The Standard Model

This is a subpage devoted to Physics 813 – The Standard Model. I will use it to post lecture notes and videos of the classes. After the class is over, it will be used as an archive of the material for those that wish to use it.

Quark Model 1Notes and Video – Intro comments, basic facts about proton, the relativistic square well, solving for the spatial wavefunctions, the quantized field and creation operators, forming the spectrum using creation operators, the Delta and the decuplet, the proton wavefunction

Quark Model 2Notes and Video – Review of the quantum field operator, other baryon and meson wavefunctions, calculating the charge and charge radius, the magnetic moment, doing spin sums, the non-relativistic quark model, magnetic moments of the baryon octet

Quark Model 3Notes and Video – review of use of creation and annihilation operators, hyperfine splitting in the quark model, the axial current matrix elements, the spin structure of the proton

Symmetry 1Notes and Video – Reading Lagrangians, U(1), conserved current, SU(2), fundamental and adjoint representations, example – pion nucleon couplings

Symmetry 2Notes and Video – More compact notation, SU(3) and SU(N), example: baryon currents, comparison to quark model, other bits of group theory, gauge symmetry for U(1), gauge symmetry for SU(N)

Symmetry 3Notes and Video – covariant derivative and field strength for SU(N), invariant Lagrangians, matrix notation.

Constructing SM 1Notes and Video – Chirality, multiplets for SU(2), the gauge sector, color SU(3), left-handed SU(2), hypercharge, summary

Constructing SM 2Notes and Video – Prelude to the Higgs sector – symmetry breaking, U(1) gauge symmetry, masses of vector particles, symmetries and masses of fermions, plan for SU(2), anti-doublet = doublet, Higgs sector, Yukawa couplings, Gauge boson masses

Constructing SM 3Notes and Video – counting D.O.F., Haag’s theorem, renaming the fields, removing unphysical particles, identifying currents, charged and neutral currents, fermion mass diagonalization and the CKM matrix.

Higgs 1Notes and Video – Higgs mass, interactions, Higgs to 2 gluons, 2 photons, Higgs production at the LHC, Higgs decay, Longitudinal gauge bosons, the equivalence theorem, unitarity

Higgs 2Notes and Video– comments on the Higg to 2 gluon calculation, naturalness, review of running couplings, perturbativity of Higgs sector, comments on background fields, top quark loops and Higgs potential, vacuum instability

Higgs 3Notes and Video – 2 Higgs doublets, vacuum selection, charged Higgs, decoupling

Leptons 1 Notes and Video– Dirac mass and Lorentz invariance, Majorana mass term, conjugate field notation

Leptons 2 Notes and Video– Majorana notation review, comments on the sign of mass terms, Majorana as its own antiparticle, Dirac as two Majorana fields, Mixed Dirac and Majorana masses in Standard Model, general solution, Seesaw solution, Integrating out heavy fields, the dimension 5 operator

Leptons 3Notes and Video – Review, lepton mixing, removing phases in CKM and PMNS, Neutrino oscillations, experimental evidence, maximal mixing angles, mass hierarchies

Leptons 4 Notes and Video – The Daya Bay measurement of theta_13, Neutrinoless double beta decay, the role of Majorana mass, nuclear weak matrix elements, Leptogenesis and the seesaw, generating CP violating asymmetries in decays

Leptons 5Notes and Video – Muon decay, calculating the decay rate, spin sums, phase space, Michel parameters, radiative corrections, Fierz identities, large logs in beta decay, general features of electric dipole moments

Lepton 6(short) – Notes and Video – edm continued, mass insertion, CP violating phase, Standard Model at one loop, Beyond the Standard Model example, The Standard Model at two and three loops.

Chiral 1Notes and Video – Chiral symmetry, chiral currents and charges, parity doubling, symmetry breaking, the linear sigma model, Goldstone realization of symmetry

Chiral 2Notes and Video – Review, the pion decay constant, the soft pion theorem, Goldberger-Trieman relation, the pion mass and quark masses, the psi-bar-psi expectaton value, relatino to cosmological constant, the ratio of light quark mass to strange quark mass, building an effective field theory from the sigma model

Chiral 3Notes and Video – Running masses in QCD, running matrix elements, what runs?, effective lagrangian in QCD, typical predictions, higher order Lagrangians in sigma model and QCD, renormalizing the non-renormalizable, principles of effective field theory, matching.

Anomalies 1 Notes and Video – The anomalies of the Standard Model, anomaly basics, the pi^0 to two gamma story, triangle diagram, getting pi to two gamma, the U(1)_A story, path integral version, the eta’ mass, large N, spin content connection, scale invariance of the SM, the trace anomaly, connection to the beta function.

Anomalies 2 Notes and Video – applications of the trace anomaly, other anomalies, the WZW anomaly lagrangian, charge assignments in SM, Baryon number anomaly

CP violation 1Notes and Video – The theta term, connection to axial anomaly, generating theta from arg det m.

CP violation 2Notes and Video – review of theta term, vacuum stability, neutron edm and the strong CP problem, CKM matrix and CP violation, rephasing invariance, conditions for CP violation, direct CP violation, particle-antiparticle mixing, B to psi K_S

Heavy quarks and HQETNotes and Video – basic features, heavy quark symmetries, consequences of symmetries, HQET, next order correction, example in mason masses, example in currents, the Isgur-Wise function, field theory aspects

Precision electroweakNotes and Video– Precision parameters, Energy dependence, example sin^2 theta_W, scheme dependence, example m_t, decoupling or not, Higgs decoupling, new physics sensitivity, Vacuum polarization functions, Z gamma mixing, S,T,U

Beyond Standard Model 1Notes and Video – What needs to be done, Technicolor, QCD breaks SM, issues with Technicolor, Detour – Weinberg sum rules, S parameter and TC, Axions, Peccei-Quinn symmetry, axion mass

Beyond Standard Model 2Notes and Video – Seeing axions, Axion dark matter, naturalness vs anthropic reasoning for Axion DM, other anthropic reasoning, landscape and multiverse, dark matter evidence, MOND, WIMP Miracle, Minimal Flavor Violation

Beyond Standard Model 3Notes and Video– motivations for weak scale SUSY, Detour – GUTS, the Wess Zumino model, supercharges and SUSY algebra, SUSY implications, constructing the MSSM, R parity, SUSY breaking, Soft SUSY breaking, the Higgs sector, the mu problem, split SUSY

Research and teaching pages for John Donoghue