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: December 9, 2010 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 . 105 12.6 Measuring b ! sγ versus b ! dγ ........................... 106 13 Meson Mixing and Oscillation 108 13.1 Open system Hamiltonian . 109 13.2 Time evolution . 112 13.3 Flavor tagging . 112 13.4 Time scales . 114 13.5 Calculating ∆m and ∆Γ . 116 14 Today's lecture: CP violation 120 14.1 CPV in mesons . 122 15 Lecture 19 124 15.1 CP violation from mixing . 127 16 Lecture 20 130 16.1 B ! ππ and isospin . 130 16.2 CP violation in mixing . 133 17 Kaon Physics 134 17.1 KL ! ππ ........................................ 134 17.2 x and y ......................................... 135 1 17.3 K ! ππ and ∆I = 2 Rule . 136 17.4 CP violation . 137 18 New Physics 139 18.1 Minimal Flavor Violation . 139 19 Supersymmetry 141 20 Monika's lecture: Flavor of little Higgs 142 20.1 Little Higgs . 142 20.2 The Littlest Higgs . 143 20.3 EWP constraints . 144 20.4 Flavor and Little Higgs . 144 3 21 Yuval Again: SUSY 144 21.1 Mass insertion approximation . 145 21.2 What can we say about models . 146 21.3 SUSY and MFV . 147 21.4 Froggat-Nielsen . 147 A Notation and Conventions 148 B Facts that you should memorize 149 C Lie groups, Lie algebras, and representation theory 150 C.1 Groups and representations . 150 C.2 Lie groups . 152 C.3 More formal developments . 155 C.4 SU(3) .......................................... 156 D Homework solutions 158 E Critical reception of these notes 174 F Famous Yuval Quotes 174 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 our Lagrangian, we need to provide three ingredients: 1. The gauge group of the model, 2. The representations of the fields under this gauge group, 3. The pattern of spontaneous symmetry breaking. The last point is typically represented by a sign, for example the sign of the Higgs mass-squared parameter at the unstable vacuum (µ2 < 0). Once we have specified these ingredients, the next step is to write the most general renormaliz- able Lagrangian that is invariant under the gauge symmetry and provides the required spontaneous symmetry breaking pattern. This is far from a trivial statement. The `most general' statement tells us that all terms that satisfy the above conditions must be present in the Lagrangian, even the terms that may be phenomenologically problematic. For example, even though we might not want to include a term that induces proton decay, we cannot simply omit it from our model without some symmetry principle that forbids it. On the other hand, renormalizability strongly constrains the form of a Lagrangian and, in fact, limits us to only a finite number of terms. This condition comes to us from the principles of effective field theory and Wilsonian renormalization group. We assume that the UV (more fundamental) theory may generate all possible operators|including non-renormalizable terms| at the UV scale..