1. 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

2. 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

3. 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

4. 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

5. cross-section (e+e-hadrons)
Centre-of-mass energy

6. cross-section ratio: (e+e-hadrons)/ (e+e-m+m- )

7. 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

8. 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

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

10. Quantum ElectroDynamics - QED

11. Quantum ElectroDynamics - QED

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

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

14. 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

15. 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

16. Data: strong coupling constant, aS
e+e-  3 jets
in OPAL detector
at LEP
( )
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

17. Data: strong coupling constant, aS
e+e-  3 jets
in OPAL detector
at LEP
( ) 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

18. 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, (2010) [