利用超環面儀器探究希格斯粒子衰變至雙 W 玻色子機制中的量子糾纏效應

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研究生：	林祥源 Lin, Siang-Yuan
論文名稱：	利用超環面儀器探究希格斯粒子衰變至雙 W 玻色子機制中的量子糾纏效應 Studies on quantum entanglement in the H → WW∗ channel with the ATLAS detector
指導教授：	徐百嫻 Hsu, Pai-Hsien
口試委員:	曾柏彥 Tseng, Po-Yen 陳凱風 Chen, Kai-Feng
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2025
畢業學年度：	113
語文別：	英文
論文頁數：	103
中文關鍵詞：	量子糾纏、機器學習、希格斯玻色子、超環面儀器、大強子對撞機、對撞機物理
外文關鍵詞：	Quantum Entanglement, Machine Learning, Higgs Boson, ATLAS, Large Hadron Collider, Collider Physics
相關次數：	點閱：7 下載：0
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糾纏現象是量子物理的核心特性，此奇妙之機制顛覆了我們對於定域性以及現實的理解。
傳統的量子糾纏實驗的能量尺度多位在原子、分子物理等級;然而，我們亦對於此機制在高能尺度之下的行為感興趣。
本論文使用超環面儀器的模擬數據，呈現在 H → WW∗ → eνμν 頻道中的量子糾纏現象之初步研究。
此研究專注於膠子融合機制下生成的標準模型希格斯玻色子，以及其在標準模型質量下的次大衰變頻道。
利用標準模型希格斯玻色子的純量特性與弱交互作用的向量流—贗向量流耦合結構，我們透過最終態輕子之投影量測進行CGLMP 不等式型式之貝爾定理的實驗驗證。
在真值完備的條件下,我們首先分析了與量子糾纏相關之可觀測量在系統中的期望值與分佈，接著探討實驗上必要的篩選條件所導致的影響。
在擬真情況下，為了重建中間態希格斯玻色子與 W 玻色子對之靜止座標系，我們必須克服最終態微中子所造成的運動資訊缺失。
本論文提出了兩種重建中間態粒子四動量的方法：一為解析近似法，二為神經網路回歸模型。
本研究結果顯示，相較於解析近似法，神經網路回歸模型表現上顯著為優。
最後，我們分析了利用神經網路回歸模型估計數值所導出的量子糾纏可觀測量之結果。

Entanglement is an intriguing phenomenon at the heart of quantum physics that challenges locality and our understanding of reality.
While traditional experiments on quantum entanglement are usually conducted at the energy scale of atomic and molecular physics, we are also interested in probing such phenomena at the high energy scale.
This thesis presents a preliminary study of quantum entanglement in the H → WW∗ → eνμν channel using simulation data from the ATLAS experiment.
Our study focuses on the dominant gluon-gluon fusion production mode of the Standard Model Higgs boson and its second-greatest decay channel at the Standard Model mass.
Exploiting the scalar property of the Standard Model Higgs boson and the V−A structure of weak interactions, we perform Bell tests using the CGLMP inequality via projective measurements of the final state leptons.
At the truth level, we first analyze the ensemble averages and distributions of observables relevant to the entanglement study, then investigate the effects of experimental selections. In practical application, we must overcome the missing kinematic information due to neutrinos in the final state in order to reconstruct the rest frames of the Higgs and both W bosons.
This thesis presents two approaches to reconstructing four-momenta of intermediate particles: an analytical approximation method and a neural network regression model.
Our findings show that the neural network regression model significantly outperforms analytical approximations.
Finally, we analyze the results of the entanglement observables calculated using predictions from the proposed neural network regression model.

Abstract (Chinese) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .II
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .III
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .IV
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .X

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
2 The Higgs boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 The LHC and ATLAS experiment . . . . . . . . . . . . . . . . . . . . . . . .9
3.1 The Large Hardon Collider . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 The ATLAS experiment . . . . . . . . . . . . . . . . . . . . . . . . . . .10

Quantum entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
1 Pure and mixed ensembles . . . . . . . . . . . . . . . . . . . . . . . . . .17
1.1 Composite systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 Bell's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
2.1 CHSH inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Quantum state tomography . . . . . . . . . . . . . . . . . . . . . . . . . .23
3.1 Weyl-Wigner transformation . . . . . . . . . . . . . . . . . . . . . . . .25
3.2 Lepton spin projection . . . . . . . . . . . . . . . . . . . . . . . . . .25
3.3 Bipartite system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
3.4 CGLMP inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

Entanglement analysis in the H → WW* → lνlν channel . . . . . . . . . . . . 33
1 Constructing the helicity coordinate system . . . . . . . . . . . . . . . . 33
2 Constructing Bell test observables . . . . . . . . . . . . . . . . . . . . .34
3 Analysis dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
3.1 Simulation sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Results at truth level . . . . . . . . . . . . . . . . . . . . . . . . . . .38
5 Selection cut effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Rest frame reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1 Analytical approximation method . . . . . . . . . . . . . . . . . . . . . . 43
1.1 Approximating the di-neutrino pz . . . . . . . . . . . . . . . . . . . . .43
1.2 Separate neutrino momentum . . . . . . . . . . . . . . . . . . . . . . . .46
1.3 Pairing with leptons . . . . . . . . . . . . . . . . . . . . . . . . . . .47
1.4 Evaluation of analytical approximation method . . . . . . . . . . . . . . 48
2 Machine learning approach . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.1 Neural network regression model . . . . . . . . . . . . . . . . . . . . . 56
2.2 Model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
3 Model comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
1 Analysis dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
2 Resolving spacelike four-momentum . . . . . . . . . . . . . . . . . . . . . 67
3 Entanglement observable calculation . . . . . . . . . . . . . . . . . . . . 71
3.1 Directional cosines ξ_0,1_xyz . . . . . . . . . . . . . . . . . . . . . . 72
3.2 Bell operator values B_CGLMP_xyz . . . . . . . . . . . . . . . . . . . . .75

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77

A Auxillary evaluation plots for selection cut effects . . . . . . . . . . . . .79
B Auxillary evaluation plots for analytical approximation method . . . . . . . .88
C Auxillary evaluation plots for neural network regression . . . . . . . . . . .92
D On and off shell W boson separation . . . . . . . . . . . . . . . . . . . . . 97

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99
                                

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