switch FDDI/GBit(XLNT Millenium)

(Cisco Catalyst 5505 SupIII)

40MHz

100Mbit Switch

Offline PC Farm

7km Gbit Ethernet Link

HIPPI

HIPPI

HIPPI

Gbit

Gbit Gbit

FDDI

100Mbit

800GByteSun 450

Disks

CS-2 (1.7 TByte disks)

S.Luitz 6/1998

ExperimentalArea

Computer Center

The NA48 Central Data Recording Infrastructure

Figure 2.29: Logical scheme of data-flow from the detectors to the tape and

disk servers.

2.6. DATA PROCESSING AND ANALYSIS 51

permit to run quickly an analysis program on the whole statistic collected

during 2002, so another analysis framework is provided: SuperCOmPACT.

SuperCOmPACT files have essentially the same physical informations

that are contained in the COmPACT files with the exclusion of the informa-

tion that usually are not needed during the analysis phase. The size of the

SuperCOmPACT files is about 1/10 of the corresponding COmPACT files

thanks to a lossy compression approach. Instead of storing numbers 32 bits

long, only the significative part (according to the detector sensibility) is re-

ally stored on disk, this allows a reduction of the number of bits needed for

a number. To write the SuperCOmPACT files, the zlib library is used, as

well.

To read the COmPACT and SuperCOmPACT files, the COmPACT pro-

gram is used. It provides a framework that allows users to write their analysis

code within predefined functions and so have access to the data structures,

either in FORTRAN or in C.

For my analysis I implemented a set of C++ classes to hold the informa-

tions read from either COmPACT of SuperCOmPACT files and to be able

to use the ROOT data analysis framework[5] facilities.

Chapter 3

Analysis

3.1 Overview

To be able to obtain |Vus| with good accuracy is essential to measure precisely

the branching ratio. Data collected by NA48 allow to measure the branching

fractionΓ(Ξ0 → Σ+eνe)

Γ(Ξ0 → Λπ0)(3.1)

with an accuracy of about 2%.

The measurement is performed by estimating the number of Ξ0 decays

for each of the two channels in the decay volume of the experiment. The

correction factors applied to obtain the numbers of decays in the volume

from the numbers of the decays observed are obtained by a Montecarlo.

3.1.1 Signal channel

To measure the branching ratio of Ξ0 → Σ+eνe with the NA48 detector, we

have to take into account that is not possible to observe directly the Σ+ and

we must rely on detection of its decay products. The main decay modes of

the Σ+ are

Σ+ → pπ0 BR = (51.57 ± 0.30)%

Σ+ → np+ BR = (48.31 ± 0.30)%

53

54 CHAPTER 3. ANALYSIS

Since neutrons are not detectable by the NA48 detector, we have to select

the decay mode

Ξ0 → Σ+ eνe

→ pπ0

The π0 is also not observable directly, but we can detect the daughter

photons1 (π0 → γγ).

Thus the detectable particles in the final state of the decay will be one

electron, one proton and two photons.

Ξ0

νe

Σ+

π0

γ

γ

p

e

Figure 3.1: Scheme of the signal channel

3.1.2 Normalization channel

The mode used to normalize to, the normalization channel, is

Ξ0 → Λπ0 BR = (99.522 ± 0.032)%

where the Λ following decay mode is detected

Λ → pπ− BR = (63.9 ± 0.5)%

The final state of the decay is very similar to that of the signal: two

charged particles and two photons, the differences being that this decay is

1The NA48 detector can also see other decay modes of the π0, but we can safely ignore

them.

3.2. TRIGGER SETUP 55

fully contained (no missing energy) and, instead of an electron, we have a

π−.

Ξ0Λ

π0

γ

γ

p

π−

Figure 3.2: Scheme of the normalization channel

3.2 Trigger setup

During the data taking of 2002 for NA48, the trigger was configured to collect

many different physical channels

For the hyperon semileptonic decays, a dedicated trigger was setup, which

also included the Ξ0 β-decay.

The normalization channel was taken with the so called charged minimum

bias trigger (see later).


The trigger used to select Ξ0 β-decays was a logic combination of some of the

informations provided by MassBox. To be accepted, an event was required

to satisfy the L1TS request (allowing the event to be sent to the MassBox),

the L2TS request (to be processed by the L3), and finally the L3 filter re-

quirements.

The L1TS requests for a good event were the following.

• one particle detected by the charged hodoscope


• nothing seen by the AKL

• hits in DCH1 compatible at least on track

• at least 15GeV in the LKR or at least 30GeV summing LKR and HAC

The L2TS conditions to record an event on disk as signal candidate, to

be later analyzed by the software trigger, were

• two tracks forming a vertex, with a closest distance of approach (CDA)

smaller than 5 cm

• the distance between the hit-points of the two tracks in DCH1 must be

greater than 5 cm (DCH1dist)

• the ratio between the larger momentum of the two tracks and the

smaller one must be grater than 3.5 (P-ratio)

• assuming the two tracks to be a proton (antiproton) and a π+ (π−) the

squared invariant mass of them must differ from the squared mass of a

Λ (Λ) by at least 25 MeV2

• if the P-ratio is smaller than 5, assuming the two tracks to be pions

the squared invariant mass of them must differ from the mass of a K

by at least 20 MeV2

In addition, to make the computation faster, some shortcut triggers were

implemented in the MassBox algorithm. The conditions that triggered those

shortcuts are also considered signatures of a possible good event.

The Ξ0 β-decay subfilter of the hyperon semileptonic filter of in L3 ac-

cepted an event with

• at least two clusters in the LKR with energy above 2GeV

• at least one positive and one negative tracks

• P-ratio > 3.5

3.2. TRIGGER SETUP 57

• one track with momentum above 20GeV/c

• distance between clusters and tracks not associated to them bigger than

5 cm

• one track with E/p > 0.85 (energy of the associated cluster divided by

the momentum of the track)

• another track with E/p < 0.95


During the run, the configuration for the trigger that was intended to collect

normalization channel events changed many times. To maximize the length

of the period with a stable trigger, instead of the dedicated L2TS trigger, we

use the so called charged minimum bias trigger.

The main purpose of the charged minimum bias trigger is the study of the

trigger efficiency, so it consists of the L1TS request downscaled by a factor

D = 35. Therefore the final sample only contains about 1/35 of the events

that the dedicated trigger should have collected. Nevertheless, for the huge

amount of Ξ0s produced, we still have enough events that the contribution

of the normalization channel to the statistical error is far below the signal

channel one.

Thus the trigger condition in the L2TS to accept an event as a candidate

for Ξ0 → Λπ0 is the same as that in the L1TS for the signal channel:

• one particle detected by the charged hodoscope

• nothing seen by the AKL

• hits in DCH1 compatible with one or more tracks

• at least 15GeV in the LKR or at least 30GeV summing LKR and HAC

but downscaled by a factor D = 35.

The L3 requests for the normalization channel were


• at least one vertex

• P-ratio > 3.5

• invariant mass of the two tracks (under the assumption that one was

a proton and the other a pion) equal to the mass of the Λ within

10 MeV/c2

• distance between clusters and tracks not associated to them larger than

5 cm

• at least two clusters in the LKR with energy above 2GeV

3.3 Data set

During 2002 data taking, after a first period dedicated to the setup of the

detector systems, some tests were made in order to configure the trigger for

maximum efficiency.

The trigger configuration was stable from the 1st of August (from run

13941) up to the 18th of September (up to run 14186), the last day of data

taking.

3.4 Reconstruction

The laboratory reference frame is defined with the z axis parallel to the axis

of the detector and pointing from the collimator to the calorimeter, the x

axis horizontal and pointing to the left looking at the calorimeter from the

collimator, and the y axis vertical and pointing upward. The origin is placed

6m upstream the end of the final collimator.


The reconstruction of an event is based on the information collected by the

LKR and the spectrometer.

3.4. RECONSTRUCTION 59

From the energies and the positions of two clusters in the LKR without

an associated track, and assuming that they are the result of a π0 decay,

one can calculate the z coordinate of the decay vertex of the π0, under the

assumption that it was close to the z axis and the angle between the photons

and the z axis was small enough that one can assume sin(α) ' α, using the

formula

zvertex = zLKR −

√

∑

i,j,i>j EiEj

(

(xi − xj)2 + (yi − yj)

2)

M(3.2)

where Ei are the energies of the clusters, xi and yi are the coordinates of

the clusters on the calorimeter surface, and M is the mass of the particle

decayed. With only two clusters, (3.2) simplifies to

zπ0 = zLKR −√

E1E2r212

Mπ0

(3.3)

where r12 is the distance between the two clusters.

Using the z of the π0 vertex, which coincides with the vertex of the Σ+,

and using the information of the track of the proton, we can estimate also

the x and y coordinates of the vertex of the Σ+. We can then use the vertex

obtained to calculate the vector momenta of the photons. Summing the 4-

momenta of the photons we have the 4-momentum of the π0 which, summed

with the 4-momentum of the proton (obtained imposing the mass of the

proton and the momentum of the track), gives the 4-momentum of the Σ+.

The crossing point of the Σ+ reconstructed flight path and the electron

track is taken as the Ξ0 vertex. The 4-momentum of the Ξ0 cannot be

reconstructed because of the missing neutrino 4-momentum.


The decay vertex of the Λ is reconstructed upon finding the intersection of

the proton and π− tracks. Its 4-momentum is calculated by adding together

the 4-momenta of the two tracks, taken as a proton and a π−.

The z coordinate of the π0 vertex, coinciding with that of the Ξ0, is cal-

culated from the two photons clusters using (3.3). The other two coordinates


of the vertex are obtained by tracing the reconstructed path of the Λ back

to zπ0 . The point is used to calculate the 4-momenta of the photons and

the π0 as we do for the signal channel. The 4-momentum of the Ξ0 is then

calculated adding the 4-momenta of the Λ and the π0.

3.5 Selection

When setting up a trigger, one cannot have high efficiency together with high

purity of the sample. Usually it is preferred to reduce the purity in order to

increase the efficiency.

The good events are so mixed with a number of mistaken events. In order

to extract from the sample only the events that belong to the signal channel

or the normalization channel, and to reject background events a set of cuts

was devised.


To select the decay Ξ0 → Σ+eνe with Σ+ → pπ0 and π0 → γγ, I request that

• the event was selected by the L2TS as a Ξ0 β-decay (or one of the

MassBox shortcuts)

• the L3 flagged the event as a Ξ0 β-decay

• two electromagnetic clusters

– have energy between 3GeV and 50GeV

– have distance from the beam pipe between 15 cm and 110 cm

– have no dead cell closer than 2.5 cm

– have RMS below 1.2 cm

– have no cluster closer than 15 cm in space and 10 ns in time

• the π0

3.5. SELECTION 61

– has the z of the vertex between 6m and 60m

– has energy between 15GeV and 65GeV

– its clusters have no tracks closer than 20 cm in space and 10 ns in

time

– the two clusters closer in time than 2 ns

• the proton

– has momentum between 30GeV/c and 180GeV/c

– has E/p < 0.85

– has the space-point at DCH1 between than 12 cm and 40 cm far

from the beam pipe center

– has the space-point at DCH2 and DCH4 between than 12 cm and

110 cm far from the beam pipe center

• the electron


– has E/p between 0.95 and 1.05

– has the space-point at DCH1, DCH2 and DCH4 between than

12 cm an 110 cm far from the beam pipe center

• the Σ+


– has dt between proton and π0 lower than 2 ns

• for the Ξ0

– the distance between the 2 tracks at DCH1 must be greater than

8 cm

– pp/pe > 5

– CDA between Σ+ and e below 3 cm


– invariant mass of the pair Σ+e between 1.170 GeV/c2 and 1.315 GeV/c2

– the distance of the vertex from the “ideal” flight path below 1.8 cm

– transverse momentum with respect to the ideal direction below

0.16GeV/c

– invariant mass of the tracks, under the assumption that they are

pions, different from the mass of the K0 within 36 MeV/c2 if the

P-ratio is below 7

– invariant mass of the tracks, under the assumption that they

are a proton and a π−, different from the mass of the Λ within

17 MeV/c2

– zΣ+ − zΞ0 between −10 m and 30m

– distance between the impact point of the electron onto the LKR,

and the associated cluster below 2 cm

– dt between Σ+ and electron lower than 2 ns

If, after the cuts, in the event more than two clusters or two tracks are

present, thus giving more than one Ξ0 beta decay candidate, I select only the

candidate that has the better χ2 defined as

χ2 =∆tclusters

2

0.36+

∆ttracks2

0.16+

(∆tΞ0 − 0.1)2

0.09(3.4)

where ∆tclusters and ∆ttracks are the differences in time between the clusters

and the tracks, and ∆tΞ0 is the difference between the time of the Σ+, evalu-

ated as the average of the time of the π0 and the time of the proton, and the

time of the electron, being the time of the π0 given by the weighted average

of the times of the two clusters. The numbers at the denominators are the

variances of the distributions of the time differences fitted on the data.

The signal region is defined as being the reconstructed mass of the Σ+

equal to the world average within 8MeV (Fig. 3.3).

3.5. SELECTION 63

SigmaMassEntries 6993

Mean 1.179

RMS 0.0196

2GeV/c1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.220

100

200

300

400

500

600

SigmaMassEntries 6993

Mean 1.179

RMS 0.0196

Mass+Σ

Figure 3.3: Reconstructed Σ+ mass. The red arrows indicate the limits of the

signal region. The peak on the left is essentially composed of the irreducible

background of Ξ0 → Λπ0 with the Λ decaying β.


To select the decay Ξ0 → Λπ0 with Λ → pπ− and π0 → γγ, I request that

• the event was selected by the L2TS as a charged minimum bias

• the L3 flagged the event as a Ξ0 radiative decay

• two electromagnetic clusters

– have energy between 3GeV and 50GeV

– have distance from the beam pipe between 15 cm and 110 cm

– have no dead cell closer than 2.5 cm

– have RMS below 1.2 cm

– have no cluster closer than 15 cm in space and 10 ns in time

• the π0

– has the z of the vertex between 6m and 60m


– has energy between 15GeV and 65GeV

– its clusters have no tracks closer than 20 cm and 10 ns in time

– the two clusters closer in time than 2 ns

• the proton


– has E/p < 0.85

– has the space-point at DCH1 between than 12 cm an 40 cm far


• the π−


– has E/p < 0.85

– has the space-point at DCH1 between than 12 cm an 110 cm far


• for the Λ

– the distance between the 2 tracks at DCH1 must be greater than

8 cm

– pp/pπ− > 5

– CDA between p and π− below 2 cm

– momentum between 50GeV/c and 210GeV/c

– invariant mass of the tracks, under the assumption that they are

pions, different from the mass of the K0 within 36 MeV/c2 if the

P-ratio is below 7

– reconstructed mass equal to the world average within 4 MeV/c2

– dt between the two tracks lower than 2 n

• for the Ξ0

3.6. MEASUREMENT PROCEDURE 65

– momentum between 70GeV/c and 250GeV/c

– zΛ − zΞ0 between −10 m and 40m

– extrapolated impact point onto the LKR closer to the center of

the detector than 8 cm

– dt between Λ and π0 lower than 2 n

As for the signal channel, if, after all the cuts, we still have more than

one Ξ0 → Λπ0 decay candidate, we take only the one with best χ2 defined

similarly to (3.4)

χ2 =∆tclusters

2

0.36+

∆ttracks2

0.16+

(∆tΞ0 + 0.1)2

0.16(3.5)

where ∆tclusters and ∆ttracks are the same as in (3.4), while ∆tΞ0 is now defined

as the difference between the time of the π0 (weighted average of the times of

the clusters) and the time of the Λ (average of the time of the tracks). As for

the signal channel, the denominators are the variances of the distributions of

the time differences obtained by fitting the data.

The signal region is defined as being the reconstructed mass of the Ξ0

equal to the mean within 4MeV (Fig. 3.4).

3.6 Measurement procedure

The number of Ξ0 β-decays that I observe is

Nobserved = Ndecayed · BR(Ξ0 → Σ+eνe) · BR(Σ+ → pπ0) · A · ε (3.6)

where Nobserved is the number of events I reconstruct, Ndecayed is the number

of Ξ0 decayed in the fiducial volume, A is the acceptance of the detector and

ε is the efficiency of the trigger ε = εL1TSεL2TSεL3TS.

For the normalization channel we have an analogous relation

Nobserved = Ndecayed · BR(Ξ0 → Λπ0) · BR(Λ → pπ−) · A · ε/D (3.7)


Xi0MassEntries 264364

Mean 1.315

RMS 0.002045

/ ndf 2χ 121.3 / 97

Constant 9.203± 3156

Mean 4.31e-06± 1.315

Sigma 5.178e-06± 0.001562

2GeV/c1.3 1.305 1.31 1.315 1.32 1.325 1.330

500

1000

1500

2000

2500

3000

Xi0MassEntries 264364

Mean 1.315

RMS 0.002045

/ ndf 2χ 121.3 / 97

Constant 9.203± 3156

Mean 4.31e-06± 1.315

Sigma 5.178e-06± 0.001562

mass0Ξ

Figure 3.4: Reconstructed Ξ0 mass. The red arrows indicate the limits of the

signal region.

where · indicates the quantity related to the normalization channel, D is the

downscaling factor applied in the L2TS and the trigger efficiency is now given

by ε = εL1TSεL3TS. We assume that the efficiencies of the L1TS for the two

channels are the same because we used the same trigger logic.

The branching ratio of the Ξ0 β-decay relative to the decay Ξ0 → Λπ0 is

thus given by

BR(Ξ0 → Σ+eνe)

BR(Ξ0 → Λπ0)=Nobserved

Nobserved

· BR(Λ → pπ−) · A · εL3TS/D

BR(Σ+ → pπ0) · A · εL2TS · εL3TS

(3.8)

where I already simplified the common terms.

The measure of the branching ratio is thus reduced to the counting of the

events for both signal and normalization channel, the measure of the trigger

efficiencies and the acceptances.

Chapter 4

Montecarlo

In order to accurately evaluate the acceptance ratio between the signal and

normalization channels, a Montecarlo program was written, as an evolved

version of the standard NA48 simulation program NASIM[12]. The main

requirements for this version of NASIM were to satisfactorily reproduce the

experimental cascade energy spectrum, and to add generators for both the

signal and the normalization channels.

4.1 NASIM structure

The program NASIM is a Montecarlo simulation software based on the CERN

package GEANT321[10].

The behavior of NASIM can be tuned with a configuration file, allowing

one to change almost all the parameters of the simulation.

The simulation is done in three stages: decay simulation, physical simu-

lation of the detector and data simulation.

4.1.1 Decay simulation

The simulation of the decay chain is implemented by user-made routines.

This allow for a complete control on the decay properties, to study the effect

of different theoretical models or parametrizations.

67

68 CHAPTER 4. MONTECARLO

The kinematical parameters of the mother particle are generated accord-

ing to a distribution based on experimental data. Using the Ξ0 → Λπ0 decays

observed during a special run in 1999, the Ξ0 momentum distribution was

fitted and parametrized by the analytical function

W (pΞ0) =0.144p2

Ξ0

pp

e−13.37p

Ξ0pp (4.1)

where pp is the momentum of the primary proton. In 2002, the proton beam

intensity and momentum changed with respect to those of 1999, the necessary

adjustment to the momentum distribution are fitted by a third order poly-

nomial multiplied to W (pΞ0). This parametrization does not include angular

dependence, but it can be ignored at the first order approximation because

of the small aperture of the final collimator (∼ 1 mrad). Nevertheless, an

inaccurate angular distribution can originate sizeable systematic effects to

the measurement of the form factors.

The decay vertex of the mother particle is generated according to the

PDG lifetime value. The flight length in the laboratory frame (between 0

and Zmax = 100 cm) is calculated as

λ = Zmax − βγcτ ∗ log(

1 +(

eZmaxβγcτ∗ − 1

)

R)

(4.2)

where the product βγ is calculated from the momentum and the mass of

the decaying particle, cτ ∗ is the life time in cm and R is a random number

uniformly distributed between 0 and 1.

The kinematical parameters of the mother particle are passed to the rou-

tine that implements the decay generator. Each decay mode uses a dedicated

routine, selected by an option in the configuration file. A description of the

generators of the Ξ0 decays will be given in subsection 4.2.

The generator routines take care of filling an event sub-record, contain-

ing the kinematical parameters of all the decay products. The 4-momenta,

generated in the rest frame of the decaying particle, are finally boosted to

the laboratory frame. The decays of secondary particles, like Σ+ and Λ, are

generated by the routine also handling the primary decay.

4.1. NASIM STRUCTURE 69

All the kinematical parameters of the decay chain are then stored into

an array and passed to the GEANT engine to perform the simulation of the

common physical processes.

In order to increase the speed of the event production, it is possible to

avoid the simulation of the full event when one of the detectable particles is

going outside the detector acceptance. The rejection algorithm (kinematical

cut) is implemented by requiring that all the charged particles have a distance

from the axis of the detector at DCH1 between 6 and 150 cm, and that all

the photons hit the LKR between 6 and 125 cm from the axis (Fig. 4.1).

Being the geometrical acceptance small (about 2-5%) the time needed for a

Montecarlo production can be thereby reduced by a factor ∼ 20.

Kinematics cuts for DCH

-150

-100

-50

0

50

100

150

-150 -100 -50 0 50 100 150

Kinematics cuts for LKr

-150

-100

-50

0

50

100

150

-150 -100 -50 0 50 100 150

Figure 4.1: Kinematic cuts applied for charged (left) and neutral (right)

particles.

The kinematical cuts has been applied in the production of the Montecarlo

samples used for this analysis after having verified that it does not affect the

number of accepted events.

4.1.2 Physical simulation

The geometry of all the subdetectors of NA48, except AKL and NHOD, is

accurately described by NASIM and used by the GEANT library.


The simulation of the dipole magnetic field of the spectrometer can be

done either using a measured map or with a fixed momentum kick. The

configuration file permits to selects which polarity of the dipole to use, in

order to allow for a comparison between Montecarlo and data for a given

configuration of the spectrometer.

The GEANT engine propagates all the the detectable particles through

all parts of the detector, simulating the interaction with the encountered

media. The physical processes simulated by GEANT are:

• positron annihilation

• bremsstrahlung

• Compton scattering

• decay in flight

• δ-ray production

• hadron interaction

• continuous energy loss

• multiple scattering

• photoelectric effect

The photoelectric effect is the only process that NASIM does not require

GEANT to simulate.

The simulation of a full electromagnetic shower in the LKR is possible

with GEANT, but it is a very intensive task that can take several seconds. To

speed up the simulation, many prebuilt showers are collected in libraries[9],

containing the energy deposited in each calorimeter channel by single particle,

fully simulated events. A use of these libraries, instead of the full simulation,

increases the generation rate to ∼ 10 Ξ0 decays per second.

The energy released in the HAC is obtained from the scintillator energy

in the shower library. Notwithstanding a non-linear relationship between the

4.1. NASIM STRUCTURE 71

scintillator energy and the true particle energy, for sake of speed NASIM

uses a straight line. This means that the results are about correct for low

energies but for high energies the simulated HAC energies are too low. For

this reason, to avoid avoid systematic effects due to differences between the

simulation and the real detectors, the information provided by the HAC is

not used in the analysis.

4.1.3 Data digitization

After the tracing of the particle through the detector, the energies left in the

detectors are converted to the same format of real data.

Several routines perform a reconstruction quite similar to the one done

on the real raw data. The output is then processed by the same code used

for the real data to produce COmPACT files, with the only addition of the

kinematics generated by NASIM.

In spite of the this general similarity, Montecarlo data files are somewhat

different from the real data files. The most important differences being that

the event times are not reconstructed properly, and the NHOD is not present

at all. The absence of NHOD is not particularly relevant, as it is used mainly

to collect minimum bias triggers or to check the time resolution of the LKR.

The time informations are used in the real data mostly to reject accidental

background. Since in the Montecarlo accidentals are not simulated, it is not

important to have time information with event record.

The simulated distribution of the energy measured by the LKR is not

exactly the same as in data. In NASIM it is gaussian while in the data

non-gaussian tails are present which tend to underestimate the energy of the

photon or the electron. The effect is small, but methods to study the effect

of non-gaussian tails have been developed within the collaboration.

As already said, the simulated HAC data cannot be used when the energy

released in the HAC is high (like it happens for the protons present in the

decay considered).

The trigger system is only partially implemented, and only in a simplified


fashion. There is the possibility to include the MassBox code in NASIM, but

it is used only to study the efficiency of particular algorithms before their

actual implementation for the data taking.

4.2 Hyperon decays implementation

The version of NASIM used before 2002 was not able to simulate Ξ0 decays,

because they were not needed in the analysis of kaon decays. Those decays

has been now implemented to be able to analyze the hyperon decays.

4.2.1 Simulation of Ξ0 → Λπ0 decay

The Ξ0 → Λπ0 decay amplitude can be written in the form[11]

M = GFm2π0 · Bf (A− Bγ5)Bi (4.3)

where A and B are constants. From this formula, one can find that the

transition rate, in the initial hyperon rest frame, is proportional to

R =1 + γωf · ωi + (1 − γ)(ωf · n)(ωi · n)+

α(ωf · n + ωi · n) + βn · (ωf × ωi) ,(4.4)

where n is a unit vector in the direction of the final Λ momentum, and ωf

and ωi are unit vectors in the directions of, Ξ0 and Λ spins respectively. The

parameters α, β and γ are defined as

α =2Re(s∗p)

|s|2 + |p|2 (4.5)

β =2Im(s∗p)

|s|2 + |p|2 (4.6)

γ =|s|2 − |p|2|s|2 + |p|2 (4.7)

where s = A and p = |pf |B/(Ef +mf ), Ef and pf being the energy and the

momentum of the Λ. The parameters α, β and γ satisfy the relationship

α2 + β2 + γ2 = 1 (4.8)

4.2. HYPERON DECAYS IMPLEMENTATION 73

If we sum over the Λ polarizations, the (4.4) becomes

R = 1 + αωi · n (4.9)

which implies that the Λ is emitted anisotropically with respect to the Ξ0

spin direction, with asymmetry coefficient α.

The polarization of the Λ in its rest frame can be expressed as[16]

~PΛ =(α+ ~PΞ0 · n)n + β(~PΞ0 × n) + γn × (~PΞ0 × n)

1 + α~PΞ0 · n(4.10)

where ~PΞ0 is the polarization of the Ξ0 and both ~PΞ0 and n are defined in

the rest frame of the Ξ0.

By replacing Ξ0 by Λ, Λ by p and π0 by π−, the same formulae describe

the decay Λ → pπ−.

The values of the parameters α, β and γ, for both the Ξ0 and the Λ decay

generators, have been taken from [16].

The description of the decay given above has been implemented by gener-

ating the direction of the emitted Λ in the Ξ0 rest frame in polar coordinates.

The cosine of the angle θ between the direction of the Λ and the polarization

of the Ξ0 is generated according the distribution

p(cos θ) =1

2(1 + αP cos θ) (4.11)

where α = −0.411 is the one defined in (4.4) and P is the module of the

polarization of the Ξ0. The angle ϕ around the direction of the polarization

is generated uniformly between 0 and 2π. The momentum of the Λ is fixed

because it is a two body decay. The momentum of the π0 is obtained from

the one of the Λ by sign reversal.

The decay of the Λ is generated in its rest frame by using a reference

frame where its polarization, calculated with the (4.10), is along the positive

z direction. The direction of the proton is generated similarly to the one of

the Lambda described above. The momentum of the proton is then rotated to

a reference frame with all axes along the laboratory frame. The momentum

of the π− is the same as the proton with opposite sign. Both proton and


π− momenta are then boosted to the Ξ0 rest frame and from there to the

laboratory frame. This double boost is needed to preserve the correct angular

distributions, keeping in mind that the product of two Lorentz boosts is

equivalent to a boost ⊕ a rotation.

The momentum of the π0 is directly boosted to the laboratory rest frame.

Its decay is implemented by generating the direction of one the photons, in

the π0 rest frame, as a 3-vector with a uniform distribution in the whole

solid angle. The momenta of the photons is obtained from the two body

decay kinematics. The momenta are then boosted to the laboratory frame

without passing through the Ξ0 rest frame. Here the double boost is not

needed because the angular distributions are uniform and the extra rotation

associated to the combination of boosts does not change them.

Ξ0 R.F.

x

y

z

P

Λϕ

θ

Figure 4.2: Definition of the angles used in the Ξ0 → Λπ0 decay.

4.2.2 Simulation of Ξ0 β-decay

In the amplitude of the Ξ0 β-decay, the presence of the two small parameters

q/M , where q is the momentum transfer and M is the mass of the Ξ0, and

me/M , where me is the mass of the electron, allow one to use an effective

Hamiltonian, where only terms of the second order in q/M are included, and

the terms with me/M are neglected. Labeling the Ξ0 as B and the Σ+ as b,

4.2. HYPERON DECAYS IMPLEMENTATION 75

we can write for the decay B → beν

M = 〈be|Heff|Bν〉 (4.12)

where

Heff =√

2GS

1 − σl · e2

[GV +GAσl · σb

+GeP σb · e +Gν

Pσb · ν]1 − σb · ν

2

(4.13)

HereGS is the same defined in (1.12), e and ν are unit vectors in the directions

of the electron and the neutrino, and σb and σl are spin operators acting

respectively on the lepton and on the baryon final state.

The effective coupling coefficients GV , GA, GeP and Gν

P are functions of

the form factors and depend on the reference frame. In the Ξ0 rest frame we

have

GV = f2 − δf2 − ν+e2MΞ0

(f1 + ∆f2)

GA = −g1 + δg2 + ν−e2MΞ0

(f1 + ∆f2)

GeP = e

2MΞ0[−(f1 + ∆f2) + g1 + ∆g2]

GνP = ν

2MΞ0(f1 + ∆f2 + g1 + ∆g2)

(4.14)

where ν and e are the energies of the neutrino and the electron, δ = (MΞ0 −MΣ+)/MΞ0 and ∆ = (MΞ0 +MΣ+)/MΞ0 = 2 − δ. [8]

The differential decay rate is then given by

dΓ =|M|2(2π)5

EΣ+ +MΣ+

2MΞ0

e2ν3

emax − ededΩedΩν (4.15)

After summing over the final spins and averaging over the initial spins,

|M|2 is given by

|M|2 =G2Sξ[1 + ae · ν + APΞ0 · e+ BPΞ0 · ν

+ A′(PΞ0 · e)(e · ν) + B

′(PΞ0 · ν)(e · ν)+ DPΞ0 · (e× ν)]

(4.16)

where PΞ0 is the polarization vector of the Ξ0 and the coefficient can be


expressed as

ξ = |GV |2 + 3|GA|2 − 2Re[GA∗(Ge

P +GνP )] + |Ge

P |2 + |GνP |2

ξa = |GV |2 − |GA|2 − 2Re[GA∗(Ge

P +GνP )] + |Ge

P |2 + |GνP |2

+2Re(GeP∗Gν

P )(1 + e · ν)ξA = −2Re(GV

∗GA) − 2|GA|2 + 2Re(GV∗Ge

P +GA∗Gν

P )

ξB = −2Re(GV∗GA) + 2|GA|2 + 2Re(GV

∗GνP −GA

∗GeP )

ξA′ = 2Re[GeP∗(GV +GA)]

ξB′ = 2Re[GνP∗(GV −GA)]

ξD = 2Im(GV∗GA) + 2Im(Ge

PGνP∗)(1 + e · ν)

+2Im[GA∗(Gν

P −GeP )].

(4.17)

The decay of the Σ+ is described in the same way as the Λ decay in the

normalization channel.

The actual implementation of the decay is done generating, in the Ξ0 rest

frame, the three 4-momenta of Σ+, electron and νe in the same way of a usual

3-body decay. Quantity obtained are then adapted to the distribution given

in (4.15) with the acceptance-rejection method (Von Neumann)[16], i. e. a

number y is randomly chosen with uniform distribution between 0 and dΓmax,

and if the value of dΓ obtained with the generated 4-momenta is lower than

y, the 4-momenta are kept otherwise they are rejected and the procedure

starts again.

The decay of the Σ+ is implemented in the same way as the Λ, with the

appropriate asymmetry parameter. Also in this case the 4-momenta in the

laboratory frame are calculated with a double boost, from the Σ+ rest frame

to the Ξ0 rest frame and from there to the laboratory frame.

4.3 Polarization of the Ξ0

The generators implemented in NASIM for the two new decays include the

Ξ0 polarization.

From previous experiments[18], it was observed that Ξ0s produced at a

non zero angle by a proton beam are polarized orthogonal to the production

4.3. POLARIZATION OF THE Ξ0 77

hXi0BetaEnergy

Entries 4475

Mean 148.1

RMS 35.37

GeV0 50 100 150 200 250 300

0

50

100

150

200

250

300

hXi0BetaEnergy

Entries 4475

Mean 148.1

RMS 35.37Montecarlo

Data

energy (Signal)0Ξ hXi0LambdaEnergy

Entries 264364

Mean 135.4

RMS 27.37

GeV0 50 100 150 200 250 300

0

5000

10000

15000

20000

25000

hXi0LambdaEnergy

Entries 264364

Mean 135.4

RMS 27.37Montecarlo

Data

energy (Normalization)0Ξ

(a) (b)hXi0BetaElMomentum

Entries 4475

Mean 10.34

RMS 3.476

GeV/c0 5 10 15 20 25 30 35 40 45 50

0

100

200

300

400

500

600

hXi0BetaElMomentum

Entries 4475

Mean 10.34

RMS 3.476

Montecarlo

Data

electron momentum hXi0LambdaEnergy

Entries 264364

Mean 135.4

RMS 27.37

GeV0 50 100 150 200 250 300

0

5000

10000

15000

20000

25000

hXi0LambdaEnergy

Entries 264364

Mean 135.4

RMS 27.37Montecarlo

Data

energy (Normalization)0Ξ

(c) (d)

Figure 4.3: Comparison between MC and data. (a) Energy of the Ξ0 for

the β-decay. (b) Energy of the Ξ0 for the normalization channel. (c) Mo-

mentum of the electron in the β-decay. (d) Momentum of the proton in the

normalization channel.


plane

P ∝ pp × pΞ0

|pp × pΞ0 | (4.18)

where P is the polarization vector of the Ξ0s, pp is the momentum of the

proton and pΞ0 is the Ξ0 momentum.

The formula (4.18) does not give any information about the module of

the polarization, which also leaks a satisfactory theoretical explanation. In

order to know the polarization of the NA48 Ξ0 beam, we have therefore to

measure it1.

The straightforward method to measure the polarization in the Ξ0 → Λπ0

decay, is to sort the events in bins of Ξ0 energy and for each bin look at the

distribution of the angle between the direction of the Λ and the direction

of the x axis in the Ξ0 rest frame. We use the x axis because, according to

(4.18), the direction of the polarization of the Ξ0 beam in NA48 is expected

to be parallel to that axis.

Due to acceptance effects, the distributions are not straight lines, as they

should be according to (4.11), rather they look more like that in Fig. 4.4.

Assuming that the acceptance in bins of energy and cos θ∗ do not change

too much for different polarizations, it would be possible to measure the

polarization by correcting for the acceptance the distributions and measuring

the asymmetry. Indeed, the basic assumption is not applicable, because the

acceptance in bins of cos θ∗, obtained with the Montecarlo, heavily depends

on the polarization. Moreover, the effect of the acceptance is such that

the asymmetry of the cos θ∗ distributions are almost washed out whichever

polarization. The strong suppression of the asymmetry is mainly due the

cut on the distance of the proton from the center of DCH1. To show this, I

generated a million of Ξ0 → Λπ0 decays with the (exaggerated) polarizations

of −100%, 0% and +100% along the x axis direction. In those three samples,

I selected the events which passed the cut on the proton radius, for different

1From [18] we can expect to have a polarization between 5% an 20% toward the negative

x axis direction, however our beam setup is different from their one, so we cannot use easily

their results.


cts_lam_rEntries 5495Mean 0.006181RMS 0.4789

)*θcos(-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

100

200

300

400

500

600

700


Λ) *θcos(

Figure 4.4: Example of distribution of cos θ∗Λ, i. e. the cosine of the angle

between the Λ direction in the Ξ0 rest frame and the direction of the Ξ0

polarization (x axis). The plot represents Montecarlo data for unpolarized

Ξ0s in one energy bin.

values of the minimum radius. The distributions of the cosine of the angle

between the x axis and the direction of the Λ in the Ξ0 rest frame, cos θ∗Λ,

for different cuts are shown in Fig. 4.5. As can be seen, the asymmetry of

the distribution is quickly vanishing, as opposed to the acceptance integrated

over cos θ∗Λ, which stays rather constant.

While the simple method for the measurement of the Ξ0 polarization

cannot be used, by looking at Fig. (4.6), one sees clearly that the asymmetry

is not completely washed out by the acceptance. Therefore it should be

possible, by fitting data with Montecarlo, to measure the polarization of

the Ξ0 beam with a resolution better than 5%. What is needed is a huge

amount of Montecarlo events, at least of the same order of magnitude of the

real events in the data, which are about 9 · 106. If we consider an average

acceptance of 0.8%, we need at least 1 · 109 generated events.

Another more promising way to measure the Ξ0 polarization bears on a

fit of statistical distributions of the proton angle in the Λ rest frame (which

indeed depends on the Ξ0 polarization) with a hybrid Montecarlo technique.

No final result is available yet, but if we consider that most likely the po-


-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

6000

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

6000

Pol -100%

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

6000

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

6000

No Pol

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

6000

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

0

1000

2000

3000

4000

5000

6000

Pol +100%

Figure 4.5: The distribution of cos θ∗Λ for polarization of the Ξ0 beam of −1,

0 and 1 along the x axis (MC). The lines correspond to different values (from

0 to 18 cm in steps of 2 cm) of the cut on the distance of the proton from the

axis of the detector. The red line is the one corresponding to the cut applied

in the analysis (12 cm).



-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 10

100

200

300

400

500

600

700


pol = 0pol = +1pol = -1

(reconstructed)Λ) *θcos(

Figure 4.6: Comparison between the distributions of cos θ∗Λ for unpolarized,

+100% polarized and -100% polarized Ξ0s (Montecarlo simulation).

larization of the Ξ0 beam is between −20% and 0% along the x axis, and

the acceptance integrated over cos θ∗Λ is almost independent of the polariza-

tion, we can assume that the effect of the polarization on the branching ratio

measure is below our statistical sensitivity. So it will be estimated and taken

into account as a systematic error.

For the measurement of the form factors, instead, the precise knowledge

of the polarization of the Ξ0 beam is crucial.

Chapter 5

Results

5.1 Acceptances

The acceptance for a decay mode, as it is intended here, is defined as the

ratio between the number of decays reconstructed after all the selection cuts

and the number of decays occurred in the detector decay volume, and in-

cludes both the detector geometrical acceptance and the efficiency of the

selection cuts. The convolution of the two is computed because of their tight

correlation. In fact the geometrical acceptance depends on the size of the

detector, but the cuts applied restrict the effective dimensions of both the

spectrometer and the calorimeter.

The acceptance depends on many parameters, so in principle it should

be computed in bins of all these parameters and applied to the data bin by

bin. With too many bins of too many parameters, the number of events in

each bin is bound to be very small. In order to reduce problems due the

small bin statistics, only the energy of the Ξ0s and the longitudinal position

in the detector of their decay vertex are taken as parameters. The bins in

energy are 10GeV wide, while the longitudinal position is measured in units

of proper timecτ

cτ ∗=

1

cτ ∗MΞ0

EΞ0

(zvtx − z0) (5.1)

where cτ ∗ is the life time of the Ξ0, MΞ0 and EΞ0 are its mass and its energy

83

84 CHAPTER 5. RESULTS

respectively, zvtx is the z coordinate of the decay vertex and z0 is an offset

used to define the position from where we start to measure the life times.

The value of z0 has been fixed at 30 cm downstream the final collimator to

avoid collimator effects, not accurately simulated in the Montecarlo. It is

possible of course to have also negative values for cτ , meaning that the decay

occurred upstream z0. The bins in cτ/cτ ∗ have a width of 0.2 .

5.1.1 Energy of Ξ0 in the β-decay

It is not difficult to measure the energy of the Ξ0 in the decay mode Ξ0 → Λπ0,

because all the final state particle are detected. For the β-decay, instead, the

energy of the neutrino is unknown, and the total energy of the Ξ0 cannot be

reconstructed.

From the 4-momentum conservation, constraints on the masses of the

neutrino (assumed massless) and Ξ0, and the direction of the Ξ0 momentum

obtained, with good approximation, connecting the center of the target with

the decay vertex, we can write a system of eight equations with eight unknown

variables: the components of the 4-momenta of the neutrino and the Ξ0. The

system is

pΞ0 = pQ + pν

|pν|2 = 0

|pΞ0 |2 = MΞ02

(pΞ0)x/(pΞ0)z = ∆x/∆z

(pΞ0)y/(pΞ0)z = ∆y/∆z

(5.2)

where pΞ0 and pν are the unknown 4-momenta of the Ξ0 and the neutrino, ∆x,

∆y and ∆z indicate the position of the decay vertex relative to the position

of the target in the laboratory reference frame and pQ is the 4-momentum of

the pair (Σ+e).

The system can be solved to obtain the energy of the Ξ0 (EΞ0) from known

5.1. ACCEPTANCES 85

quantities. If we define the quantities

MQ2 = |pQ|2 ~d =

(

∆x∆y∆z

)

f =~pQ · ~d|~d|

M =MΞ0

2 +MQ2

2

and

A =EQM

f 2B =

M2

f 2

C =EQ

2

f 2− 1

the energy of the Ξ0 can be written as

EΞ0 =A±

√

B − CMΞ02

C(5.3)

The ± uncertainty, mathematically due to the fact that is a second order

system of equations, physically correspond to the impossibility to tell whether

the neutrino, in the Ξ0’s rest frame, is emitted forward or backward with

respect to the direction of the momentum of the Ξ0.

In principle, use of the Montecarlo should allow to disentangle the un-

certainty. This unfortunately proves to be unrealistic. Moreover, the term

under square root (B − CMΞ02) is quite small and the measurements errors

make it often negative (about a 60% of the times). Therefore it is not pos-

sible to measure the Ξ0 energy from what we can detect of the decay. One

is thus led to apply an average correction to the visible energy EQ. Always

using the Montecarlo, the (generated) energy of the Ξ0 was fitted by a second

order polynomial in the energy released in the detector

EΞ0 = p0 + p1 ·EQ + p2 · EQ2 (5.4)

Fig. 5.1 show the result of the fit. The plots show that a second order

polynomial is a good average correction and that the error on the corrected

energy is mainly below 7-8GeV.


EnergyCorrectionEntries 14773

Mean 144.8

RMS 35.77

/ ndf 2χ 0.3693 / 31

p0 3.876± 1.515

p1 0.06769± 1.063

p2 0.0002459± -0.0001674

(GeV)QE60 80 100 120 140 160 180 200 220 240

(G

eV)

0Ξ

E

0

50

100

150

200

250

EnergyCorrectionEntries 14773

Mean 144.8

RMS 35.77

/ ndf 2χ 0.3693 / 31

p0 3.876± 1.515

p1 0.06769± 1.063

p2 0.0002459± -0.0001674

Q vs. E0ΞE

(a)

EnergyCorrection_3s

Entries 14773

Mean 144.9

RMS 35.74

(GeV)QE60 80 100 120 140 160 180 200 220 240

E (

GeV

)∆

-5

0

5

10

15

EnergyCorrection_3s

Entries 14773

Mean 144.9

RMS 35.74

QE vs. E∆

(b)

Figure 5.1: Correction to the observed energy. (a) Fit of EΞ0 as a quadratic

polynomial of the EQ. (b) ∆E = EΞ0 − EQ as a function of EQ with the

result of the fit superimposed. In the plots, the error bars correspond to the

standard deviations of the distribution of EΞ0 for a given EQ.

5.1. ACCEPTANCES 87

5.1.2 Acceptance computation

The acceptance for the signal channel has been computed using a sample

of 1108965 Montecarlo generated events with energies between 40GeV and

300GeV and the decay vertex between 2m and 55.5m from the origin of the

NA48 reference frame. The polarization used to simulate the Ξ0 decay is

−5% along the x direction. The events that pass the selection cuts are about

2.4 · 104.

For the normalization channel, in order to have a number of Montecarlo

accepted events comparable to the data, a sample of 5157528 events were

generated. The polarization and the ranges in both energy and z of the vertex

used are the same as those used for the simulation of the signal channel. The

acceptance for this kind of events is smaller than that of the Ξ0 β-decay, so

only 4.1 · 104 events pass all the cuts.

In Fig. 5.2 and 5.3, acceptances as a functions of E and cτ are shown.

For high values of cτ the statistics is low and the error (not shown) on the

acceptance value is large. That is the reason for the big fluctuations visible

on the right of the plots.

*τc12

34

5GeV

80100

120140

160180

200220

2400

0.01

0.02

0.03

0.04

0.05

0.06

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Acceptance for the Signal

Figure 5.2: Acceptances for the signal channel as functions of E and cτ .


*τc12

34

5GeV

80100

120140

160180

200220

2400

0.005

0.01

0.015

0.02

0.025

0.03

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

Acceptance for the Normalization

Figure 5.3: Acceptances for the normalization channel as functions of E and

cτ .

5.2 Trigger efficiency

The trigger efficiency measures how many events that had the characteristics

to be accepted by the trigger system were, instead, not recognized:

ε =N(good events triggered)

N(good events)(5.5)

To measure the trigger efficiency, one has to record also the events that

the trigger did not flag. Obviously it is impossible to record all the events,

and it is not needed as well. It is, in fact, enough to record some events

regardless what the trigger decision it was. This sample is called “minimum

bias sample” and it is collected via dedicated triggers (minimum bias trig-

gers). Not all the events flagged by the minimum bias triggers are stored,

only a fraction of them, selected with the downscaling functionality of the

L2TS, is actually written on disk.

Of course, the minimum bias triggers have their own efficiency as well,

5.2. TRIGGER EFFICIENCY 89

which is not relevant because it cancels in the ratio:

N(good events triggered and with m.b.t.)

N(good events with m.b.t.)

=N(good events triggered)/(εmb ∗D)

N(good events)/(εmb ∗D)=

=N(good events triggered)

N(good events)=

= ε

(5.6)

For the trigger efficiency of L1TS, the neutral minimum bias trigger

(T0N) is used. This trigger is given by a signal from the neutral hodoscope

and is downscaled by a factor 100.

The charged minimum bias trigger (ChMB) is used to measure the effi-

ciency of L2TS. It is the same trigger condition that an event needs to be

passed to the MassBox, downscaled by a factor 35.

For the trigger efficiency of the software trigger, the minimum bias sample

is not collected via a real trigger, but just by selecting a 2% of all the events

that enter one filter regardless to what is the final decision of the filter. These

events are called autopass events.

The errors on the measure of the trigger efficiencies are considered sources

of systematic uncertainties.

5.2.1 Level 1

The trigger efficiency of the L1TS is in principle the same for both the signal

and the normalization channel, thus it cancel in the formula used to calculate

the branching ratio. We any way expect it to be high.

In the neutral minimum bias sample, 55481 good normalization events

were found of which 55220 with the L1TS trigger condition set. Thus the

L1TS trigger efficiency is

εL1TS =N(good events triggered)

N(good events)=

55220

55481= (99.53 ± 0.03)% (5.7)


Being the neutral minimum bias trigger downscaled by a factor 100, we

expect about 50 good events, too few to have a measurement of the L1TS

trigger efficiency for the signal channel.

5.2.2 Level 2

The MassBox is used only to flag the Ξ0 β-decays, thus we do not have to

calculate the L2TS trigger efficiency for the normalization channel.

The number of good signal events found in the sample is 207 of which

176 with the right trigger condition, 175 having the main trigger bit set and

1 having one of the shortcuts. The efficiency is thus given by

εL2TS =N(good events triggered)

N(good events)=

176

207= (85.0 ± 2.5)% (5.8)

The reason for the low efficiency of the Level 2 trigger can imputed to

the difficulty that the MassBox had in reconstructing some events, mainly

for the large number of hits in the drift chambers.

5.2.3 Level 3

Being the L3 a software trigger, we expect it to be highly efficient, but it is

still quite important to measure its efficiency.

In the autopass sample, 5888 good normalization events were found and

every one was flagged as Ξ0 radiative decay. We can assume the efficiency to

be

εL3TS > 99.949% 95% c.l. (5.9)

For the signal channel, 229 good events were found in the sample, all of

them with the requested L3 trigger bit set, so

εL3TS > 98.69% 95% c.l. (5.10)

5.3. OBSERVED EVENTS 91

5.3 Observed events

5.3.1 Fiducial region

In some regions of the plane cτ -EΞ0 , the acceptance is quite low, either for

the signal channel or the normalization channel, or else affected by large

uncertainty. Events of the normalization channel with high Ξ0 energy are

collected less efficiently than those with low energy. Conversely, the signal

channel events are collected more efficiently if the Ξ0 has high energy.

In order to reduce the uncertainty due to small acceptance, which can

amplify small inaccuracies in the Montecarlo,only a reduced section of the

cτ -EΞ0 plane is used, defined as the fiducial region.

The boundary of the fiducial region are chosen as a compromise to have

acceptances not too small on both signal and normalization channels. The

limits on the upper part of the plane are tailored around the acceptance of

the normalization channel, while, on the low energy side, the acceptance for

the signal channel is taken to fix the limits. The ranges of cτ used for each

energy bin considered are shown in Table 5.1 and in Fig. 5.4 the region is

shown on top of the acceptances.

EΞ0 (GeV) cτ min cτ max

130 0 2

140 0 2.2

150 0 2.4

160 0 2

170 0 1.8

180 0.2 1.4

190 0.2 1.2

200 0.2 0.8

210 0.2 0.6

220 0.2 0.4

Table 5.1: cτ ranges for each energy bin used.



The total number of events passing all the selection criteria that identify a

good Ξ0 β-decay is 6993. Among them, only 4474 are inside the signal region.

Considering only the region used in the cτ -energy plane, 2193 events are

found. Applying the acceptance correction bin by bin and the correction for

the trigger efficiency and the branching ratio of Σ+ → pπ0, the total number

of Ξ0 β-decays in the fiducial region is 2.069 · 105 with a statistical error of

4.6 · 103.


The total number of events passing all the cuts to define a Ξ0 → Λπ0 decay

is 264364. Applying the signal region cut, only 250641 survive.

In the fiducial region 119256 good events are found. After the acceptance

and downscaling corrections and taking into account the branching ratio of

Λ → pπ−, one is left with 7.482 · 108 events in the fiducial region, with a

statistical error of 2.5 · 106.

5.3.4 Background

After all the selection cuts, a small fraction of background events is still

present. For the normalization channel the fraction of background events is

negligible, i. e. much smaller than the statistical error expected for the final

measurement (see Fig. .3.4). For the signal channel, the background is still

a sizeable fraction of the events in the signal region.

The Σ+ mass distribution plot (Fig. 5.5) can be fitted with the sum of

three components: two gaussians with the same mean and a constant term,

p(m) = b +N1e(m−M

Σ+)2

σ21 +N2e

(m−MΣ+)2

σ22 (5.11)

The constant term b gives a measurement of number of background events

under the mass peak, which is approximated as 4.06 ± 0.32 evts/bin, that,

with a bin width of 0.5MeV, corresponds to 8.12±0.64 evts/MeV. The signal

5.3. OBSERVED EVENTS 93

0

0.002

0.004

0.006

0.008

0.01

0.012

*τ/cτc-0.5 0 0.5 1 1.5 2 2.5 3

(G

eV)

0Ξ

E

60

80

100

120

140

160

180

200

220

240

0

0.002

0.004

0.006

0.008

0.01

0.012

Acceptance for the Normalization

region used

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

*τ/cτc-0.5 0 0.5 1 1.5 2 2.5 3

(G

eV)

0Ξ

E

60

80

100

120

140

160

180

200

220

240

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Acceptance for the Signal

region used

Figure 5.4: Fiducial region used in the cτ -energy plane compared to the

acceptance for the normalization channel (top) and the signal channel (bot-

tom).


region considered is 8MeV wide, translating into an estimated background

of 130±10 events. Considering that we have 4474 events in the signal region,

the correction on the branching ratio is expected to be of the order of

130 ± 10

4474= (2.9 ± 0.2)% (5.12)

which is of the same order of the expected statistical error.

To better estimate the correction to the branching ratio, two side bands

are used: one on the left of the peak (from 1.170GeV to 1.177GeV) and one

on the right of the peak (from 1.202GeV to 1.211GeV). The side bands are

chosen far enough from the signal region to be populated only by background

events (shown in Fig. 5.5) and have the same total width as the signal region.

The left one is also far enough from the background due to the β-decay of

the Λ to be not contaminated by it.

SigmaMassEntries 6993Mean 1.179RMS 0.0196

/ ndf 2χ 110.3 / 73bg 0.3169± 4.067

1N 24± 429.3 µ 2.709e-05± 1.19 1σ 7.339e-05± 0.001212 2N 26.77± 120.5 2σ 0.0002026± 0.002821

2GeV/c1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.220

100

200

300

400

500

600

SigmaMassEntries 6993Mean 1.179RMS 0.0196

/ ndf 2χ 110.3 / 73bg 0.3169± 4.067

1N 24± 429.3 µ 2.709e-05± 1.19 1σ 7.339e-05± 0.001212 2N 26.77± 120.5 2σ 0.0002026± 0.002821

Mass+Σ

Figure 5.5: Mass of the Σ+. In the plot are visible the fit to the mass (black

line), the signal region (red arrows) and the side bands used to estimate the

background (blue arrows).

The events in the side bands are used to correct, in each cτ -EΞ0 bin, the

number of events in the signal region.

5.4. BRANCHING RATIO 95

5.4 Branching ratio

The actual measure of the branching ratio is done only in bins of energy to

increase the statistics in each bin, leaving open an investigation of energy

dependent systematic effects.

The number of events in each energy bin is obtained by integrating over

cτ (within the limits in Table 5.1) after the correction for the acceptance,

the trigger efficiencies and the downscaling if needed. The branching ratio

is calculated in each bin dividing the number of events of the signal channel

by the events in the normalization channel.

In Fig. 5.6, the branching ratio, without correction for the background,

is shown. The errors in the plot are statistical only.

To compute the statistical error, for each energy bin, I consider the cor-

rected number of events as given by

N(E) = C∑

i

Ni(E)

Ai(E)(5.13)

where N(E) is the number of decays occurred for the considered channel, i

is the index running over the cτ bins, Ni(E) is the number of events found in

each bin, Ai(E) is the acceptance measured for the bin and C is, depending

if we consider normalization or signal channel,

C =

1/(BR(Σ+ → pπ0) · εL2TS · εL3TS) signal channel

D/(BR(Λ → pπ−) · εL3TS) normalization channel(5.14)

The statistical error squared is thus given by

σ2N(E) = C2

∑

i

(σNi(E))2

(Ai(E))2(5.15)

where σN i(E) is the poissonian error 1/√

Ni(E).

The statistical (relative) error on the branching ratio is then obtained,

bin by bin, summing in quadrature the relative errors of the two numbers of

events

σBR(E)

BR(E)=

√

(

σNsig(E)

Nsig(E)

)2

+

(

σNnorm(E)

Nnorm(E)

)2

(5.16)


h_brEntries 0Mean 177.4

RMS 28.5

/ ndf 2χ 12.43 / 9

p0 5.979e-06± 0.0002725

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

BR

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004-1x10

h_brEntries 0Mean 177.4

RMS 28.5

/ ndf 2χ 12.43 / 9

p0 5.979e-06± 0.0002725

Branching Ratio (w/o BG corr.)

Figure 5.6: Branching ratio without correction for the background. The

errors in the plot are only statistical.

h_brbgEntries 0

Mean 176

RMS 31

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

bac

kgro

un

d(B

R)

0

0.05

0.1

0.15

0.2

0.25

0.3-4x10

h_brbgEntries 0

Mean 176

RMS 31

Background estimated effect on BR

Figure 5.7: Background estimated correction as a function of EΞ0 . To ob-

tain this estimation, the same procedure used for the measurement of the

branching ratio is applied only to the side bands.

5.5. SYSTEMATIC ERRORS 97

The final branching ratio, obtained averaging the results in Fig. 5.8, is

BR(Ξ0 → Σ+eνe)

BR(Ξ0 → Λπ0)= (2.665 ± 0.060) · 10−4 (5.17)

h_brbgcorrEntries 0Mean 177.4

RMS 28.44

/ ndf 2χ 12.21 / 9

p0 5.979e-06± 0.0002665

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

BR

co

rrec

ted

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004-1x10

h_brbgcorrEntries 0Mean 177.4

RMS 28.44

/ ndf 2χ 12.21 / 9

p0 5.979e-06± 0.0002665

Branching Ratio (with BG corr.)

Figure 5.8: Branching ratio obtained applying the background correction

before integrating over cτ .

5.5 Systematic errors

5.5.1 Acceptance

The error on the estimated number of decays depends also on the uncertainty

on the acceptance. The contribution of the error on the acceptance to the

systematic error in a bin of energy, for one channel, can be evaluated from

(5.13):

σ2N,acc(E) = C2

∑

i

(

Ni(E)

Ai(E)

)2

·(

σAi(E)

Ai(E)

)2

(5.18)


These errors contribute to systematic error on the branching ratio in each

energy bin, by

σBR,acc(E)

BR(E)=

√

(

σN,acc,sig(E)

Nsig(E)

)2

+

(

σN,acc,norm(E)

Nnorm(E)

)2

(5.19)

In Fig. 5.9, the systematic errors due to the acceptance uncertainty are

plotted against EΞ0 .

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

acc

σ

0

0.001

0.002

0.003

0.004

0.005

-2x10Systematic error: acceptance

Figure 5.9: Systematic error on the branching ratio due to the error on the

acceptance for each energy bin.

To evaluate the systematic error on the averaged branching ratio, I fit

the values obtained for the branching ratio using the errors given in Fig. 5.9

instead of the statistical errors. The error on the average branching ratio

yielded by this fit is (Fig. 5.10):

σBR,acc(E) = 0.044 · 10−4 (5.20)


h_br_accerrEntries 0Mean 177.4

RMS 28.44

/ ndf 2χ 17.42 / 9

p0 4.439e-06± 0.0002695

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

BR

co

rrec

ted

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004-1x10

h_br_accerrEntries 0Mean 177.4

RMS 28.44

/ ndf 2χ 17.42 / 9

p0 4.439e-06± 0.0002695

Branching Ratio (accept. errors)

Figure 5.10: Branching ratio as a function of EΞ0 , with the systematic errors

due to the error on the acceptance.

5.5.2 Trigger efficiency

For the systematic error due to the uncertainty on the measure of the trigger

efficiency, things are simpler, because we have only one value for all the bins.

ThusσBR,ε

BR=σε

ε(5.21)

The trigger efficiency of the L1TS may contribute only with an error of

the order of 2 ·10−4, negligible if compared with the contribution of the L2TS

trigger efficiencyσεL2TS

εL2TS

=2.5%

85.0%= 2.9 · 10−2 (5.22)

The uncertainty on the trigger efficiency of the L3 for the normalization

channel is smaller than 5 · 10−4 and so negligible. For the signal channel, the

uncertainty on the L3 trigger efficiency is larger:

σεL3

εL3

< 1.3% (5.23)

For the final value of the systematic error, the L3 trigger efficiency uncer-

tainty will be accounted for by a separate unknown term smaller than 1.3%


5.5.3 Branching ratio of the secondary decays

The contribution of the error on the world average of the branching ratios

for Σ+ → pπ0 and Λ → pπ− are

Σ+ → pπ0 =⇒ σBRΣ+/BRΣ+ = 5.8 · 10−3

Λ → pπ− =⇒ σBRΛ/BRΛ = 7.8 · 10−3

5.5.4 Energy scale

The calibration of the NA48 electromagnetic calorimeter is performed in

two complementary ways: the intercalibration between cells and the overall

calibration.

The first one ensures that the response of the calorimeter is uniform on

the whole surface.

The second one is needed to adjust the raw measure of energy to the real

energy. In principle, the correct energy can be an arbitrary function of the

measured energy, but the correction is so small that the function can safely

be approximated with a polynomial of the second order

E = E0 + αE + βE2 (5.24)

where E is the real energy, E the measured one and E0, α and β are fixed

parameters (α is also called energy scale).

For the data taken in the year 2002, the parameters of (5.24) have been

measured and they are

E0 = 0 β = 0

α = 1

A variation of the parameters can lead to a different measurement of the

branching ratio, so the uncertainty on the parameters is a source of systematic

error.

Since it is difficult to evaluate analytically how the effect of differences

in the energy scales propagates to the branching ratio, in order to estimate


this contribution to the systematic error, the energy scale is changed by plus

and minus one standard deviation (1 · 10−4) and the branching ratio is re-

evaluated. Fig. 5.11 shows the branching ratio in each energy bin for the

three considered values of α (1, 0.9995 and 1.0005).

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

BR

co

rrec

ted

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004-1x10

Systematic error: energy scale

nominal energy scale

energy scale = 1 - 5e-4

energy scale = 1 + 5e-4

Figure 5.11: Branching ratio obtained using the different values of the en-

ergy scale parameter (red and blue lines), compared to the one obtained the

nominal value of the energy scale (black).

The result obtained with the fits are

BR+ = 2.660 · 10−4 for α = 1.0005

BR− = 2.635 · 10−4 for α = 0.9995

By taking the systematic error as half of the maximum deviation between

the three branching ratios obtained (the one in (5.17) plus the results given

here) the following estimation is obtained:

σBR,escale = 0.015 · 10−4 (5.25)

5.5.5 Distance of the proton track from the beam pipe

One of the most critical cuts of the analysis is the minimum distance of the

proton track from the center of the detector.


If the simulation of the detector and the decay are not accurate, it is

possible that the distributions of the distance of the proton track from the

center of the detector at DCH1 are different in Montecarlo and data. In the

decays considered, the protons direction is generally close to the beam axis,

thus close to the center of DCH1 (Fig.5.12). In this situation, a little change

ProtDistBPmcEntries 200000

Mean 11.55

RMS 7.585

cm0 5 10 15 20 25 30 35 40

0

200

400

600

800

1000

1200

1400ProtDistBPmcEntries 200000

Mean 11.55

RMS 7.585

Dist. of the proton from BP (MC norm.)

Figure 5.12: Distribution of the distance of the proton from the center of

the detector at DCH1 in the generated values for the normalization channel.

The red lines indicate the region rejected by the selection cut.

in the value of the cut parameter, can yield to to changes in the number of

accepted events not fully accounted for by the simulation. The net effect is

that some of the numbers involved in the formula of the branching ratio can

vary.

In order to measure the effect of the cut on the distance of the proton

from the beam pipe, one can measure the branching ratio for different values

of the cut.

In Fig. 5.14 the values of the branching ratio obtained by changing the

minimum distance of the proton track from the center of DCH1 are shown.

The large fluctuations for high energies are due to the small statistics in

both the data and Montecarlo. In fact, as it can be seen in Fig. 5.13, the


(GeV)0ΞE100 150 200 250 300

> (c

m)

p<r

0

2

4

6

8

10

12

14

16

18

20

22

(MC)0ΞAverage dist. of the proton track from BP vs. E

Figure 5.13: Average distance of the proton track from the center of the

detector as a function of EΞ0 for the normalization channel (Montecarlo gen-

erated values).

cut considered reduce more the statistics at higher Ξ0 energy. Fig. 5.15

shows how the acceptance systematic errors change for the effect of the small

statistics at high energies.

In order to estimate the systematic error, I have to compare the average

value obtained in the three cases. In order to use the same sample with the

three distributions only the values of the branching ratio for energies between

130 and 180GeV are used.

The results are shown in Table 5.2. The systematic error on the branching

ratio is estimated as

σBR,pr.rad. = 0.19 · 10−4 (5.26)

5.5.6 Polarization of the Ξ0

As already said, we expect an energy dependent Ξ0 polarization between

5% an 20% toward the negative x axis. The systematic error due to the


130 140 150 160 170 180 190 200 210 220 2300.001

0.0015

0.002

0.0025

0.003

0.0035

0.004-1x10

min. proton radius

12cm

14cm

16cm


Figure 5.14: Branching ratio for different values of the cut on the distance

of the proton from the center of DCH1. The variation for energies above

190GeV are essentially due to the small statistics.

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

10-5

10-4

10-3

min. proton radius

12cm

14cm

16cm

Systematic error due to the acceptance

Figure 5.15: Systematic errors due to the acceptance for different values of

the cut on the distance of the proton from the center of DCH1. Null values

mean that the acceptance was not computed.


Min. Radius BR (10−4)

12 cm 2.76

14 cm 2.40

16 cm 2.38

Table 5.2: Averages of the branching ratio for different values of the cut on

the distance of the proton from the center of DCH1.

uncertainty on the polarization can be estimated measuring the branching

ratio for different values of the polarization.

Six Montecarlo samples, three for the normalization channel and three

for the signal channel, have been generated with Ξ0 polarizations (toward

the negative x axis): 0% (unpolarized), 5% and 15%. For the final result the

samples with 5% polarization are used.

From Fig. 5.16, one can see that using different polarizations the branch-

ing ratios do not a particular trend.

(GeV)0ΞE130 140 150 160 170 180 190 200 210 220 230

0.001

0.002

0.003

0.004

0.005

0.006

0.007-1x10

Polarization (x)-5%

0

-15%

)-4

Fits Results (10

Pol = -5% -> BR = 2.665

Pol = 0 -> BR = 2.723

Pol = -15% -> BR = 2.779


Figure 5.16: Comparison between the branching ratios measured with Mon-

tecarlo samples generated with different Ξ0 polarizations.

In Table 5.3, the average results are summarized. The systematic error,


polarization branching ratio

0% 2.723 · 10−4

5% 2.665 · 10−4

15% 2.779 · 10−4

Table 5.3: Branching ratio for different polarization values used in the Mon-

tecarlo samples.

evaluated as the half of the maximum variation, is

σBR,pol = 0.059 · 10−4 (5.27)

Chapter 6

Conclusions

The measurement of the branching ratio of the Ξ0 β-decay has been per-

formed and the main sources of systematic errors have been studied.

In Table 6.1, the systematic errors studied are summarized together with

their combined value of (obtained by summing in quadrature the errors)

σsyst. = 0.22 · 10−4 (6.1)

The value obtained for the branching ratio is therefore

BR(Ξ0 → Σ+eνe)

BR(Ξ0 → Λπ0)= (2.665 ± 0.060stat. ± 0.22syst.) · 10−4 (6.2)

The main sources of systematic errors are identified as the cut on the

minimum distance of the proton from the center of DCH1, probably due to a

not perfect simulation of the decays, and the trigger efficiency of the L2TS,

which cannot be improved with the data collected in 2002.

The result obtained is in good agreement with both the current experi-

mental result obtained by KTeV[1]

BR(Ξ0 → Σ+eνe)

BR(Ξ0 → Λπ0)= (2.71 ± 0.22stat. ± 0.31syst.) · 10−4 (6.3)

and the current theoretical estimation provided by Cabibbo in 1963[6]:

BR(Ξ0 → Σ+eνe)

BR(Ξ0 → Λπ0)= 2.6 · 10−4. (6.4)

107

108 CHAPTER 6. CONCLUSIONS

Source σ(10−4)

Acceptance 0.044

Trigger Efficiency (L2) 0.078

Trigger Efficiency (L3) (< 0.035)

BR(Σ+) 0.015

BR(Λ) 0.021

Energy Scale 0.015

Proton Radius 0.19

Polarization 0.059

Combined 0.22

Table 6.1: Summary of the systematic errors evaluated. The combined value

is obtained by summing in quadrature the errors, except the one on L3 Trigger

Efficiency.

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