Just a Taste Lectures on Flavor Physics Lecturer: Yuval Grossman(a) (b) LATEX Notes: Flip Tanedo Institute for High Energy Phenomenology, Newman Laboratory of Elementary Particle Physics, Cornell University, Ithaca, NY 14853, USA E-mail: (a) [email protected], (b) [email protected] This version: March 1, 2012 Abstract This is a set of LATEX'ed notes from Cornell University's Physics 7661 (special topics in theoretical high energy physics) course by Yuval Grossman in Fall 2010. The lectures as given were flawless, all errors contained herein reflect solely the typist's editorial and/or intellectual deficiencies! Contents 1 Introduction 1 2 Model building 2 2.1 Example: the Standard Model . .3 2.2 Global, accidental, and approximate symmetries . .4 2.3 Learning how to count [parameters] . .5 2.4 Counting parameters in low-energy QCD . .6 2.5 Counting parameters in the Standard Model . .8 3 A review of hadrons 10 3.1 What we mean by `stable' . 10 3.2 Hadron quantum numbers . 12 3.3 Binding energy . 14 3.4 Light quarks, heavy quarks, and the heaviest quark . 15 3.5 Masses and mixing in mesons . 16 3.6 The pseudoscalar mesons . 19 3.7 The vector mesons . 20 3.8 Why are the pseudoscalar and vector octets so different? . 25 3.9 Hadron names . 26 4 The flavor structure of the Standard Model 29 4.1 The CKM matrix . 29 4.2 Parameterizations of the CKM matrix . 32 4.3 CP violation . 33 4.4 The Jarlskog Invariant . 35 4.5 Unitarity triangles and the unitarity triangle . 36 5 Charged versus neutral currents 38 6 Why FCNCs are so small in the Standard Model 39 6.1 Diagonal versus universal . 39 6.2 FCNCs versus gauge invariance . 39 6.3 FCNCs versus Yukawa alignment . 40 6.4 FCNCs versus broken gauge symmetry reps . 41 7 Parameterizing QCD 43 7.1 The decay constant . 47 7.2 Remarks on the vector mesons . 50 7.3 Form factors . 52 7.4 Aside: Goldstones, currents, and pions . 53 8 Flavor symmetry and the CKM 57 8.1 Measuring jVudj ..................................... 57 8.2 Measuring jVusj ..................................... 61 8.3 Measuring jVcsj ..................................... 69 8.4 Measuring jVcdj ..................................... 73 9 Intermission: Effective Field Theory 77 9.1 EFT is not a dirty word . 78 9.2 A trivial example: muon decay . 81 9.3 The trivial example at one loop . 83 9.4 Mass-independent schemes . 86 9.5 Operator Mixing . 86 10 Remarks on Lattice QCD 86 10.1 Motivation and errors . 87 10.2 `Solving' QCD . 87 10.3 The Nielsen-Ninomiya No-Go Theorem . 88 10.4 The quenched approximation . 90 11 Heavy quark symmetry and the CKM 90 11.1 The hydrogen atom . 91 11.2 Heavy quark symmetry: heuristics . 92 11.3 Heavy quark symmetry: specifics . 93 11.4 HQET . 95 2 11.5 Measuring jVcbj ..................................... 97 11.6 Measuring Vub ...................................... 101 12 Boxes, Penguins, and the CKM 102 12.1 The trouble with top . 102 12.2 Loops, FCNCs, and the GIM mechanism . 103 12.3 Example: b ! sγ .................................... 103 12.4 History of the GIM mechanism . 104 12.5 Measuring the b ! sγ penguin . 106 12.6 Measuring b ! sγ versus b ! dγ ........................... 106 13 Meson Mixing and Oscillation 108 13.1 Open system Hamiltonian . 109 13.2 CP versus short and long . 113 13.3 Time evolution . 113 13.4 Flavor tagging . 115 13.5 Time scales . 117 13.6 Calculating ∆m and ∆Γ . 119 14 CP violation 123 14.1 General aspects of CPV . 123 14.2 CP Violation in decay (direct CP violation) . 126 14.3 CP Violation in Mixing . 128 15 Lecture 19 128 15.1 CP violation from mixing . 130 16 Lecture 20 134 16.1 B ! ππ and isospin . 134 16.2 CP violation in mixing . 137 17 Kaon Physics 137 17.1 KL ! ππ ........................................ 138 17.2 x and y ......................................... 138 1 17.3 K ! ππ and ∆I = 2 Rule . 140 17.4 CP violation . 140 18 New Physics 142 18.1 Minimal Flavor Violation . 143 19 Supersymmetry 145 20 Monika's lecture: Flavor of little Higgs 146 20.1 Little Higgs . 146 20.2 The Littlest Higgs . 146 20.3 EWP constraints . 147 3 20.4 Flavor and Little Higgs . 147 21 Yuval Again: SUSY 148 21.1 Mass insertion approximation . 148 21.2 What can we say about models . 149 21.3 SUSY and MFV . 150 21.4 Froggat-Nielsen . 151 A Notation and Conventions 152 B Facts that you should know 152 B.1 Facts . 152 B.2 Meson Mixing and CP formulae . 153 B.3 Derivation of mixing and CP formulae . 154 C Lie groups, Lie algebras, and representation theory 157 C.1 Groups and representations . 157 C.2 Lie groups . 159 C.3 More formal developments . 162 C.4 SU(3) .......................................... 163 D Homework solutions 165 E Critical reception of these notes 185 F Famous Yuval Quotes 185 4 1 Introduction \What is the most important symbol in physics? Is it this: +? Is it this: ×? Is it this: =? No. I claim that it is this: ∼. Tell me the order of magnitude, the scaling. That is the physics." {Yuval Grossman, 21 August 2008. These notes are transcriptions of the Physics 7661: Flavor Physics lectures given by Professor Yuval Grossman at Cornell University in the fall of 2010. Professor Grossman also gave introduc- tory week-long lecture courses geared towards beginning graduate students at the 2009 European School of High-Energy Physics and the 2009 Flavianet School on Flavor Physics [1] and the 2010 CERN-Fermilab Hadron Collider Physics Summer School [2]. A course webpage with homework assignments and (eventually) solutions is available at: http://lepp.cornell.edu/~yuvalg/P7661/. There is no required textbook, but students should have ready access to the Review of Particle Physics prepared by the Particle Data Group and often referred to as `the PDG.' The lecturer explains that the PDG contains \everything you ever wanted to know about anything." All of the contents are available online at the PDG webpage, http://pdg.lbl.gov/. Physicists may also order a free copy of the large and pocket PDG which is updated every two years. The large version includes several review articles that make very good bed-time reading. The data in the PDG will be necessary for some homework problems. Additional references that were particularly helpful during the preparation of these notes were the following textbooks, • Dynamics of the Standard Model, by Donoghue, Golowich, and Holstein. • Gauge theory of elementary particle physics, by Cheng and Li. Both of these are written from a theorist's point of view but do so in a way that is very closely connected to experiments. (A good litmus test for this is whether or not a textbook teaches chiral perturbation theory.) Finally, much of the flavor structure of the Standard Model first appeared experimentally in the decays of hadrons. The techniques used to describe these decays are referred to as the current algebra or the partially conserved axial current and have fallen out of modern quantum field theory courses. We will not directly make use of these methods but will occasionally refer to them for completeness. While many reviews exist on the subject, including [3] and [4], perhaps the most accessible and insightful for modern students is the chapter in Coleman's Aspects of Symmetry on soft pions [5]. Problem 1.1. Bibhushan missed part of the first lecture because he had to attend the course that he's TA'ing, \Why is the sky blue?" As a sample homework problem, what is the color of the sky on Mars? (Solutions problems in these notes appear in Appendix D.) Finally, an apology. There are several important topics in flavor physics that we have been unable to cover. Among the more glaring omissions are lepton flavor (neutrino physics), soft collinear effective theory for b decays, non-relativistic QCD, chiral symmetries, and current algebra techniques. 1 2 Model building In this lecture we will briefly review aspects of the Standard Model to frame our study of its flavor structure. Readers looking for more background material can peruse the first few sections of [1]. The overall goal of high-energy physics can be expressed succinctly in the following form: L = ? (2.1) That is, our job is to determine the Lagrangian of nature and experimentally determine its pa- rameters. In order to answer this question we would like to build models. In fact, it is perhaps more accurate to describe a theorist's job not as model building, but rather model designing. In order to design.