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Just a Taste Lectures on Flavor Physics

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Just a Taste Lectures on Flavor Physics UCR-TR-2017-FLIP-K-2SO Just a Taste Lectures on Flavor Physics Yuval Grossmana and Philip Tanedob [email protected], [email protected] a Department of Physics, lepp, Cornell University, Ithaca, ny 14853 b Department of Physics & Astronomy, University of California, Riverside, ca 92521 Abstract We review the flavor structure of the Standard Model and the ways in which the flavor param- eters are measured. This is an extended writeup of the tasi 2016 lectures on flavor physics. Earlier versions of these notes were presented at pre-susy 2015 and Cornell University's Physics 7661 course in 2010. Contents 1 Introduction 3 2 Model building 4 2.1 The Standard Model . .5 2.2 Global, accidental, and approximate symmetries . .7 2.3 How to count physical parameters . .8 2.4 Counting parameters in the Standard Model . .9 3 The flavor structure of the Standard Model 11 3.1 The CKM matrix . 11 3.2 Parameterizations of the CKM matrix . 13 3.3 CP violation . 15 3.4 The Jarlskog Invariant . 17 3.5 Unitarity triangles and the unitarity triangle . 17 3.6 Flavor Symmetries . 19 4 Tree-level FCNCs in the Standard Model 21 4.1 Charged versus neutral currents . 21 arXiv:1711.03624v1 [hep-ph] 9 Nov 2017 4.2 The possible sources of FCNCs . 22 4.3 Photon and gluon FCNCs: gauge invariance . 22 4.4 Higgs FCNCs: Yukawa alignment . 22 4.5 Z FCNCs: broken gauge symmetry . 23 5 Loops and the GIM mechanism 25 5.1 Example: b ! sγ ......................................... 26 5.2 History of the GIM mechanism . 27 6 Connecting to experiment: meeting the hadrons 28 6.1 What we mean by `stable' . 29 6.2 Hadron quantum numbers . 30 6.3 Binding energy . 32 6.4 Light quarks, heavy quarks, and the heaviest quark . 33 1 6.5 Masses and mixing in mesons . 34 6.6 The light, pseudoscalar mesons . 36 6.7 Hadron names . 37 7 Parameterizing QCD 39 7.1 The decay constant . 43 7.2 Remarks on the vector mesons . 46 7.3 Form factors . 47 8 The CKM: Light quarks 47 8.1 Measuring jVudj .......................................... 48 8.2 Measuring jVusj .......................................... 51 9 The CKM: Heavy quarks 56 9.1 Measuring jVcsj .......................................... 56 9.2 Measuring jVcdj .......................................... 59 9.3 Measuring jVcbj .......................................... 61 9.4 Measuring jVubj .......................................... 63 10 The trouble with top 64 10.1 Tops in loops . 65 10.2 Measuring the b ! sγ penguin . 65 10.3 Measuring b ! sγ versus b ! dγ ................................ 66 11 Meson Mixing and Oscillation 67 11.1 Open system Hamiltonian . 68 11.2 Time evolution . 72 11.3 Time scales . 72 11.4 Flavor tagging . 75 11.5 Calculating ∆m and∆Γ..................................... 77 12 CP violation 80 12.1 General aspects of CPV . 80 12.2 CP Violation in decay . 83 12.3 CP violation from mixing . 87 A Some Useful Facts 90 B Goldstones, currents, and pions 90 B.1 Goldberger{Treiman Relation . 93 B.2 Ademollo{Gatto from current algebra . 94 B.3 K`4 ................................................. 94 C The vector mesons 96 C.1 Why are the pseudoscalar and vector octets so different? . 100 D Heavy Quark Symmetry 103 D.1 The hydrogen atom . 104 D.2 Heavy quark symmetry: heuristics . 105 D.3 Heavy quark symmetry: specifics . 106 D.4 Heavy Quark Effective Theory . 107 D.5 HQET for jVcbj .......................................... 109 2 UCR-TR-2017-FLIP-K-2SO E Meson Mixing and CP formulae 111 F Solutions to Problems 114 1 Introduction In this set of lectures, we introduce basics of flavor physics, that is, the part of Nature where the differences between the quarks plays a role. While this writeup includes more material than presented at the lectures, this write up is still just a taste of the entire field; for more in-depth reading we refer to other recent tasi lectures [1{3], reviews [3{19] and books [20,21] on the subject. To start off, here's a list of branching ratios collected from the pdg.1 Br(B ! Xµν) = 0:1086(16) (1.1) Br(B ! Xeν) = 0:1086(16) (1.2) −4 Br(B ! Xsγ) = 3:49(19) × 10 (1.3) + − −9 Br(Bs ! µ µ ) = 2:4(8) × 10 (1.4) Br(B+ ! D¯ 0`+ν) = 2:27(11) × 10−2 (1.5) Br(B− ! π0`−ν¯) = 7:80(27) × 10−5 (1.6) + − −9 Br(KL ! µ µ ) = 6:84(11) × 10 (1.7) Br(K+ ! µ+ν) = 0:6356(11) (1.8) Br( ! µ+µ−) = 5:961(33) × 10−2 (1.9) Br(D ! µ+µ−) < 6:2 × 10−9 : (1.10) Stare at these for a moment|do you see a pattern? If you were trapped on a desert island without your smart phone and only the pdg, some of the observations from these branching ratios that you may come up with are: 1. Lepton universality. Swapping one generation of leptons with another does not appear to affect the branching ratios of these transitions. 2. Flavor-changing neutral currents are small. On the other hand, processes that change flavor are suppressed for charge-neutral transitions compared to transitions between hadrons of different charge. 3. Generation hierarchy. Decays between third and first generation are suppressed compared to that of third to second generation. In these lectures we uncover why these properties and others exist in the Standard Model (sm) of particle physics. We elucidate that these features are, in fact, predicted once we specify the particle content and electroweak charges of the sm. In contrast, other features of the theory are particular to specific parameters of this effective theory. In the second part of these lectures, we tackle the question of how these parameters are actually measured in low-energy systems where qcd confines the quarks into hadrons. Problem 1.1. Using the PDG. Use the pdg to answer the following questions: 1The Review of Particle Physics is prepared by the Particle Data Group and is often referred to as 'the pdg'[22]. It just about contains everything you ever wanted to know about particle physics. 3 1. What are the component quarks of the D+ meson? What is its mass? 2. What are the component quarks of the Λ baryon? What is its spin? 3. What is Br(τ ! µνν¯)? 4. What is the width (in eV) of the B+ meson? 5. What is the average distance a B+ meson will travel if γ = 4? 2 Model building A theorist excitedly runs into an experimentalist's office one day, exclaiming that not only has the theorist uncovered an elegant model that solves the biggest outstanding questions in particle physics, but that it makes a robust experimental prediction. The excitement is contagious, and the experimentalist applies for grants, hires postdocs, builds new laboratory equipment, and starts to take data. Many years after the ini- tial encounter, the experimentalist's entire research group|now exclusively focused on proving this one, elegant model|is ready to unblind its data. That afternoon, the ex- perimentalist sulks despondently into the theorist's office. \Prof. Theorist? I'm really sorry to break this to you, but the data rules out the model." The theorist looks up at the experimentalist, considers the streaks of white hair and their many years of collab- oration on this project, and finally says, \What a shame! Did you know that I spent two whole weeks of my life developing that model?" {Tim M.P. Tait The goal of high-energy physics is to fill in the right-hand side of the following equation: L = ? (2.1) Our job is to find the effective Lagrangian of nature and experimentally determine its parameters. In order to do this, we build models: these are our hypotheses. In fact, it is perhaps more accurate to say that a theorist's job is not model building, but rather model designing. In order to design our Lagrangian, we need 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, such as 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' qualifier 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 limits us to only a finite number of terms. This condition comes to us from the principles of effective field theory and Wilsonian renormalization. We assume that the more fundamental ultraviolet (uv) theory generates all possible operators|including non-renormalizable terms|at the uv scale. By 4 dimensional analysis, the non-renormalizable operators depend on negative powers of the uv scale Λ. Thus at the low energies µ Λ where the theory is valid, we expect that these operators are suppressed by powers of µ/Λ 1. Thus such non-renormalizable operators exist in principle but they should come with small coefficients. The effect of these terms on low-energy observables is something we want to understand, but we expect them to be subdominant to phenomenology induced by renormalizable terms.
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