标题： Higgs玻色子的黄金衰变通道的QCD修正 显示英文标题

标题： QCD corrections to the Golden decay channel of the Higgs boson

摘要： 精确研究标准模型希格斯部分对于加深我们对基本相互作用的理解以及揭示超出标准模型的新物理现象至关重要。 为了充分利用未来精密机器的潜力，这些机器旨在提供对希格斯特性高度精确的实验测量，必须最小化希格斯部分可观测量的理论误差，例如产生和衰变率。 在本论文中，我们专注于为与希格斯玻色子的黄金衰变通道相关的可观测量提供精确预测。 我们通过在微扰理论中引入NNLO混合QCD-电弱修正，改进了该通道的部分衰变宽度，特别是$H \to Z^{(*)}Z^{(*)} \to e^+ e^- \mu^+ \mu^-$的理论预测。 我们还描述了在$\mathcal{O}(\alpha \alpha_s)$修正中出现的两个环主积分的完整解析计算，针对$HZZ$顶点，其中两个$Z$玻色子均为非定域的，采用微分方程方法并保留完整的质量依赖性。 所有主积分的解析结果以陈的迭代积分形式给出，其对数核按维度正则化参数$\epsilon$的顺序展开，同时包括解析边界常数。 本论文还展示了在$\mathcal{O}(\alpha \alpha_s)$下$H \to e^+ e^- \mu^+ \mu^-$衰变的现象学研究，通过在公开代码Hto4l中实现衰变振幅的全部计算，对最终态轻子进行相空间积分。 我们研究这些混合QCD-电弱修正对最终态轻子的不变质量分布和角度变量的影响，特别是中间$Z$-玻色子衰变平面相对于领先阶预测和NLO电弱修正的角度。 显示英文摘要

摘要： Precision studies within the Higgs sector of the Standard Model are crucial to deepen our understanding of the fundamental interactions and uncovering new physics phenomena beyond the Standard Model. To fully leverage the potential of future precision machines aiming to provide highly precise experimental measurements of the Higgs properties, it is crucial to minimize theoretical errors in the Higgs sector observables, such as production and decay rates. In this thesis, we focus on providing precise predictions for observables associated with the Golden decay channel of the Higgs boson. We improve theoretical predictions for the partial decay width of this channel, specifically $H \to Z^{(*)}Z^{(*)} \to e^+ e^- \mu^+ \mu^-$, by incorporating NNLO mixed QCD-electroweak corrections in perturbation theory. We also describe the full analytical evaluation of the two-loop master integrals appearing in the $\mathcal{O}(\alpha \alpha_s)$ corrections to the $HZZ$ vertex with both $Z$-bosons being off-shell, employing the method of differential equations retaining full mass dependence. The analytic results for all the master integrals are obtained in terms of Chen's iterated integrals with logarithmic kernels order-by-order in the dimensional regularization parameter $\epsilon$, along with analytic boundary constants. This thesis also presents a phenomenological study of the $H \to e^+ e^- \mu^+ \mu^-$ decay at $\mathcal{O}(\alpha \alpha_s)$ by implementing the entire calculation of the decay amplitude in the public code Hto4l to perform the phase space integration over final state leptons. We study the impact of these mixed QCD-electroweak corrections on the invariant mass distribution of the final-state leptons and angular variables, specifically the angle between the decay planes of the intermediate $Z$-bosons relative to leading-order predictions and NLO electroweak corrections.