Symmetry and Flavour

Hadrons, Quark Mixing, CP Violation and Neutrinos in 16 chapters — from “Four-vectors at work: boosts, invariants and the shape of a final state” to “The relativistic string: action, light-cone quantisation, spectrum and D-branes”.

Chapters

  1. Four-vectors at work: boosts, invariants and the shape of a final state
    • Natural units and index notation
    • The Lorentz boost and rapidity
    • Pseudorapidity and detector coordinates
    • The Mandelstam variables
    • Decay in flight
    • The Jacobian peak and transverse mass
    • The Dalitz plot
    • Recoil mass at a lepton collider
    • Problems
  2. From amplitude to rate: Lorentz-invariant phase space, widths and cross sections
    • Fermi's golden rule
    • Relativistic normalisation and the invariant amplitude
    • Lorentz-invariant phase space and the two-body width
    • The flux factor
    • The two-to-two cross section for muon pairs
    • Three-body phase space
    • The muon decay rate
    • Helicity suppression
    • Problems
  3. Resonances: the relativistic Breit-Wigner, unitarity and the Z line shape
    • The partial-wave expansion
    • The resonance propagator
    • The relativistic Breit-Wigner
    • The unitarity limit
    • Spin from the resonance angular distribution
    • The narrow-width approximation and resonance area
    • Initial-state radiation
    • Neutrino counting
    • Problems
  4. The collider experiment: from bunch populations to a measured cross section
    • Luminosity in the uncertainty budget
    • Luminosity from beam parameters
    • Pile-up and the trigger
    • Energy loss in matter
    • Momentum resolution from the sagitta
    • Calorimeter resolution and missing momentum
    • Particle identification by velocity
    • Displaced vertices and lifetime tagging
    • A cross-section measurement in the muon channel
    • Summary
    • Problems
  5. Isospin as a group: SU(2), Clebsch-Gordan ratios and G-parity
    • Two peaks and the unitarity limit
    • Clebsch-Gordan coefficients for SU(2)
    • Symmetry and degeneracy
    • Isospin generators for the light quarks
    • The antiquark doublet and the pions
    • Isospin coupling and reduced amplitudes
    • Isospin selection rules in decays
    • G-parity
    • The size of isospin breaking
    • Summary
    • Problems
  6. SU(3) flavour: weights, tensor products and the mass formulas
    • Symmetry and degeneracy in the decuplet
    • Gell-Mann matrices and two labels
    • Weight diagrams
    • Tensor products split by symmetry
    • U-spin and electromagnetic splittings
    • First-order shifts and the Gell-Mann-Okubo formula
    • Octet-singlet mixing of the isosinglet mesons
    • The size of flavour symmetry breaking
    • Summary
    • Problems
  7. Parity, charge conjugation and time reversal as operators, and the CPT theorem
    • Unitary and antiunitary operators
    • The parity operator
    • Intrinsic parity and the pion
    • C-parity and photon counting
    • Meson quantum numbers and their gaps
    • Spin-parity analysis of Dalitz plots
    • Neutrino helicity
    • The time-reversal operator
    • The CPT theorem
    • Electric dipole moments
    • Problems
  8. The constituent quark model: wave functions, magnetic moments and hyperfine masses
    • The symmetrisation postulate
    • Colour antisymmetry
    • Spin-flavour wave functions
    • Constituent quark masses
    • Baryon magnetic moments
    • Hyperfine splitting of baryons
    • Meson hyperfine splitting
    • Colour counting
    • Problems
  9. Hadron spectroscopy: quarkonium, orbital excitations and exotic states
    • The quarkonium spectrum
    • The Cornell potential
    • The OZI rule
    • P-wave fine structure
    • Heavy-quark hyperfine scaling
    • Regge trajectories
    • Exotic hadrons
    • Problems
  10. Quark mixing: the Cabibbo angle, the GIM mechanism and the CKM matrix
    • Charged-current vertex and universality
    • The Cabibbo angle
    • Neutral currents and the GIM mechanism
    • The CKM matrix and its phase
    • The Wolfenstein parametrisation
    • The Jarlskog invariant
    • First-row unitarity
    • Problems
  11. Heavy flavour: charm and beauty decays and the magnitudes of the CKM elements
    • The spectator model
    • The b-quark lifetime
    • The lepton endpoint
    • The inclusive-exclusive tension
    • The Cabibbo hierarchy in charm
    • Top-quark decay
    • Heavy-flavour factories
    • Problems
  12. Neutral kaons: mixing, strangeness oscillation and CP violation
    • The non-Hermitian two-state system
    • The effective mixing Hamiltonian
    • CP eigenstates and short- and long-lived kaons
    • Strangeness oscillation
    • Regeneration in matter
    • CP violation in mixing
    • The semileptonic charge asymmetry
    • CP violation in decay
    • Problems
  13. B mesons: mixing, time-dependent CP asymmetries and the unitarity triangle
    • B-meson mixing and the heavy top
    • Bs​ mixing and ∣Vtd​/Vts​∣
    • Coherent B pairs and unequal beams
    • The time-dependent CP asymmetry
    • Measuring sin2β
    • The unitarity triangle
    • Direct CP violation in B decays
    • The Sakharov conditions
    • Problems
  14. Neutrino masses, mixing and oscillations
    • Flavour and mass states
    • The vacuum oscillation formula
    • The solar neutrino problem
    • The SNO neutral-current measurement
    • Oscillation in matter and the MSW effect
    • Atmospheric and accelerator neutrinos
    • Reactor oscillations at two baselines
    • The PMNS matrix
    • Neutrino mass ordering and absolute scale
    • Dirac, Majorana and the seesaw mechanism
    • Problems
  15. Grand unification: running couplings, SU(5), proton decay and the hierarchy problem
    • Hypercharge assignments of one generation
    • Anomaly cancellation in one generation
    • Running couplings at one loop
    • Near-unification of the three couplings
    • SU(5) multiplets and gauge bosons
    • Charge quantisation and the weak mixing angle
    • The proton lifetime
    • Proton decay searches in water
    • The hierarchy problem
    • Problems
  16. The relativistic string: action, light-cone quantisation, spectrum and D-branes
    • Straight Regge trajectories
    • The point-particle action
    • The Nambu-Goto action
    • Equations of motion and string boundary conditions
    • The rotating string and the Regge slope
    • Light-cone gauge
    • Mode expansion and quantisation
    • Mass formula and critical dimension
    • The closed-string graviton
    • D-branes and gauge fields
    • The critical dimension and experiment
    • From isospin generators to running couplings
    • Problems