本研究使用 KamLAND 的數據與理論模擬進行擬合，以評估暗物質是否會與微
中子相互作用。我們將所得模型應用於探索暗物質是否介入微中子震盪過程的
可能性，並將實驗觀測結果與模型預測進行比較。在此基礎上，進一步探討其
他可能性，並與其他實驗結果，如太陽微中子觀測極限相對照。最終，我們可
以提出關於暗物質性質的一個極限條件。

This study utilizes data from KamLAND and theoretical simulations for fit-
ting, aiming to assess whether dark matter interacts with neutrinos. We apply the
obtained model to explore the possibility of dark matter involvement in neutrino
oscillation processes, comparing experimental observations with model predictions.
Building upon this foundation, we further investigate other possibilities and con-
trast them with additional experimental results, such as limits on solar neutrino
observations. Ultimately, we can propose a constraint on the properties of dark
matter.

Contents
Contents ii
List of Tables iii
List of Figures v
1 Introduction 1
1.1 Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 The Discovery of Neutrino . . . . . . . . . . . . . . . . . . . 1
1.1.2 The Neutrino Oscillation in the Standard Model . . . . . . . 2
1.2 The History of Dark Matter . . . . . . . . . . . . . . . . . . . . . . 6
2 The Neutrino Oscillation at KamLAND 10
2.1 The Kamioka Liquid Scintillator Antineutrino Detector . . . . . . . 10
2.2 The Data of KamLAND . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Neutrino coupling to the Dark Matter 14
3.1 Ultralight Scalar Dark Matter . . . . . . . . . . . . . . . . . . . . . 14
3.2 Theoretical to Experimental . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Time Modulation (τexp ≫ τϕ ≳τevt) . . . . . . . . . . . . . . 16
3.2.2 Averaged distorted neutrino oscillations(τexp ≫ τϕ ≫ τν) . . 16
i
3.2.3 Dynamical distorted neutrino oscillations(τϕ ∼ τnu) . . . . . 17
4 Analysis and Result 18
4.1 Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Mass Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Mixing Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.5 Mass Splitting and Mixing Angle . . . . . . . . . . . . . . . . . . . 25
4.5.1 Same Parameter . . . . . . . . . . . . . . . . . . . . . . . . 26
4.5.2 Different Parameter . . . . . . . . . . . . . . . . . . . . . . 27
4.6 Compare with Solar Neutrino Data . . . . . . . . . . . . . . . . . . 28
5 Conclusion 31
A Appendix 33
A.1 Normalized Data in KamLAND . . . . . . . . . . . . . . . . . . . 33

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