剑桥标准模型讲义
Cambridge Lectures on The Standard Model
AI总结：
本讲义从第一性原理构建标准模型，以EFT为主线系统讲解其理论基础、唯象学、反常抵消及超出标准模型的物理。
摘要：
这些讲义涵盖了2020至2023年间为剑桥数学荣誉学位考试（Mathematical Tripos）第三部分开设的标准模型（SM）课程。该课程包含25讲和4次习题课。在简要的历史介绍之后，讲义从第一性原理构建标准模型。我们首先利用时空对称性、软定理、规范冗余、Ward恒等式和微扰幺正性，证明基本上只有自旋/螺旋度为0、1/2、1、3/2、2的粒子能够描述物质和相互作用。剩余的自由度在于Yang-Mills规范群和物质表示的选择。有效场论（EFT）是贯穿本课程的核心主题，其中四费米相互作用和手征微扰论是关键例子。引力和标准模型本身都被作为EFT处理，具体而言是作为SMEFT（Standard Model Effective Field Theory，标准模型有效场论）处理。讲义涵盖标准模型的关键唯象方面，包括Higgs机制、Yukawa耦合、CKM矩阵、GIM机制、中微子振荡、跑动耦合和渐近自由。讲义还详细讨论了反常及其在标准模型中的非平凡抵消。文中给出了散射振幅和衰变率等简单计算示例。课程最后简要概述了标准模型的局限性，并介绍了标准模型之外物理的主要候选方案。
英文摘要：
These lecture notes cover the Standard Model (SM) course for Part III of the Cambridge Mathematical Tripos, taught during the years 2020-2023. The course comprised 25 lectures and 4 example classes. Following a brief historical introduction, the SM is constructed from first principles. We begin by demonstrating that essentially only particles with spin/helicity $0, \frac{1}{2}, 1, \frac{3}{2}, 2$ can describe matter and interactions, using spacetime symmetries, soft theorems, gauge redundancies, Ward identities, and perturbative unitarity. The remaining freedom lies in the choice of the Yang-Mills gauge group and matter representations. Effective field theories (EFTs) are a central theme throughout the course, with the 4-Fermi interactions and chiral perturbation theory serving as key examples. Both gravity and the SM itself are treated as EFTs, specifically as the SMEFT (Standard Model Effective Field Theory). Key phenomenological aspects of the SM are covered, including the Higgs mechanism, Yukawa couplings, the CKM matrix, the GIM mechanism, neutrino oscillations, running couplings, and asymptotic freedom. The discussion of anomalies and their non-trivial cancellations in the SM is detailed. Simple examples of calculations, such as scattering amplitudes and decay rates, are provided. The course concludes with a brief overview of the limitations of the SM and an introduction to the leading proposals for physics beyond the Standard Model.
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