大亞灣微中子振盪實驗中宇宙射線所產生之同位素鋰-9及氦-8分析

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國立臺灣大學理學院物理學研究所碩士論文

Department of Physics College of Science

National Taiwan University master thesis

大亞灣微中子振盪實驗中宇宙射線所產生之同位素鋰-9 及氦-8 分析

Analysis of cosmogenic isotopes Lithium-9 and Helium-8 in the Daya Bay Reactor Neutrino Experiment

潘孝儒 Hsiao-Ru Pan

指導教授：熊怡博士

Advisor: Yee Bob Hsiung, Ph.D.

中華民國 108 年 7 月 July, 2019

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Acknowledgements

I would like to give my most sincere gratitude to my advisor Dr. Yee Bob Hsiung who gave me this opportunity to participate in one of, if not the most, important experiments of Physics. During the years of my study, he had taught me the real meaning of physics and how to think like a physicist. Thanks to him again for whom he gave me the once in a lifetime experience.

Aside from my advisor, I would also like to thank our local collaborators Dr. Guey- Lin Lin and Dr. Chung-Hsiang Wang for their insightful discussions and guidance during our countless hours of meetings. I also acknowledge our worldwide collaborators Chris Marshall, Haoqi Lu, Juan Pedro Ochoa-Ricoux and Zhe Wang for their interests and feedbacks about my works.

Next I want to thank Dr. Yu-Chen Tung who taught me the basics of data analysis and gave me the initial boost I needed to start my career in data analysis. I would also like to thank Dr. Bei-Zhen Hu for the discussions on the various technical details of the analysis and helping me out when we were taking shifts or having meetings outside of Taiwan.

I am also pleased to say thank you to my colleagues Kuo-Lun Jen who not only had brought up interesting ideas from time to time but also brought me tons of joys during our meetings, Po-An Chen for the inspiring discussions and listening to all my rants, and Chia-Hao Wu for the fruitful discussions.

My times at the high energy physics group wouldn’t be complete without my friends and fellow lab mates Chieh Lin, Shih-Hsuan Chen, Yu-Cheng Lin, Yu-Tan Chen, You- Ying Lee and Chun-Ting Lin. I will never forget the times when we had lunches together and chatted all day long.

Finally, my utmost gratitudes to my parents and sister who had gave me the courages to chase my dreams and the supports I needed during my most desperate moments, words simply cannot express how grateful I am. This thesis would not be possible without you, thank you.

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摘要

大亞灣微中子振盪實驗利用八個相同設計的反微中子探測器以及六個位於中國東南沿海大亞灣地區之核能反應爐作為反微中子源來進行測量。將探測器放置於遠點及近點兩種不同的相對於反應爐位置的測量方法，我們的測量結果為微中子振盪理論提供顯著的證據。透過一千九百五十八天所累積之數據，大亞灣實驗組在微中子振盪模型參數 (sin²θ13, ∆m²₃₂) 的測量上獲得空前的準度。

儘管如此，宇宙射線所產生之放射性同位素鋰-9 以及氦-8 仍然是實驗中一項重要的系統誤差來源。在過去的研究裡，我們透過量測微中子訊號以及渺子訊號的時間差分佈來估計這些同位素的含量。但是這個方法在渺子訊號的出現頻率很高時無法有效的測量這些同位素，而大亞灣實驗中的近點由於地底深度較淺所以宇宙射線的頻率較高剛好符合這種特性，因此許多方法被提出以解決這個問題。

不過這些方法大多缺乏理論支持也因此在可能導致系統誤差遭到低估。

本論文開發一種新的方法來測量這些同位素，除了渺子以及微中子訊號的時間資訊外，我們將微中子訊號的頻譜資訊同時納入以增加測量的準確度。將此方法用於大亞灣實驗之數據，我們在同位素含量的測量上得到了和先前結果一致的結果以及相似或是更低的誤差。不僅如此，由於在測量中加入了頻譜資訊讓我們得以檢驗這些同位素在不同變數上之分佈以及發現先前所忽略的其他同位素所產生之訊號。最後我們將數個不同實驗所測量到的鋰-9 及硼-12 之產率利用冪律分布進行分析，此分析將可為未來的實驗進行預測。

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Abstract

The Daya Bay Reactor Neutrino Experiment aimed to measure the neutrino oscillation parameter θ13 by utilizing eight identically designed anti-neutrino detectors with six reactor cores from the nuclear power plants at Daya Bay in south east China. Using the near-far relative measurements, strong evidences of neutrino oscillation were found. In 2018, with over 1958 days of data collection, the group achieved unprecedented precision on measurements of the three flavour oscillation parameters sin²θ13and ∆m²₃₂.

Despite the huge success, cosmogenic isotopes,⁹Li and⁸He in particular, remain one of the lesser understood systematic uncertainties in the experiment. Previously a method based on temporal distribution between muons and anti-neutrino signals was developed to measure the yields of these isotopes. However, the method was known to be unreliable when muon rates are high which happened to be the case for some of the near detectors in the Daya Bay experiment. Heuristics were developed to reduce the statistical uncertainties of these measurements, but such heuristics lack theoretical justifications and can lead to underestimation of systematic uncertainties.

In this thesis, we develope a new method in cosmogenic isotope measurements by incorporating spectral information and temporal distributions. Based on the analysis of 1958 days of data from Daya Bay, we show empirically that this method not only could achieve similar or lower uncertainties in rate measurements, but also provide insights into the spectra of cosmogenic isotopes. Lastly, we combine our measurements with other experiments with similar setups to provide a power law estimation for the yields of⁹Li and¹²B which can be used for next generation experiments.

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List of Figures

2.1 Layout of the Daya Bay experiment . . . 12

2.2 Survival probability and the baselines of near and far experimental halls. . 13

2.3 Cross-section diagram of the Daya Bay anti-neutrino detector . . . 14

2.4 Diagram of the near site detectors and water pool. . . 15

2.5 Light yield variation due to z and r measured with ACUs. . . . 19

2.6 Light yield variation due to z and r measured with spallation neutrons. . . 20

2.7 Energy resolution of the detectors. . . 21

2.8 Comparison of simulated¹²B and data. . . 22

2.9 Resulting energy model for positrons. . . 23

2.10 Example of PMT hit charge map for a flasher event. . . 25

2.11 Response of the flasher discriminating variable f_IDfor delayed candidates. 25 2.12 Joint distribution of prompt energy and delayed energy for EH1 AD1. . . 27

2.13 Illustration of the multiplicity cut and capture time cut. . . 28

2.14 Energy spectrum of isolated events in each AD. . . 30

2.15 Prompt and delayed energy distribution for paired uncorrelated signals in EH1AD1. . . 30

2.16 Prompt and delayed energy distribution for accidental background subtracted IBDs in EH1AD1. . . 31

2.17 ⁹Li/⁸He measurements with different prompt energy cuts for EH1. . . 33

2.18 Background subtracted spectrum at the far site with best fit weighted near sites spectrum. . . 39

2.19 Best fit of sin²2θ₁₃and ∆m²_eeand their confidence regions using spectral analysis with 1230 days of data. . . 41

3.1 Ground state decays of lithium-9. . . 44

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3.2 Ground state decays of helium-8. . . 45

3.3 Illustration of time-since-last-muon for muon induced isotopes. . . 45

3.4 Naive application of the statistical model to EH1 nGd data. . . 51

3.5 Simulated IBD,⁹Li and⁸He decay prompt energy spectra. . . 52

3.6 Comparison of measured and predicted spectrum of⁹Li and⁸He. . . 53

3.7 Illustration of how decays of¹²B/¹²N can mimic IBD signals. . . 54

3.8 Illustration of how to incorporate spectral information into cosmogenic isotope measurements. . . 57

4.1 EH1 IBD candidate prompt energy, delayed energy, capture time and prompt-delayed distance distributions. . . 63

4.4 Illustration of neutron tagging. . . 66

4.5 Energy distribution of events succeeding muons. . . 67

4.6 Illustration of correlated muons. . . 68

4.7 Joint distribution of time-since-last-muon for low/mid energy tagged muons vs. high energy muons. . . 69

4.8 Temporal difference distribution of time-since-last-muon for low/mid energy tagged muons and high energy muons. . . 70

4.9 Joint distribution of time-since-last-muon for low/mid energy tagged muons vs. high energy muons after isolation cut. . . 71

5.1 Example time-since-last-muon fit. . . 74

5.2 Example of EH1 fitted 4-slice prompt energy distributions. . . 75

5.3 Estimated daily rates of⁹Li and⁸He for each site with respect to different number of slices and free/fixed⁹Li prompt energy spectrum for the nGd analysis. . . 77

5.4 nGd EH1 low E_µregion 4-slice free fits . . . 79

5.5 nGd EH1 mid Eµregion 4-slice free fits . . . 80

5.6 nGd EH1 high E_µregion 4-slice free fits . . . 81

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5.7 nGd EH2 low E_µregion 4-slice free fits . . . 82

5.8 nGd EH2 mid Eµregion 4-slice free fits . . . 83

5.9 nGd EH2 high E_µregion 4-slice free fits . . . 84

5.10 nGd EH3 low Eµregion 4-slice free fits . . . 85

5.11 nGd EH3 mid E_µregion 4-slice free fits . . . 86

5.12 nGd EH3 high Eµregion 4-slice free fits . . . 87

5.13 nGd 4-slice free fitted spectra. . . 88

5.14 nGd 4-slice fix fitted spectra. . . 89

5.15 nGd 10-slice free fitted spectra. . . 90

5.16 nGd 10-slice fix fitted spectra. . . 91

5.17 Simulated beta energy of beta decays of¹²B and¹²N. . . 92

5.18 nGd EH3 estimated prompt-delayed distance spectra. . . 94

5.19 Estimated daily rates of⁹Li and⁸He for each site with respect to different number of slices and free/fixed ⁹Li prompt energy spectrum for the nH analysis. . . 96

5.20 nH EH1 low Eµregion 4-slice free fits . . . 97

5.21 nH EH1 mid E_µregion 4-slice free fits . . . 98

5.22 nH EH1 high Eµregion 4-slice free fits . . . 99

5.23 nH EH2 low E_µregion 4-slice free fits . . . 100

5.24 nH EH2 mid Eµregion 4-slice free fits . . . 101

5.25 nH EH2 high E_µregion 4-slice free fits . . . 102

5.26 nH EH3 low Eµregion 4-slice free fits . . . 103

5.27 nH EH3 mid E_µregion 4-slice free fits . . . 104

5.28 nH EH3 high Eµregion 4-slice free fits . . . 105

5.29 nH 4-slice free fitted spectra. . . 106

5.30 nH 4-slice fix fitted spectra. . . 107

5.31 nH 10-slice free fitted spectra. . . 108

5.32 nH 10-slice fix fitted spectra. . . 109

5.33 Estimated daily rates of⁹Li and⁸He for each site with respect to different number of slices and free/fixed⁹Li prompt energy spectrum for the unified analysis. . . 110

5.34 unified EH1 low Eµregion 4-slice free fits . . . 112

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5.35 unified EH1 mid E_µregion 4-slice free fits . . . 113

5.36 unified EH1 high Eµregion 4-slice free fits . . . 114

5.37 unified EH2 low E_µregion 4-slice free fits . . . 115

5.38 unified EH2 mid Eµregion 4-slice free fits . . . 116

5.39 unified EH2 high E_µregion 4-slice free fits . . . 117

5.40 unified EH3 low Eµregion 4-slice free fits . . . 118

5.41 unified EH3 mid E_µregion 4-slice free fits . . . 119

5.42 unified EH3 high Eµregion 4-slice free fits . . . 120

5.43 unified 4-slice free fitted spectra. . . 121

5.44 unified 4-slice fix fitted spectra. . . 122

5.45 unified 10-slice free fitted spectra. . . 123

5.46 unified 10-slice fix fitted spectra. . . 124

6.1 ⁹Li yield power-law fit. . . 126

6.2 ¹²B yield power-law fit. . . 127

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List of Tables

2.1 Detector baselines and overburdens . . . 11 3.1 Summary of free parameters in the combined model. . . 59 3.2 Summary of free parameters in a single likelihood function of muon range

r, slice variable v and slice s. . . . 59 4.1 Summary of IBD selection criteria for unified, nGd and nH analyses. . . . 61 4.2 Summary of properties of muon energy regions. . . 65 4.3 Comparison of low/mid energy muon ⁹Li/⁸He measurements with and

without shower muon veto and isolation cut at EH1. . . 72 5.1 Live time and related efficiencies for each detector. . . 75 5.2 Variables of slicing and their ranges for the nGd analysis. . . 76 5.3 Estimated daily rates of⁹Li/⁸He and χ² per degree of freedom for each

number of slices and sites for the nGd analysis. . . 78 5.4 Estimated daily rates of⁹Li and⁸He for each site for the nGd analysis. . . 78 5.5 Data used to predict rates of¹²B and¹²N induced accidentals. . . 92 5.6 Comparison of predicted and measured rates of ¹²B and ¹²N induced

accidentals. . . 93 5.7 Variables of slicing and their ranges for the nH analysis. . . 94 5.8 Estimated daily rates of⁹Li/⁸He and χ² per degree of freedom for each

number of slices and sites for the nH analysis. . . 95 5.9 Estimated daily rates of⁹Li and⁸He for each site for the nH analysis. . . . 95 5.10 Variables of slicing and their ranges for the unified analysis. . . 96 5.11 Estimated daily rates of ⁹Li/⁸He and χ² per degree of freedom for each

number of slices and sites for the unified analysis. . . 111

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5.12 Estimated daily rates of⁹Li and⁸He for each site for the unified analysis. 111

6.1 Yield conversion parameters. . . 126

6.2 Summary of ⁹Li and ¹²B yields, and average muon energies for each experiment. . . 127

C.1 Naming convention for the fitting paramters. . . 137

C.2 nGd 4 slice free fit parameters. . . 138

C.3 nGd 4 slice fix fit parameters. . . 139

C.4 nH 4 slice free fit parameters. . . 140

C.5 nH 4 slice fix fit parameters. . . 141

C.6 Unified 4 slice free fit parameters. . . 142

C.7 Unified 4 slice fix fit parameters. . . 143

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Chapter 1

Introduction

1.1 A brief history of neutrinos

The story began in the early 20th century. Physicists were puzzled by the spectrum of beta particle energy in beta decays. Unlike alpha and gamma decays which have discrete spectrum, beta decays have a continuous spectrum. The continuous spectrum was problematic because beta decay was originally understood as a two body decay which had the following form

A

ZX →^A_Z+1X^′ + e⁻ (1.1)

It was well known that for a two body decay, the energy spectrum should be a line spectrum for both particles under the conservation laws of momentum and energy. During the time, many theories were proposed to explain the spectrum, some believed that electrodynamic laws do not apply in the atomic scale, others believed that the conservation laws only hold statistically[1]. It was this atmosphere that urged Austrian physicist Wolfgang Pauli to propose a desperate remedy to save the holy grails of physics. In his letter sent to a radioactive meeting in Tübingen in 1930, Pauli hypothesized a particle with no electric charge, negligible mass and high penetrability, named neutron at the time, was also emitted in the beta decay such that the sum of the energies of neutron and electron is constant[2].

However, the name neutron was soon taken by British physicist James Chadwick in 1932 for another neutral particle with similar mass to that of protons[3]. It was Italian physicist Enrico Fermi who later proposed the name neutrino (which meant “little neutron” in

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Italian) for the hypothetical particle as we know today.

Following the neutrino hypothesis by Pauli and the discovery of neutron by Chadwick in 1932, Fermi constructed his theory of beta decay in 1934 based on relativistic quantum mechanics which was able to explain the shape of the beta spectrum. The theory also predicted the inverse beta decay reaction[4]

1

1p + ¯ν_e →¹0 n + e⁺ (1.2) which is the underlying principle of many modern neutrino detectors. Most importantly, Fermi’s interaction paved the way for the theory of weak interaction in one of the most successful particle physics model, the Standard Model.

However, it was believed at the time that the detection of neutrinos was not possible due to their exteremely small cross section (∼10⁻⁴³cm²) which is about 20 orders smaller than the usual order of cross section (1barn = 1× 10⁻²⁴cm²) in nuclear physics [4]. Two decades later since Fermi’s theory, Cowan and Reines from the Los Alamos Scientific Laboratory used a nuclear reactor as a source of neutrinos and approximately 400 litres of water dissolved with cadmium chloride (CdCl₂) as the detector to study the process of inverse beta decay (1.2). The process can be distinctively identified by a prompt gamma ray signal corresponding to the annihilation of positron and a delayed gamma ray signal corresponding to the neutron absorption with cadmium.

108Cd + n→¹⁰⁹Cd + γ (1.3)

With nearly two months of running time and about three events per hour, they measured a reactor-power-dependent signal with a cross section in agreement with the one predicted in the process of inverse beta decay (∼6.3 × 10⁻⁴⁴cm²) thus confirming the existence of neutrinos[5].

It was the discovery of neutrino that led to one of the most important problem in modern physics, neutrino oscillation, which we shall discuss in the following sections.

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1.2 Neutrino oscillation

The idea of neutrino oscillation was first proposed by Italian physicist Bruno Pontecorvo in 1957 inspired by K⁰− ¯K⁰ oscillation. In his theory, he discussed the possibility that there exist other neutral particles, namely the neutrino, which the particle to anti-particle transitions are not strictly forbidden[6]. The theory was later used by Japanese physicists Maki, Nakagawa and Sakata to construct the theory of neutrino flavour mixing between electron neutrino and muon neutrino[7]. Neutrino flavour mixing is a quantum mechanical effect which happens when the mass eigenstates differ from the flavour eigenstates. The relation between these eigenstates can be described by the Pontecorvo-Maki-Nakagawa- Sakata (PMNS) matrix as below

|να⟩ =X

i

U_αi^∗ |νi⟩ (1.4)

where ν_α, ν_i and U_αi are the flavour eigenstates, mass eigenstates and the PMNS matrix respectively. In the three flavour setting, the PMNS matrix can be parametrized by three mixing angles (θ₁₂, θ₁₃, θ₂₃) and a CP-violating phase δ_CP as follow

U =







1 0 0

0 c₂₃ s₂₃ 0 -s₂₃ c₂₃













c₁₃ 0 s₁₃e^-iδ^CP

0 1 0

-s₁₃e^iδ^CP 0 c₁₃













c₁₂ s₁₂ 0 -s₁₂ c₁₂ 0

0 0 1





 (1.5)

where c_ij = cos θ_ij and s_ij = sin θ_ij. One of the most important consequences of neutrino mixing is that the flavour eigenstates can evolve into other flavour eigenstates while propagating in the vacuum as we will show below. Assuming the neutrino is in the flavour eigenstate|να⟩ initially then the probability that the state evolves into another eigenstate|νβ⟩ at time t can be calculated by

P (ν_α → νβ) =| ⟨νβ| e^−iHt|να⟩ |² (1.6)

=

X

i,j

⟨νj| Ujβe^−iEⁱ^tU_αi^∗ |νi⟩

2

(1.7)

=

X

i

e^−iEⁱ^tU_αi^∗U_iβ

2

(1.8)

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Since neutrinos have negligible mass we have E =p

p²+ m² ≈ p +^m_2E² and the distance travelled by the neutrino L≈ t, the above expression can be further approximated by

P (ν_α → νβ)≈

X

i

e⁻ⁱ

( p+^m2_2Eⁱ

)

LU_αi^∗U_iβ

2

(1.9)

=X

i,j

e

−i∆m2ij L

2E U_αi^∗U_αjU_jβ^∗ U_iβ (1.10)

= δ_αβ −X

i<j

4 sin² ∆m²_ijL

4E Re (M_αβij) + 2 sin∆m²_ijL

2E Im (M_αβij)

(1.11) where ∆m²_ij = m²_i − m²j and M_αβij = U_αi^∗U_αjU_jβ^∗ U_iβ. From this equation we can see that as long as the mass eigenstates are not degenerative (∆m²_ij ̸= 0) and the matrix is not identity (U ̸= I), the above probability is allowed to be non-zero for cases where α ̸= β.

This phenomena is now known as neutrino oscillation.

Neutrino oscillation is of great importance in modern physics. For one, the Standard Model of physics assumes the neutrinos to be massless, however, recent experiments have observed neutrino oscillations which require neutrinos to be massive and this might be a hint for physics beyond the Standard Model. Second, neutrino oscillations can violate charge-parity (CP) symmetry if

P (ν_α → νβ) − P (¯να → ¯νβ) = 4X

i<j

sin∆m²_ijL

2E Im (M_αβij) ̸= 0 (1.12)

. CP violation is important for it might be able to explain the matter and antimatter imbalance of our universe.

1.3 Neutrino oscillation experiments

Since the theory of neutrino oscillation, many experiments have been conducted to measure the oscillation parameters (θ_ij and ∆m²_ij) in equation 1.11 over a wide range of energy. In this section, we shall review the methods and implications of the results from some of these experiments.

In equation 1.11, we can see that the oscillation probability depends on the factor L/E.

This factor is essential to the detection of neutrino oscillation because we can now place

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detectors at different distances with respect to the sources of neutrinos and measure the oscillation probability P (να → νβ) as a function of L/E and the oscillation parameters. In general, the probability can be measured in two ways. First, the appearance method where we measure the number of neutrinos with unexpected flavours, for example the detection of ν_µ from a pure source of ν_e. On the other hand, one can also measure the probability by the disappearance method where one compare the expected number of neutrinos in a certain flavour to the actual number of neutrinos in the same flavour. In reality, the choice of method depends on the purity of the source and the capability of the detectors.

The sources of neutrinos can be divided into two categories, namely artificially generated sources and naturally generated sources. One of the major artificial sources of neutrinos is reactor neutrinos where electron antineutrinos are generated by neutron- rich nuclei from nuclear fissions undergoing beta decay. Another artificial source is accelerator neutrinos where one uses particle accelerators to collide nuclei to produce unstable particles that have neutrinos as their daughters. For example, in the MINOS experiment protons were collided with a graphite target to produce charged kaons and pions which have νµ or ¯νµ as their daughters[8]. As for the major natural sources, we have geoneutrinos from radioactive nuclei in the Earth, atmospheric neutrinos from cosmic ray’s interactions with air nuclei and the solar neutrinos from the Sun generated by nuclear fusions.

Below we shall review some of the most important experiments in the history of neutrino.

1.3.1 Solar neutrino experiments

The Homestake experiment, started around 1970, was the first experiment that aimed to measure the flux of solar neutrinos. Based on the inverse beta decay process (³⁷Cl + ν→ e⁻+³⁷Ar), the experiment was able to measure neutrinos with energy above 0.81 MeV[9].

However, the flux measured by the experiment was much smaller than the flux predicted by the standard solar model and this was known as the solar neutrino problem. The deficit was later also confirmed by two other experiements, namely the Super-Kamiokande (Super-K) and Sudbury Neutrino Observatory (SNO).

The Super-K experiment used a 50 kton water Cherenkov detector utilizing the

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charged-current interactions of neutrinos on nuclei

ν + N → l + X (1.13)

Notice that the process is sensitive to all types of neutrinos, although the sensitivity for ν_µand ν_τ is much lower than ν_e. With this setup, they were able to measure electron-like events and muon-like events to determine the ratio of incoming ν_eand ν_µand determine if there was a deficit between the predictions and the observations. In 1998, with over 500 days of exposure, they reported a non zero mass different at 90% confidence level assuming a two-flavor (ν_µ↔ ντ) oscillation model[10].

On the other hand, the SNO experiment used a 1000 tons heavy water (D₂O) detector to measure the solar neutrino flux. Unlike Super-K, the use of heavy water allowed the experiment to observe neutrinos through neutral current (NC) reactions

ν_x+ d→ p + n + νx, (x = e, µ, τ ) (1.14)

which is sensitive to all flavours of neutrinos and charged current (CC) reactions

ν_e+ d→ e⁻+ p + p (1.15)

which is sensitive only to electron-type neutrinos. This is crucial to the resolution of the solar neutrino problem for if the deficit was caused by flavour oscillations, then the fluxes between CC and NC should be different. With 306 days of live time, the team reported a significant excess of NC flux over CC and elastic scattering flux in favor of neutrino oscillations. Furthermore, the NC flux (sensitive to all neutrinos) is in agreement with the solar model predictions thus solving the solar neutrino problem.[11]

In summary, both experiments have shown strong evidences of neutrino oscillations.

But this is only the beginning of a new chapter in the history of neutrino oscillation. A natural question to ask is what are the values of the mixing angles and, most importantly, whether the CP violating term is non zero.

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1.3.2 Reactor neutrino experiments

Since the discovery of neutrino oscillation from solar neutrino experiments, several reactor neutrino experiments were proposed to measure the mixing angles θ_ij. By placing the neutrino detectors at different distances relative to the nuclear reactors, we can measure the survival probabilities of the electron anti-neutrinos originated from the reactor cores and hence the oscillation parameters (θij and ∆m²_ij). Unlike solar neutrinos, reactor neutrinos are much more controllable and the reactions of the reactors are better understood.

In the Kamioka Liquid Scintillator Anti-Neutrino Detector (KamLAND) experiment, a 13-m-diameter spherical detector filled with liquid scintillator was used to detect the neutrinos from the reactors via inverse beta decay. By identifying coincidence of a prompt signal of e⁺ and a delayed signal of 2.2MeV γ-ray neutron capture on a hydrogen from IBD, they were able to greatly reduce the backgrounds. With nearly 150 days of running time, KamLAND showed disappearances of electron antineutrino with high significance in favor of neutrino oscillation. Furthermore, they successfully measured the mixing angle θ₁₂assuming the three flavour oscillation.[12]

With θ12 measured by KamLand and θ23 measured by solar neutrino experiments, it remained to measure the last, and arguably the most important, mixing angle θ₁₃. The mixing angle θ13 is of great physical interest because the CP violation term (e^iδ^CP) is directly coupled with sin θ₁₃ as shown in equation 1.5, so a nonzero sin θ₁₃ is necessary for CP violation in the lepton sector.

In 1999 the Chooz experiment, a short baseline (L ∼ 1 km) reactor neutrino experiment, found strong evidences that there is no disappearances of electron antineutrino under certain assumptions. [13] In other words, the experiment set a limit on how small the oscillation parameter sin θ13could be. Therefore, to test whether sin θ13̸= 0 would be very challenging and require precise measurements.

Until recently, three other short baseline reactor neutrino experiments were done by three independent groups to measure the mixing angle θ₁₃, namely the Double Chooz experiment (successor of the Chooz experiment), the Reactor Experiment for Neutrino Oscillation (RENO) and the Daya Bay Reactor Neutrino experiment. All of the above experiments have reported strong evidences of neutrino oscillation and a nonzero sin θ₁₃[14, 15].

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1.4 Cosmogenic isotopes

⁹

Li and

⁸

He in reactor neutrino experiments

Cosmogenic isotopes ⁹Li and ⁸He are the most problematic background in the reactor neutrino experiments.[16] Recent reactor neutrino experiments benefit from deploying identically manufactured detectors at different baselines to reduce major systematics from detection efficiency and reactor flux. Utilizing the inverse beta decay reaction from neutrinos interacting with liquid scintillator, neutrino events can be identified by a prompt signal from the annihilation of e⁺ with energy in the range of 1 MeV to 8 MeV and a delayed signal from the neutron capture on other atoms. However, high energy cosmic muons can also interact with the nuclei in the detectors and produce numerous isotopes.

Among these isotopes,⁹Li and⁸He were known to have β−n cascade which can mimic the IBD signals so an event-by-event rejection can not be used in this scenario. Furthermore, due to their long half-lives (178ms and 119ms), they can escape muon vetos by chance.

In previous experiments, estimation of cosmogenic background relies heavily on the temporal information (time between muons and candidate signals) since cosmogenic products are correlated with muons while neutrinos from reactors are not, we would expect different temporal distributions from them. By exploiting this difference, we can measure statistically the fraction of cosmogenic background in our neutrino candidates.

Such methods, however, were known to be unreliable when muon rate increases as can be seen from the following equation derived in [16]

σ_b = s

(1 + τ R_µ)²− 1

N (1.16)

where σb is the statistical uncertainty of the cosmogenic background fraction, τ is the lifetime of the isotope, R_µis the muon rate and N is the total event number. It is obvious that as Rµincreases, so does σb.

Such characteristics can be undesirable for underground detectors with light overburden which happen to be the case for some of the detectors in the Daya Bay experiment. To solve this problem, we improve on the existing method by dividing the muons into various regions to reduce the muon rates in each measurement and using the spectral information of the decay product of the isotopes to further constrain the

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measurements. More details shall be discussed in later chapters.

1.5 Thesis outline

In chapter 2 we provide a general overview of the Daya Bay Reactor Neutrino Experiment including the design of the experiments and the implications of its results. In chapter 3 we first review the previously used method on cosmogenic⁹Li and⁸He measurements, secondly we discuss how to improve on the existing method and its application in the Daya Bay experiment. In chapter 4 we shall discuss possible future improvements on the method.

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Chapter 2

Daya Bay Reactor Neutrino Experiment

2.1 Introduction

The Daya Bay Reactor Neutrino Experiment, referred to as Daya Bay hereafter, was designed to measure the oscillation parameter θ₁₃ with anti-neutrinos generated by the Daya Bay Nuclear Power Plant (NPP), the Ling Ao NPP and the Ling Ao-II NPP in southeast China. Prior to Daya Bay, the most sensitive limit on θ₁₃ was reported by the Chooz experiment with sin²(2θ₁₃) < 0.17 at 90% confidence level[13]. The original goal of Daya Bay was to achieve a precision of 0.01 or better at sin²(2θ₁₃), which is an order of magnitude smaller than the previous result. To achieve this goal, a few critical design choices were made. First of all, the detectors were designed to have large target volumes to increase the flux of incoming anti-neutrinos and placed deeply underground to reduce the production of cosmogenic backgrounds. Secondly, to reduce systematic uncertainties from the neutrino flux of the reactors, identically designed detectors were placed at different experimental halls with different baselines (near and far) relative to the reactor cores with the far site located near the local minimum of the survival probability to maximise the sensitivity of sin²(2θ₁₃) measurements. Finally, to further reduce the systematic uncertainties of detection efficiencies, detectors were placed in a side-by-side fashion at each experimental hall and calibrated with the same sets of radioactive sources.

These features allowed Daya Bay to achieve unprecedented sensitivity on θ₁₃

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Distance to reactor cores [m]

Hall Depth [m] Detector D1 D2 L1 L2 L3 L4

EH1 93 AD1 362 371 903 817 1353 1265

AD2 358 368 903 817 1354 1266

EH1 100 AD3 1332 1358 468 490 558 499

AD8 1337 1363 473 495 559 501

EH1 324

AD4 1920 1894 1533 1534 1551 1525 AD5 1918 1892 1535 1535 1555 1528 AD6 1925 1900 1539 1539 1556 1530 AD7 1923 1898 1541 1541 1560 1533

Table 2.1: The detector baselines to the reactor cores (D for Daya Bay NPP, L for Ling Ao NPP). The detectors are labeled according to the order of assembly and installation.[17]

measurements as we shall see in the following sections.

2.2 Experiment layout

The Daya Bay experiment utilized 8 (6 at launch, 2 were added later) identically designed anti-neutrino detectors and 6 reactor cores from the Daya Bay NPP, Ling Ao NPP and Ling Ao-II NPP. The detectors were placed in three different experimental halls (EH1, EH2 and EH3) with EH1 and EH2 being the near sites and EH3 being the far site as shown in figure 2.1 and their relative distances listed in table 2.1. The baselines were chosen to optimize the sensitivity of sin²(2θ₁₃), to see this, one can first calculate the survival probability Pν¯e→¯νe(L) using equation 1.11, the result is shown below

P_ν_¯_e_→¯ν_e(L) = 1− cos⁴θ₁₃sin²2θ₁₂sin²∆₂₁

− sin²2θ₁₃ cos²θ₁₂sin²∆₃₁+ sin²θ₁₂sin²∆₃₂ (2.1)

where ∆_ji ≈ 1.267∆m²ji(eV²)L(m)/E_ν(MeV). Since sin²(2θ₁₃) is only presented in the third term of the above equation, it is essential to put the detectors at the extremum of that term as shown in figure 2.2

Another geographical advantage of Daya Bay was the surrounding mountains which acted as natural shieldings for the experimental halls to reduce cosmic ray induced background such as⁹Li and⁸He.

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Figure 2.1: Layout of the Daya Bay experiment. The figure shows the relative locations of the experimental halls (EH1, EH2 and EH3) and the reactor cores of the Daya Bay NPP and the Ling Ao NPP. The detectors were first built and tested at the surface assembly building (SAB) and filled with liquid scintillator (LS) at the LS Hall before transported and installed in the experimental halls with two detectors in the near sites (EH1 and EH2) and four detectors in the far site (EH3). Reference from [17].

2.3 Anti-neutrino Detector

Similar to previous neutrino experiments, the Daya Bay experiment used the inverse beta decay (IBD) reaction to detect anti-neutrinos originated from the reactor cores and the eight anti-neutrino detectors were identically designed to reduce variations of detection efficiencies. The IBD process can be identified using coincidence of a prompt signal from the annihilation of the e⁺with energy E_prompt = E_e⁺+ 2m_e(energy peak∼ 3 MeV) and a delayed signal from the neutron capture from other nuclei (mostly gadolinium).

The detector was designed in a nested structure where the inner most region, the target mass region, consisted of 20 tons of linear-alkyl-benzene-based liquid scintillator (LS) doped with 0.1% of Gd by mass (GdLS) contained in a 3 by 3 m cylindrical acrylic vessel.

Studies have shown that Gd can efficiently capture neutrons and release gamma rays of total energy around 8 MeV[18]. The 8 MeV signals, which has energy much higher than most natural radioactive background, paired with the annihilation signals from e⁺ can

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Figure 2.2: The figure shows the survival probability calculated using equation 2.1 assuming Eν = 4MeV (approximately the peak energy of reactor neutrinos) and sin²2θ₁₃ = 0.1. The blue line represents the survival probability with all terms taken into consideration while the orange line shows only the contribution from the third term in the equation (the term correlated with sin²2θ13). The green band and the red band shows roughly where the near sites and the far site are located relative to the reactor cores respectively.

form distinctive coincidence signals crucial to the identification of IBDs in Daya Bay. The inner acrylic vessel (IAV) was immersed in 20 tons of pure LS to increase the efficiency of gamma ray detections which was futher contained in a 4 by 4 m acrylic vessel, the outer acrylic vessel (OAV). Finally, the OAV is contained in a 5 by 5 m stainless steel vessel (SSV) filled with mineral oil (MO) with similar density to the LS and GdLS to balance the pressure. Between the OAV and the SSV 192 8-inch Hamamatsu R5912 photomultiplier tubes (PMTs) were mounted on the SSV to detect scintillation light. The PMTs were distributed in a cylindrical fashion with each ring consisting of 24 PMTs and 8 rings in total. On the top and the bottom of the rings, two specular reflectors were placed to prevent light leakage and improve light collection. On top of the SSV three automated calibration units (ACUs) with radioactive sources (⁶⁰Co,⁶⁸Ge and²⁴¹Am-¹³C) and LEDs were used to calibrate the detectors. See figure 2.3 for the cross-section diagram of the detector.

After the assembling and testing at the SAB and the LS Hall, the detectors were moved to each experimental halls. Inside each experimental hall there was a 10 m deep water pool acting as a water-Cherenkov muon detector and the detectors were placed inside the pool. The water pool was divided into two regions, the inner water shield (IWS) and the outer water shield (OWS) with multiple PMTs mounted on the walls to detect Cherenkov

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ACU-A

stainless steel vessel bottom reflector 4-m acrylic vessel 3-m acrylic vessel

PMTs

overflow tank

ACU-B ACU-C

calibration pipe top reflector

PMT cable dry box

PMT cables radial shield

...

5 m

Figure 2.3: Cross-section diagram of the Daya Bay anti-neutrino detector. The diagram shows the relative position of each component in the detector. Reference from [17].

light from energetic muons. On top of the water pool, a four-layer modular resistive plate chamber (RPC) was installed to provide additional information for muon identifications.

The detectors (ADs, IWS, OWS and RPCs) worked independently with a local trigger board for each system. For each system, a trigger was issued under the following conditions:

1. AD: The total count of channels over threshold (NHIT)≥ 45 or analog sum (ESUM) was≥ 65 PE (∼ 0.4 MeV)

2. IWS: NHIT≥ 6

3. OWS: NHIT≥ 7 for EH1 and EH2, ≥ 8 for EH3

4. RPC: Three of four layers of a module were above threshold

5. Random: Randomly issued to monitor the level of subthreshold or accidental activity

6. Calibration: Simultaneous with each pulse of light emitted from a LED

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RPCs

inner water shield

AD

PMTs Tyvek outer water shield

AD support stand

concrete

Figure 2.4: Diagram of the near site detectors and water pool. Two ADs were immersed in the water pool Cherenkov detector which was further divided into two optically separate regions IWS and OWS with RPCs installed ontop of the pool. Reference from [17].

7. Cross detector: A master trigger board (MTB) at each site could forward triggers from one detector to another. Used to capture activities within the muon systems when ADs detected potential ν.

When a trigger was issued, the time to digital converter (TDC), peak ADC and pedestal ADC values for each channel within the past 1.2 µs were recorded. The trigger was then saved for later offline analysis.

2.4 Event Reconstruction

One of the most important aspect of the experiment was to eliminate the variation of detector-to-detector detection efficiencies which was strongly correlated with energy reconstruction because the identification of IBDs depended on the identification of the prompt signals (Eprompt ∼ 3 MeV) and the delay signals (Edelay ∼ 2MeV for nH or ∼ 8 MeV for nGd) which in turn depended on the reconstructed energy.

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In Daya Bay, the reconstructed energy was calculated using

E_rec=

PMTsX

i

Q_i Q¯^SPE_i

!

f_act(t)f_pos(r_rec, t)

N^{P E}(t) (2.2)

where

• Q_i: ADC^peak_i − ADC^pedi for each PMT in the detector.

• ¯Q^SPE_i : Average ADC counts per single photoelectron (SPE).

• f_act(t): Time dependent PMT correction term accounted for the ratio between total and active PMTs.

• N^PE: Time dependent scalar defined as the mean deposited energy per SPE.

• fpos(rrec, t): Time dependent spatial non-uniformity correction term used to compensate for the variations of energy against the reconstructed position (r_rec) of an event.

In the following subsections we shall discuss how these terms were measured.

2.4.1 PMT calibration

First, the operating voltage of each PMT to achieve the gain of 10⁷was measured prior to installation. Since the gain can drift from channel to channel, a calibration method based on dark noise was developed to ensure stability over time. In this method, each time a detector is triggered, a few hundred nanoseconds window is opened prior to the trigger to capture the uncorrelated signals mostly from thermal emissions (also known as PMT dark noise) and then the triggered signal could be subtracted from the dark noise to estimate the gain of each PMT.

The charge distribution could be modeled using

f (Q) = X∞ n=0

P (n|µ)Gn(Q| ¯Q^SPE, σ_SPE² ) (2.3)

where P (n|µ) is the Poisson distribution with rate constant µ and Gn is the convolution of n independent Gaussians with mean and variance equal to ¯Q^SPEand σ_SPE² . Using this

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equation, we could estimate the mean SPE charge ( ¯Q^SPE) and the resolution (σ²_SPE) by fitting this equation to the measured charge distrubtion.

Another active PMT correction f_actis applied to account for active PMTs. During data monitoring, PMTs with abnormal behaviors (poor gain, hign noise etc.) were temporarily disabled. To compensate for the bias in light collection caused by disabled PMTs, the factor fact= Ntotal/Nactivewas introduced in equation 2.2.

2.4.2 Light yield conversion

To determine the deposited energy of a trigger, we need to convert the light yield gathered from PMTs to energy. In Daya Bay, two independent methods were used to calibrate this factor.

• Weekly⁶⁰Co deployment at the detector center

• Spallation neutrons captured by Gd (nGd)

Both methods had known energy peaks (∼ 2.5MeV for ⁶⁰Co or ∼ 8.0 MeV for nGd) which could be used to determine N^PE.

2.4.3 Nonuniformity

It was known that the light yield can vary from position to position. This phenomenon, also known as nonuniformity, was mostly due to optical properties of the detector. To correct for this effect, we first need to reconstruct the position of the physical event. In Daya Bay, two independent methods were developed.

In the first method, one first calculates the center of charge for the signal,

⃗ r_COC =

P_PMTs

i ⃗r_i _ˆ^Qⁱ

Q^SPE_i

PPMTs i

Qi

Qˆ^SPE_i

(2.4)

where ⃗r_i is the position of the i-th PMT. We then use the center of charge position to

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reconstruct the position of the actual event in cylindrical coordinates

r_rec= c₁r_COC− c2r²_COC (2.5)

z_rec= (z_COC− c3z³_COC)(c₄− c5r_COC) (2.6)

ϕ_rec= ϕ_COC (2.7)

where c_is are constants to be determined with calibration sources deployed at known positions in the detectors.

In the second method, a pattern matching technique was used to determine the position of the event. By dividing the detector into 9600 regions (20× 20 × 24 bins in the (r, z, ϕ) coordinate) and simulate the interactions in each region to find the charge pattern for each region. With these templates, one can find the recontructed position by maximizing the likelihood

⃗r_rec= argmax

⃗r

PMTsX

i

lnP (N_iôbs|Ni(⃗r)) P (N_iôbs|N_iôbs)

(2.8)

where P (n|µ) is the probability of n events given Poisson distribution with mean value µ, N_i^obsis the observed number of PEs in the i-th PMT and N_i(⃗r) is the number of PEs in the i-th PMT given the interaction position ⃗r from the template.

Both reconstruction methods were checked by⁶⁰Co sources placed at known positions and showed consistent results with < 20 cm bias and < 40 cm resolution.

With the reconstructed positions, we could proceed to correct for light yield nonuniformity in the detectors. The correction term was modeled by f_pos(⃗r, t), which could be further decomposed into

fpos(⃗r, t) = (fa(ϕ)fb(z, r)fc(t, r))⁻¹. (2.9)

The dependence on ϕ is mostly due to the relative orientation of PMTs and local geomagnetic field which can be modeled by

f_a(ϕ) = 1 + α sin(ϕ− ϕ0) (2.10)

where α and ϕ₀ were determined using light yield of spallation neutrons. The effect of

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r (mm)

0 1000 2000 3000

z (mm)

-2000 0 2000 0.8

1 1.2

Figure 2.5: Light yield variation due to z and r. The value shown in the vertical axis corresponds to the light yield relative to the center of the detector. The red points represent the calibration data from ACUs (r = 0mm, 1350mm, 1772.5mm) and were used to constrain the surface. Reference from [17].

this term was found to be around 1% for all detectors.

The f_b(z, r) component was independently modeled in two different ways depending on how the position was reconstructed. For the first reconstruction method, this term was modeled by

f_b(z, r) = (α₀r²)(α₁ + α₂z + α₃z²+ α₄z³) (2.11)

where α_i were constants determined with calibration sources at known positions. The final effect is shown in figure 2.5

In the other method, a nonuniformity map with 10× 10 pixels in the (z, r²) coordinate was constructed using spallation neutrons as the calibration source to find the relative yield in each pixel as shown in figure 2.6. Both methods showed light yield variations about 10% and 17% depending on the position and a < 3% variations between all detectors.

Finally, we have the time-dependent term f_c(t, r) to account for the change of

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2

)

2

(m r

0 0.5 1 1.5 2 2.5 3 3.5 4

z (m)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0.85 0.9 0.95 1 1.05 1.1 1.15

Figure 2.6: Light yield variation due to z and r measured with spallation neutrons. The heatmap shows the light yield relative to the center of the detector. The dashed line represents the boundary of GdLS and LS regions. Reference from [17].

nonuniformity over time. This change was modeled using

f_c(t, r) = (α₀+ α₁r²)t (2.12)

where α_i were time-dependent parameters determined with calibration sources (⁶⁰Co or spallation neutrons) over time.

2.4.4 Energy resolution

The energy resolution of the detectors was modeled by

σ_E Erec

= s

a²+ b² Erec

+ c²

E_rec² (2.13)

which was inspired by previous study [19]. In the above expression each term was used to modeled different effects

• a: nonuniformity, time drifting (∼ 0.016)

• b: photon statistics (∼ 0.081MeV^1/2)

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Reconstructed energy (MeV)

0 1 2 3 4 5 6 7 8 9

Energy resolution (%)

0 2 4 6 8 10 12

14 MC

Calibration sources IBD neutrons Natural alphas Best fit to all peaks Naked gammas Data

137Cs

54Mn

68Ge

215Po

214Po

212Po ⁴⁰K

n-H ⁶⁰Co

12C*

12C n-

16O*

n-Gd

Figure 2.7: Energy resolution of the detectors. The best fit lines was modeled using equation 2.13. Naked gammas (dashed orange line) showed the intrinsic (without certain optical effects) resolution of the detectors. Reference from [17].

• c: dark noise (∼ 0.026MeV)

The parameters were determined with various calibration sources and checked with Monte Carlo simulations. The result is shown in figure 2.7.

2.4.5 Anti-neutrino energy

In reactor neutrino experiments, E_ν plays an important role in determining the mass difference ∆m²_ee, therefore it is desirable that we can transform the reconstructed energy E_recback to E_ν. Due to the mass difference between neutrons and positrons, most of the antineutrino energy was transferred to the positron after inverse beta decay. The kinetic energy of the positron can be calculated by

E_k,e⁺ ≈ Eν + m_p− mn− me⁺ ≈ Eν − 1.8MeV (2.14)

The deposit energy of the positron in LS (E_prompt) is then

Eprompt= E ⁺ + (m ⁺ + m −)≈ E ⁺ + 1.0MeV (2.15)

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Reconstructed Energy (MeV)

0 2 4 6 8 10 12 14 16 18

Events / 0.25 MeV

500 1000 1500 2000 2500 3000 3500 4000 4500

Reconstructed energy (MeV)

0 2 4 6 8 10 12 14 16 18

Data / best fit 0.8 1 1.2

B decays

12

Data Best Fit Model

B signal

12

N backg.

12

Figure 2.8: Comparison of simulated ¹²B and data. Non-linearity corrections were included in the simulations. Reference from [17].

where the term in the parantheses corresponds to the annihilation of a positron and an electron. Combining both equations we have

E_ν ≈ Eprompt+ 0.8MeV (2.16)

To estimate the true energy of the prompt signal, additional corrections on the interactions of positrons in scintillator were required as listed below.

1. Scintillator non-linearity due to ionization quenching.

2. Cherenkov light yield.

3. Electronics non-linearity due to the temporal profile of scintillation light and readout electronics.

These effects were modeled based on simulations and estimated using the continuous electron spectrum from the decays of spallation¹²B as shown in figure 2.8. The final energy model is shown in figure 2.9.

2.5 IBD Signal Selection

In Daya Bay, anti-neutrinos originated from reactor cores interact with protons to produce neutrons and positrons under inverse beta decay (IBD). To identify these IBD signals,