Phenomenology of Particle Physics NIU Spring 2011 PHYS 686 Lecture Notes Stephen P. Martin Physics Department Northern Illinois University DeKalb IL 60115 [email protected] For corrections, see: http://zippy.physics.niu.edu/ppp/ January 5, 2011 Contents 1Introduction 4 1.1 Fundamentalforces............................... ........ 4 1.2 Resonances,widths,andlifetimes . ............. 5 1.3 Leptonsandquarks................................ ....... 5 1.4 Hadrons......................................... .... 7 1.5 Decays and branching ratios . .......... 11 2SpecialRelativityandLorentzTransformations 13 3Relativisticquantummechanicsofsingleparticles 23 3.1 Klein-Gordon and Dirac equations . ........... 23 3.2 Solutions of the Dirac equation . ........... 29 3.3 TheWeylequation ................................. ...... 37 3.4 Majoranafermions ................................ ....... 38 4Maxwell’sequationsandelectromagnetism 40 5FieldTheoryandLagrangians 42 5.1 The field concept and Lagrangian dynamics . ............ 42 5.2 Quantization of free scalar field theory . .............. 48 5.3 Quantization of free Dirac fermion field theory . ............... 53 1 6Interactingscalarfieldtheories 57 6.1 Scalar field with φ4 coupling.................................. 57 6.2 Scattering processes and cross-sections . ................ 61 6.3 Scalar field with φ3 coupling.................................. 69 6.4 Feynmanrules .................................... ..... 76 7QuantumElectro-Dynamics(QED) 83 7.1 QED Lagrangian and Feynman rules . ......... 83 7.2 e e+ µ µ+ .......................................... 91 − → − 7.3 e e+ ff............................................ 96 − → 7.4 Helicities in e e+ µ µ+ ..................................100 − → − 7.5 Bhabha scattering (e e+ e e+)..............................107 − → − 7.6 Crossingsymmetry................................ .......112 7.7 e µ+ e µ+ and e µ e µ ...............................114 − → − − − → − − 7.8 Møller scattering (e e e e )...............................116 − − → − − 7.9 Gauge invariance in Feynman diagrams . ...........117 7.10 Compton scattering (γe γe )...............................119 − → − 7.11 e+e γγ ...........................................126 − → 8Decayprocesses 128 8.1 Decay rates and partial widths . ..........128 8.2 Two-bodydecays.................................. ......129 8.3 Scalar decays to fermion-antifermion pairs; Higgs decay..................131 8.4 Three-bodydecays ................................ .......135 9Fermitheoryofweakinteractions 137 9.1 Weaknucleardecays ............................... .......137 9.2 Muondecay....................................... ....139 9.3 Correctionstomuondecay .......................... ........149 9.4 Inverse muon decay (e ν ν µ )..............................151 − µ → e − 9.5 e ν µ ν ..........................................153 − e → − µ 9.6 Charged currents and π± decay................................154 9.7 Unitarity, renormalizability, and the W boson........................160 10 Gauge theories 165 10.1 Groups and representations . ...........165 10.2 The Yang-Mills Lagrangian and Feynman rules . ..............175 2 11 Quantum Chromo-Dynamics (QCD) 182 11.1 QCD Lagrangian and Feynman rules . ..........182 11.2 Quark-quark scattering (qq qq)...............................184 → 11.3 Renormalization . ........186 11.4 Gluon-gluon scattering (gg gg)...............................196 → 11.5 The parton model, parton distribution functions, and hadron-hadron scattering . 197 11.6 Top-antitop production in pp and pp collisions........................205 11.7 Kinematics in hadron-hadron scattering . ...............209 + 11.8 Drell-Yan scattering (ℓ ℓ− production in hadron collisions) . 211 12 Spontaneous symmetry breaking 215 12.1 Global symmetry breaking . ..........215 12.2 Local symmetry breaking and the Higgs mechanism . ..............218 12.3 Goldstone’s Theorem and the Higgs mechanism in general .................222 13 The standard electroweak model 224 13.1 SU(2) U(1) representations and Lagrangian . 224 L × Y 13.2 The Standard Model Higgs mechanism . ...........229 13.3 Fermion masses and Cabibbo-Kobayashi-Maskawa mixing .................233 13.4 Neutrino masses and the seesaw mechanism . .............241 13.5 Search for the Standard Model Higgs boson . .............243 13.5.1 Higgs decays revisited . ........243 + 13.5.2 Limits from the LEP2 e−e collider .........................246 13.5.3 Searches at the Tevatron . ........247 13.5.4 Searches at the LHC . .....248 Appendix A: Natural units and conversions 250 Appendix B: Dirac Spinor Formulas 251 Appendix C: Further Reading 253 Index 253 3 1Introduction In this course, we will explore some of the tools necessary forattackingthefundamentalquestionsof elementary particle physics. These questions include: What fundamental particles is everything made out of? • How do the particles interact with each other? • What principles underlie the answers to these questions? • How can we use this information to predict and interpret the results of experiments? • The Standard Model of particle physics proposes some answerstothesequestions.Althoughitishighly doubtful that the Standard Model will survive intact beyond this decade, it is the benchmark against which future theories will be compared. Furthermore, it is highly likely that the new physics to be uncovered at the CERN Large Hadron Collider (LHC) can be described using the same set of tools. This Introduction contains a brief outline of the known fundamental particle content of the Standard Model, for purposes of orientation. These and many other experimental results about elementary particles can be found in the Review of Particle Properties,hereafterknownastheRPP,authored by the Particle Data Group, and in its pocket-sized abridged form, the Particle Physics Booklet.The current edition of the RPP was published as K. Nakamura et al. (Particle Data Group), J. Phys. G 37,075021(2010),andisaboutthesizeofatelephonebookdirectory for a city of 50,000 people. It is updated and republished every even-numbered year. An always-up-to-date version is available on- line, at http://pdg.lbl.gov,anditisusuallyconsideredthedefinitivesourceforelementary particle physics data and analysis. Each result is referenced according to the experiments that provided it. Background theoretical material needed for interpreting the results is also included. Copies can be ordered for free from their website. 1.1 Fundamental forces The known interaction forces in the Standard Model (besides the universal attraction of gravity) are the electromagnetic force, the weak nuclear force, and the strong nuclear force. These forces are mediated by the spin-1 (vector) bosons listed in Table 1: Boson Charge Mass (GeV/c2)Width(GeV/c2)Lifetime(sec)Force photon γ 00 0 EM ∞ W 180.399 0.023 2.085 0.042 3.14 10 25 weak ± ± ± ± × − Z0 091.1876 0.0021 2.4952 0.0023 2.64 10 25 weak ± ± × − gluon g 0“0” strong Table 1: The fundamental vector bosons of the Standard Model. 4 0 The photon is the mediator of the electromagnetic force, while the W ± and Z bosons mediate the + weak nuclear force, which is seen primarily in decays and in neutrino interactions. The W and W − bosons are antiparticles of each other, so they have exactly the some mass and lifetime. The gluon has an exact 8-fold degeneracy due to a degree of freedom known as “color”. Color is the charge associated with the strong nuclear force. Particles that carry net colorchargesarealwaysconfinedbythestrong nuclear force, meaning that they can only exist in bound states, Therefore, no value is listed for the gluon lifetime, and the entry “0” for its mass is meant to indicate only that the classical wave equation for it has the same character as that of the photon. Although the fundamental spin-1 bosons are often called force carriers, that is not their only role, since theyareparticlesintheirownright. 1.2 Resonances, widths, and lifetimes Table 1 also includes information about the width Γof the W and Z particle resonances, measured in units of mass, GeV/c2.Ingeneral,resonancescanbedescribedbyarelativisticBreit-Wigner lineshape, which gives the probability for the kinematic mass reconstructed from the production and decay of the particle to have a particular value M,intheidealizedlimitofperfectdetectorresolutionandanisolated state. For a particle of mass m,theprobabilityis: f(M) P (M)= , (1.1) (M 2 m2)2 + m2Γ(M)2 − where f(M)andΓ(M)arefunctionsthatusuallyvaryslowlyovertheresonanceregion M m,and ≈ thus can be treated as constants. The resonance width Γ Γ(m)isequivalenttothemeanlifetime, ≡ which appears in the next column of Table 1; they are related by 25 2 τ (in seconds) = (6.58212 10− )/[Γ(in GeV/c )]. (1.2) × The RPP lists the mean lifetime τ for some particles, and the width Γfor others. Actually, the Standard Model of particle physics predicts the width of the W boson far more accurately than the experimentally measured width indicated in Table 1. The predicted width, with uncertainties from input parameters, is Γ =2.091 0.002 GeV/c2. W ± 1.3 Leptons and quarks The remaining known indivisible constituents of matter are spin-1/2fermions,knownasleptons(those without strong nuclear interactions) and quarks (those withstrongnuclearinteractions).Allexperi- mental tests are consistent with the proposition that these particles have no substructure. The leptons are listed in Table 2. They consist of negatively charged electrons, muons, and taus, and weakly inter- acting neutrinos. There is now good evidence (from experiments