{"title":"剑桥标准模型讲座","authors":"Fernando Quevedo, Andreas Schachner","doi":"arxiv-2409.09211","DOIUrl":null,"url":null,"abstract":"These lecture notes cover the Standard Model (SM) course for Part III of the\nCambridge Mathematical Tripos, taught during the years 2020-2023. The course\ncomprised 25 lectures and 4 example classes. Following a brief historical\nintroduction, the SM is constructed from first principles. We begin by\ndemonstrating that essentially only particles with spin/helicity $0,\n\\frac{1}{2}, 1, \\frac{3}{2}, 2$ can describe matter and interactions, using\nspacetime symmetries, soft theorems, gauge redundancies, Ward identities, and\nperturbative unitarity. The remaining freedom lies in the choice of the\nYang-Mills gauge group and matter representations. Effective field theories\n(EFTs) are a central theme throughout the course, with the 4-Fermi interactions\nand chiral perturbation theory serving as key examples. Both gravity and the SM\nitself are treated as EFTs, specifically as the SMEFT (Standard Model Effective\nField Theory). Key phenomenological aspects of the SM are covered, including\nthe Higgs mechanism, Yukawa couplings, the CKM matrix, the GIM mechanism,\nneutrino oscillations, running couplings, and asymptotic freedom. The\ndiscussion of anomalies and their non-trivial cancellations in the SM is\ndetailed. Simple examples of calculations, such as scattering amplitudes and\ndecay rates, are provided. The course concludes with a brief overview of the\nlimitations of the SM and an introduction to the leading proposals for physics\nbeyond the Standard Model.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"197 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cambridge Lectures on The Standard Model\",\"authors\":\"Fernando Quevedo, Andreas Schachner\",\"doi\":\"arxiv-2409.09211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"These lecture notes cover the Standard Model (SM) course for Part III of the\\nCambridge Mathematical Tripos, taught during the years 2020-2023. The course\\ncomprised 25 lectures and 4 example classes. Following a brief historical\\nintroduction, the SM is constructed from first principles. We begin by\\ndemonstrating that essentially only particles with spin/helicity $0,\\n\\\\frac{1}{2}, 1, \\\\frac{3}{2}, 2$ can describe matter and interactions, using\\nspacetime symmetries, soft theorems, gauge redundancies, Ward identities, and\\nperturbative unitarity. The remaining freedom lies in the choice of the\\nYang-Mills gauge group and matter representations. Effective field theories\\n(EFTs) are a central theme throughout the course, with the 4-Fermi interactions\\nand chiral perturbation theory serving as key examples. Both gravity and the SM\\nitself are treated as EFTs, specifically as the SMEFT (Standard Model Effective\\nField Theory). Key phenomenological aspects of the SM are covered, including\\nthe Higgs mechanism, Yukawa couplings, the CKM matrix, the GIM mechanism,\\nneutrino oscillations, running couplings, and asymptotic freedom. The\\ndiscussion of anomalies and their non-trivial cancellations in the SM is\\ndetailed. Simple examples of calculations, such as scattering amplitudes and\\ndecay rates, are provided. The course concludes with a brief overview of the\\nlimitations of the SM and an introduction to the leading proposals for physics\\nbeyond the Standard Model.\",\"PeriodicalId\":501339,\"journal\":{\"name\":\"arXiv - PHYS - High Energy Physics - Theory\",\"volume\":\"197 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - High Energy Physics - Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09211\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - High Energy Physics - Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
这些讲义涵盖了 2020-2023 年期间讲授的剑桥数学三科课程第三部分的标准模型(SM)课程。该课程包括 25 个讲座和 4 个示例课。在简短的历史介绍之后,我们从第一原理出发构建了标准模型。首先,我们利用时空对称性、软定理、量规冗余、沃德等效性和微扰统一性,证明基本上只有自旋/斜率为$0,\frac{1}{2}, 1, \frac{3}{2},2$的粒子才能描述物质和相互作用。其余的自由度在于对杨-米尔斯规规群和物质表征的选择。有效场理论(EFTs)是整个课程的核心主题,4-费米相互作用和手性扰动理论是主要的例子。引力和SM本身都被视为EFT,特别是SMEFT(标准模型有效场理论)。内容涉及 SM 的关键现象学方面,包括希格斯机制、尤卡瓦耦合、CKM 矩阵、GIM 机制、中微子振荡、运行耦合和渐近自由。详细讨论了 SM 中的反常现象及其非难对消。课程还提供了简单的计算实例,如散射振幅和衰变率。课程最后简要概述了 SM 的局限性,并介绍了关于标准模型之外物理学的主要建议。
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.