Double Chooz Sensitivity Analysis: Impact of the Reactor Model Uncertainty on Measurement of Sin 2 (2θ 13 )

Transcription

1 Double Chooz Sensitivity Analysis: Impact of the Reactor Model Uncertainty on Measurement of Sin 2 (2θ 13 ) Elizabeth Grace 1

2 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 2

3 Neutrino Flavor Mixing P(ν e ν e ) = 1 - sin 2 (2θ 13 ) sin 2 (1.27 m 2 L/E) Function of m 2 and L/E, which varies and causes oscillation θ 13 is mixing angle and determines amplitude Standard Model prediction: m 2 = 0, no mixing 3

4 Mixing Angle P(νe νe) = 1 - sin 2 (2θ13) sin 2 (1.27 m 2 L/E) Why do we use sin 2 (2θ 13 ) instead of some constant? In other words, what angle does θ 13 refer to? νeνµ ν2 Coordinate transformation from axes of states of definite mass to definite flavor described by rotation matrix Mass eigenstate flavor eigenstate θ Two-neutrino approximation ν1 4

5 Goal of Double Chooz Measure sin 2 (2θ 13 ) using antiν e- source: nuclear reactors Measure anti-ν e- flux as a function of L/E Neutrino flux goes like L -2, neutrino energy peaks at around 3 MeV Deficit in anti-ν e- indicates oscillation 5

6 Detector Schematic 6

7 Signal: IBD _ ν e- + p n + e + prompt delayed 7

8 Target Innermost cylinder: target containing 0.1% Gd + liquid scintillator Gd has high neutron cross section for absorption: Gd + n > γγ characteristic gammas detected 8

9 γ Catcher Second cylinder is gamma catcher containing liquid scintillator: allows gammas escaping target to deposit some of their energy in scintillator >95% gamma containment 9

10 Buffer 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) 10

11 Inner µ Veto Contains 70 tons of liquid scintillator 78 PMTs Purpose is to detect muons in order to veto events caused by them 11

12 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 12

13 Background (Noise) Uncorrelated: Accidentals Correlated: Fast n and stopping µ, 9 Li and 8 He 0.5 < E e+ < 10 MeV 6 < E n < 10 MeV 1 μs < Δt < 100 μs _ νe- prompt e + W + 13 p IBD signal n delayed

14 Motivation: My Analysis Have been using a single detector for 2-3 years in Chooz experiment Obtained results with uncertainties 14

15 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) Want to know: What will the resultant uncertainty in the measurement of sin 2 (2θ 13 ) be? Answer: Conduct sensitivity study in order to predict it 15

16 Overview: χ 2 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 16

17 Overview: χ 2 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 j th elements change together 17

18 Building χ 2 + 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 Ni pred is the number of predicted events in energy bin i. Ni obs is the number of observed events in energy bin i. 18

19 Building χ 2 : m 2 + m 2 is the parameter we allow to float in the DC fit uncertainty Measured value of m ee 2 (derived from MINOS result) used to constrain our data This term factors in any error in our measurement of m 2 by adding a penalty when m 2 m ee 2 and scaling it by the uncertainty 19

20 Building χ 2 Far Detector Near Detector We subtract 1 because the value of α would be 1 if there were no deviation from the prediction N i pred = N i ν +α i Li+He N i Li+He + α i FN+SM N i FN+SM + where N i ν = N i ν (sin 2 (2θ 13 ), m 2, ) Each α is a pull term for the relevant background error: 9 Li and 8 He; fast neutrons and stopping muons; and systematic accidentals.

21 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 M ij 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 obs -1 Pull terms can often be written in the form of a covariance matrix: α is N, 1 is N pred, and M 2 ij contains σ! 21

22 Covariance Matrices M ij is a sum of other covariance matrices: M ij = M ij stat + Mij reactor + Mij efficiency + Mij Li+He shape + Mij acc(stat) M ij stat : contains info about the statistical spread around the prediction, so there is no covariance (i.e., it is a diagonal matrix) M ij reactor : contains uncertainty in reactor prediction M ij efficiency : normalization uncertainties (translates spectrum up or down) M ij Li+He shape : shape error in Li+He background spectrum M ij acc(stat) : diagonal matrix containing statistical info about accidentals 22

23 Sensitivity Studies Create data with a known sin 2 (2θ 13 ) and plot χ 2 (sin 2 (2θ 13 ),α, m 2, ) where χ 2 = χ 2 - χ 2 min χ 2 will be zero at the known sin 2 (2θ 13 ) value Go up by 1 on the χ 2 axis to find the locations of ±1σ Use this to estimate the future ±1σ for the real data Minuit 23

24 Sensitivity Studies Want to know: What will the uncertainty in the measurement of sin 2 (2θ 13 ) 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 sin 2 (2θ 13 ) Considered FD only and ND+FD cases Plot the ±1σ error in sin 2 (2θ 13 ) as a function of time for several different scaling factors 24

25 Results Reactor Flux Assumptions no added error 10% error 50% error 100% error One detector Two detectors 25

26 Results (Far Detector Only) Reactor Flux Assumptions no added error 10% error 50% error 100% error 26

27 Conclusions Second detector adds a high level of certainty in the measurement of sin 2 (2θ 13 ) even with little to no knowledge of the reactor flux Expected result: was motivation behind adding a second detector 27

28 Acknowledgements Mike Shaevitz Rachel Carr Leslie Camilleri Georgia Karagiorgi John Parsons and the NSF 28

29 Backup 29

30 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 30

31 Inputs Background Type FD Rate (per day) ND Rate (per day) Spectrum Shape Shape uncertainty ± ± 1.29 DC-III DC-III (100% correlated between rxtrs) FN+SM 0.60 ± (different from DC-III value: 3.18 ± 0.27) flat none Accidentals ± ± 0.02 DC-III none (factored into rate unc) 31

32 Inputs Parameter 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 + shape 1 (different from DC-III value of 0.99) m -4.1%, 3.69% on m N/A (single parameter) 32

33 Accidentals Accidental coincidences Example: Gamma enters the detector Cosmic muon hits a nearby nucleus and releases a neutron, which is detected Not linked temporally 33

34 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 34

35 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 35

36 9 Li + 8 He 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 36

37 9 Li + 8 He, cont. 9 Li is 85% of this type of background Half life is 113 ms ( 8 He) and 178 ms ( 9 Li) 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 analysis Decay chain for 9 Li 37