Outline Today Previous lecture Relativistic Kinematics (4-momentum)2 invariance, invariant mass Hypothesis testing, production thresholds Cross-sections, flux and luminosity, accelerators Particle lifetime, decay length, width Classification of particles Fermions and bosons; Leptons, hadrons, quarks Mesons, baryons Quark Model Meson and baryon multiplets Isospin, strangeness, c, b, t quarks Particle Interactions Colour charge, QCD, gluons, fragmentation, running couplings Strong and weak decays, conservation rules Virtual particles and range of forces Parity, charge conjugation, CP Weak decays of quarks Charmonium and upsilon systems Electroweak Interactions Charged and neutral currents W, Z, LEP experiments Higgs and the future Higgs phenomenology - new in 2015 Dark Matter phenomenology (and searches) – new in 2015 LHC Experiments’ Results [Introduction to accelerator physics??] Today Previous lecture

Baryon wavefunction and colour Ybaryon = Yspin Yspace Yflavour Ycolour has to be overall antisymmetric (Pauli Exclusion Principle) under interchange of any 2 quarks. For J=3/2, uuu (D++), ddd(D-), sss(W-) states exist Yspin , Yspace and Yflavour are all symmetric Therefore ycolour has to be antisymmetric We extend this assertion to be true for all baryons Colour wavefunction for baryons (qqq) is always antisymmetric and is |rgb – grb + brg – rbg + gbr – bgr › /6 This is colour singlet state and only this one is allowed (of all 33 combinations – 2 x octets, 1 x decuplet, 1 x singlet) Subtle detail: identical particles are the quarks, contrast with meson case where fermions are distinguishable quark and anti-quark

Baryon wavefunction and colour For J=1/2 baryon case, Yspace is still symmetric, so Yspin Yflavour must also be symmetric In J=1/2, states, |↑↑↓› etc., clearly symmetry is “mixed” – neither fully symmetric or antisymmetric – depending on which quarks are interchanged To ensure overall symmetric behaviour of Yspin Yflavour , need Yflavour to have complementary mixed symmetry to Yspin As Yflavour is perfectly symmetric for uuu, ddd, sss states … and spin states such as |↑↑↓› are mixed symmetry, … PEP excludes existence of these combinations in J=1/2 states. This agrees with the observed baryon states Further evidence for colour quantum number In uud, etc. cases, there is 1 possibility for Yflavour to complement mixed symmetry spin wavefunction In uds case, 2 options for Yflavour corresponding to L0(1116) and S0(1193), e.g. to be antisymmetric in 1-2 exchange [(us-su)d+(ds-sd)u]/2 and [2(ud-du)s+(us-su)d-(ds-sd)u)/sqrt(12) (and similarly for 2-3 and 1-3) Further details, see course web page references, esp. Griffiths pp. 187-188.

Baryon wavefunction, example 1 For D+,J=3/2 baryon case, Yspace is still symmetric, so Yspin Yflavour must also be symmetric | D+: 3/2 -1/2› = (uud+udu+duu)/3 x (↓↓↑ + ↓↑↓ + ↑↓↓) /3 = (u(↓)u(↓)d(↑) + u(↓)d(↑)u(↓) + u(↑)d(↓)u(↓) +u(↓)d(↓)u(↑) + u(↓)d(↑)u(↓) + u(↑)d(↓)u(↓) +d(↓)u(↓)u(↑) + d(↓)u(↑)u(↓) + d(↑)u(↓)u(↓))/3 Means: e.g. prob. of quark #1 being d(↑) is 1/9 prob of quark #1 being u(↓) is 4/9 Further details, see course web page references, esp. Griffiths pp. 187-188.

cross-section (e+e-hadrons) Centre-of-mass energy http://pdg.lbl.gov/2008/reviews/hadronicrpp.pdf

cross-section ratio: (e+e-hadrons)/ (e+e-m+m- ) http://pdg.lbl.gov/2008/reviews/hadronicrpp.pdf

Evidence for colour Includes Only observe mesons and baryons, no other combinations No single-flavour members of J=1/2 baryon multiplet There are single-flavour members of J=3/2 baryon multiplet No free quarks/gluons ever see (and we do look, often) R=(cross-section of e+e-hadrons)/(cross-section of e+e-muons), vs. sqrt(s) Covered in Y2 Particles&Nuclei course Also…board

Quantum Field Theories in PP – QED and QCD QED developed ~1948 by Feynman,Tomonaga,Schwinger Locally Gauge Invariant Theory Effectively equivalent to having an arbitrary zero of electric potential Conservation of charge leads to “choice of gauge” (in Maxwell Equations) Symmetry of the theory (physics of interactions the same after any global change in potential) leads to charge conservation (Noether’s Theorem) The “local” aspect extends idea to arbitrary choice at any point in space QED, gauge symmetry group is called U(1) QCD, gauge symmetry group is called SU(3) – three colour charges “non-Abelian” theory (order of operations such as rotations important in 3d) Renormalizable Theory Can be used for real calculations in perturbation theory without introducing uncontrolled divergences (infinities) Concepts advanced, will not do any more than skim surface Interested in details, will put further references on web

Quantum ElectroDynamics - QED Measured/predicted to ~6 parts in 1010 precision D. Hanneke, S. Fogwell and G. Gabrielse, Phys. Rev. Lett. 100, 120801 (2008). Examples of what is involved in calculations to reach such precision…

Quantum ElectroDynamics - QED

Quantum ElectroDynamics - QED

Quantum ElectroDynamics - QED Measured/predicted to ~6 parts in 1010 precision Quantum ElectroDynamics - QED

g-2: from Illinois to Chicago 50 foot wide particle accelerator 3200 mile journey (as complete ring)

Strong Coupling “constant”, aS aS the fundamental, universal QCD parameter Standard Model predicts “momentum scale”, Q (~s) evolution, but not the absolute value of aS Perturbative effects, varying as ~ 1/lnQ Non-perturbative effects, varying as ~ 1/Q Test: measure different processes, energies Intuitive techniques in e+e- Precision low, O(%) cf. electroweak O(105) aS q g q - g aS

Global aS measurements, various e+e- observables [From P.A. Movilla Fernandez et al., Eur.Phys.J.C22(2001)1] BT 1-T MH2/s  C y3 BW

Data: strong coupling constant, aS e+e-  3 jets in OPAL detector at LEP (1989-2001) e+e-  4 jets (W-W+) in OPAL detector at LEP as “parton level” pictures (e+eZqqgg g g q - q - aS aS aS q q aS is strong force coupling constant Ratio of rate of 3-jet vs. 4-jet events Directly related to aS Analogous to “R”, many factors cancel Momentum scale-dependent value Illustrated by measurements at varying energy in e+e- collisions g 4-jet event 3-jet event

Data: strong coupling constant, aS e+e-  3 jets in OPAL detector at LEP (1989-2001) as “parton level” pictures g g q - q - aS aS aS q q aS is strong force coupling constant Ratio of rate of 3-jet vs. 4-jet events Directly related to aS Analogous to “R”, many factors cancel Momentum scale-dependent value Illustrated by measurements at varying energy in e+e- collisions g 4-jet event 3-jet event

as Summary Consistency of coupling measured in different physics environments “asymptotic freedom” “Confinement” Long range (low energy) Short range (low energy) K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010) [http://pdg.lbl.gov/2011/reviews/rpp2011-rev-qcd.pdf]