Double Chooz Sensitivity Analysis: Impact of the Reactor Model

Uncertainty on Measurement of Sin2(2θ13)Elizabeth Grace

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Outline• Neutrino Mixing: A Brief Overview

• Goal of Double Chooz

• Detector Schematic

• Fit Framework and Statistical Analysis

• My Work: Sensitivity Study of Reactor Uncertainty Impact

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Neutrino Flavor Mixing

• P(νe→νe) = 1 - sin2(2θ13) sin2(1.27 ∆m2 L/E)

• Function of ∆m2 and L/E, which varies and causes oscillation

• θ13 is“mixing angle” and determines amplitude

• Standard Model prediction: ∆m2 = 0, no mixing

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“Mixing Angle”

• Why do we use sin2 (2θ13) instead of some constant? In other words, what angle does θ13 refer to?

• Coordinate transformation from axes of states of definite mass to definite flavor described by rotation matrix

• Mass eigenstate ≠ flavor eigenstate

θν1

ν2νe-νµ

Two-neutrino approximation

P(νe→νe) = 1 - sin2(2θ13) sin2(1.27 ∆m2 L/E)

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Goal of Double Chooz• Measure sin2 (2θ13) using anti-νe- source: nuclear reactors

• Measure anti-νe- flux as a function of L/E

• Neutrino flux goes like L-2 , neutrino energy peaks at around 3 MeV

• Deficit in anti-νe- indicates oscillation

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Detector Schematic

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Signal: IBD

prompt

delayed

νe- + p n + e+

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_

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Target • Innermost cylinder:

target containing 0.1% Gd + liquid scintillator

• Gd has high neutron cross section for absorption: 
Gd + n —> γγ characteristic gammas detected

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• Second cylinder is “gamma catcher” containing liquid scintillator: allows gammas escaping target to deposit some of their energy in scintillator

• >95% gamma containment

γ Catcher

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• Photomultiplier Tubes: Turn a light signal into an electron signal via photoelectric effect and amplification

• PMTs are surrounded by B field shielders to cancel earth’s magnetic field so the e- do not bend

• 390 PMTs

• Surrounded by buffer oil for radiation (PMTs, external sources)

Buffer

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Inner µ Veto

• Contains 70 tons of liquid scintillator

• 78 PMTs

• Purpose is to detect muons in order to veto events caused by them

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Outer µ Veto• Similar purpose to inner

veto: signal rejection

• Plastic scintillator strips

• 2 modules: X and Y

• 2 layers per module: offset like bricks to pinpoint muon location

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Background (Noise)• Uncorrelated: Accidentals • Correlated: Fast n and stopping µ,

9Li and 8He • 0.5 < Ee+ < 10 MeV • 6 < En < 10 MeV • 1 μs < Δt < 100 μs

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W+

νe-_

p n

e+prompt

delayed

IBD signal

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Motivation: My Analysis

• Have been using a single detector for 2-3 years in Chooz experiment

• Obtained results with uncertainties

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Motivation: My Analysis• Problem: Inexact prediction of

reactor flux (initial neutrino flux)

• Solution: Replace prediction with measurement

• New, identical detector closer to reactor source (Near Detector)

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• Want to know: What will the resultant uncertainty in the measurement of sin2(2θ13) be?

• Answer: Conduct sensitivity study in order to predict it

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Overview: χ2• Main component of sensitivity study

• Measurement of how expectations compare to results, i.e. goodness of a fit

• For random, independent, Gaussian variables, the sum of their squares (i.e, chi-squared) follows a well-known distribution

• Energy bin contents are such variables and thus follow the distribution

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Overview: χ2• Binning scheme: discretize the data

into 250 keV-wide energy bins

• Pull parameter (nuisance parameter): Term that is not of interest but must be accounted for, so it floats in the fit

• Pull term: penalty term that changes as you attempt to optimize chi-squared

• Covariance matrix: a matrix containing information on how the error in the i

th

and jth

elements change together

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Building χ2

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+ …

Sums the difference between predicted and observed over B, the number of bins

Covariance matrix: contains information about the way

that the error in bin i is related to the error in bin j

Nipred is the number of predicted events in energy bin i. Niobs is the number of observed events in energy bin i.

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Building χ2: ∆m2

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+ …

This term factors in any error in our measurement of ∆m2 by adding a penalty when ∆m2≠∆mee2 and scaling it by the uncertainty

∆m2 is the parameter we allow to float in the DC fit

uncertaintyMeasured value of ∆mee2

(derived from MINOS result) used to constrain our data

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Building χ2

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Each α is a pull term for the relevant background error: 9Li and 8He; fast neutrons and stopping muons; and systematic accidentals.

We subtract 1 because the value of α

would be 1 if there were no deviation from the prediction.

+ …Nipred = ∑Niν +αiLi+He NiLi+He+ αiFN+SM NiFN+SM+…

where Niν = Niν (sin2(2θ13), ∆m2, …)

Far Detector

Near Detector

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Covariance Matrix• In our model, there are a lot of uncertain parameters. Within the set of possibilities contained

within our uncertainties, what happens to the bin contents with respect to one another, i.e., how do they correlate?

• ∆i∆j = matrix element of Mij where ∆i is the way that the predicted bin contents would be different if a parameter in our prediction were changed

• Ex. How would an incorrect neutrino flux prediction affect the contents of energy bin i?

• Off-diagonal elements describe the covariance, i.e., the amount that the ith bin’s error correlates with the jth bin’s error

• Ex. After changing neutrino flux prediction, if bin i changed in the positive direction and bin j would change in the negative direction, then the bins are anti correlated

• Pull terms can often be written in the form of a covariance matrix: α is Nobs

, 1 is Npred

, and Mij-1

contains σ

2

!

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Covariance Matrices• Mij is a sum of other covariance matrices:

Mij = Mijstat

+ Mijreactor

+ Mijefficiency

+ MijLi+He shape

+ Mijacc(stat)

• Mijstat

: contains info about the statistical spread around the

prediction, so there is no covariance (i.e., it is a diagonal matrix)

• Mijreactor

: contains uncertainty in reactor prediction

• Mijefficiency

: normalization uncertainties (translates spectrum up or down)

• MijLi+He shape

: shape error in Li+He background spectrum

• Mijacc(stat)

: diagonal matrix containing statistical info about accidentals

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Sensitivity Studies• Create data with a known

sin2(2θ13) and plot ∆χ2(sin2(2θ13),α, ∆m

2,…) where ∆χ2 = χ2 - χ2min

• ∆χ2 will be zero at the known sin2(2θ13) value

• Go up by 1 on the ∆χ2 axis to find the locations of ±1σ

• Use this to estimate the future ±1σ for the real data

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Minuit

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Sensitivity Studies• Want to know: What will the uncertainty in the

measurement of sin2(2θ13) be when we use near detector instead of reactor prediction?

• To find out: scale reactor error matrix by a multiplicative coefficient and plot ±1σ error in sin2(2θ13)

• Considered FD only and ND+FD cases

• Plot the ±1σ error in sin2(2θ13) as a function of time for several different scaling factors

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Results

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One detectorTwo detectors

50% error10% error

no added error100% error

Reactor Flux Assumptions

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Results (Far Detector Only)

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Reactor Flux Assumptions50% error

10% errorno added error

100% error

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Conclusions

• Second detector adds a high level of certainty in the measurement of sin2(2θ13) even with little to no knowledge of the reactor flux

• Expected result: was motivation behind adding a second detector

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AcknowledgementsMike Shaevitz

Rachel Carr

Leslie Camilleri

Georgia Karagiorgi

John Parsons and the NSF

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Backup

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Assumptions• Inputs for far detector are based on the most recent

DoubleChooz analysis (DCIII), and near detector are based on DCIII knowledge (conservative prediction)

• Signal from detectors scaled for live time and baseline using DCIII

• Background Rates and Uncertainty

• Energy Scale Uncertainty

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InputsBackground

TypeFD Rate (per

day)ND Rate (per

day)Spectrum

ShapeShape

uncertainty

9 0.97 ± 0.29 4.37 ± 1.29 DC-IIIDC-III (100%

correlated between rxtrs)

FN+SM 0.60 ± 0.052.00

(different from DC-III value: 3.18 ± 0.27)

flat none

Accidentals 0.0701 ± 0.0054 0.21 ± 0.02 DC-IIInone (factored into rate unc)

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InputsParameter Uncertainty (same for ND and FD)

ND-FD Correlation Coefficient

Detection Efficiency 0.62% on signal normalization 0.94

Energy Scale 1.00% on linear energy scale 0

Reactor Flux 1.73% normalization + shape1 (different from DC-III

value of 0.99)

∆m -4.1%, 3.69% on ∆m N/A (single parameter)

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Accidentals• Accidental coincidences

• Example:

• Gamma enters the detector

• Cosmic muon hits a nearby nucleus and releases a neutron, which is detected

• Not linked temporally

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Fast Neutrons• Fast neutron: high energy

neutron

• Cosmic µ hits a nearby nucleus and ejects spallation neutron

• Fast neutron enters target:

• causes a proton recoil, which mimics e+ signal

• is captured, producing a gamma signal

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Stopping Muons• Cosmic muon enters the detector from

above

• Prompt signal from muon track (ionization from scintillator): muons produce scintillation light that is in the positron energy range

• Delayed signal from decay of muon into a Michel electron

• ∆t is the muon lifetime (distribution with mean within the allowed signal range)

• Don’t apply cuts because we want to keep the signal

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9Li + 8He• Cosmic muon hits the target

and produces Li-9 or He-8

• Result is electron (mimics e+) and neutron

• Should be able to eliminate with µ veto, but their half life is so long that we would miss data

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9Li + 8He, cont.• 9Li is 85% of this type of

background

• Half life is 113 ms (8He) and 178 ms (9Li)

• Vetoing all the data after seeing a muon for the amount of time it takes these to decay would result in continuous veto

• Must deal with this in analysisDecay chain for 9Li

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