Tests are back pick up at end of class.

1

• Tests are back pick up at end of class.
• HW 6 due this Wednesday.
• HW 7 will be posted on Wednesday, due Friday
  5/9.
• Final Exam Alternative times will be considered
  only to the extent that no one is put at a
  disadvantage.
• Survey for need and feasibility.
• Drop off at end of class.

2
Spectroscopy of Mesons
As noted earlier systematic shift in mass
between PS and V mesons of given quark content.
Spin 1 (??) states have higher masses than spin 0
(??) states, suggesting a spin-spin interaction
(a.k.a. hyperfine). Much larger than in atomic
case! Details of this strong spin-spin
interaction are unknown, but we can do
phenomenology based on our experience with H
We must determine A and the quark masses m1 and
m2 by fitting data.
3
Fit the pseudoscalar and vector masses for the
best values of the constituent quark masses and A
Consistency to 1
Good fit?
Some mysteries why is ?? (958 MeV) so much more
massive than ??
4
Thats about all we can do for light-quark
mesons. Much more can be done with, and learned
from, quarkonium.
Program
terms for fine structure

• Develop/tune potential model on charmonium, then
  apply to other cases.
• Model on positronium e.g identify states with
  spectro-scopic notation.
• Singlet S states are ?c, triplet S states are ?,
  triplet P states are ?c.
• Experimental input needed.

5
Charmonium Spectroscopy Crystal Ball at SPEAR
Detect the photons from the electromagnetic
transitions between states with a highly
segmented NaI crystal calorimeter. Photon
energies ? level spacings.
SPEAR ee storage ring at SLAC Crystal Ball
Detector (78-82)
Many subsequent ee? experiments CLEO, CUSB,
BES (BES III starting 2008), BaBar, Belle, as
well as dedicated antiproton-annihilation CERN
R704, FNAL E760 and E835, PANDA (starting 2013).
- both c and b.
6
c vs. b
Before the discovery of b it was recognized that
the bottomonium system would have an even richer
structure and would be a rigorous test for the
potential models. Eichten and Gottfried predicted
level spacings similar to charm, even though mb ?
3mc. (Note linear potential very different from
Coulomb, which gives level spacing ? m.)
General features very similar n3S1 show amazing
consistency.
7
Baryons
Discussed requirement and consequences of
antisymmetric wave function. Would like to deduce
baryon properties from the quark model tougher!
Baryon masses
SU(3) breaking (ms gt mu, md), more complicated
hyperfine (spin-spin) contribution because of
three quarks.
Successfully explains empirical mass
relationships noted by Gell-Mann and others along
path to quarks
(Gell-Mann/Okubo M.F.)
8
Baryon magnetic moments
Use quark-model-inspired wave functions to
calculate magnetic moments of JP (½) octet
baryons. No orbital motion ? add up magnetic
moments of quarks.

• Wave functions for the JP (½) octet (includes
  nucleons) are symmetric under simultaneous
  flavor/spin interchange, not separately.
• Build spin-up p from a symmetrized ud (spin
  singlet, flavor-antisymmetric)

• For a fully-symmetric wave function we need to
  construct all cyclic permutations of this and
  normalize

Count configurations (weights given by squaring
coefficients)
Others can be constructed in the same way. In
particular, neutron has exactly the same form
except roles of u and d are reversed.
9
Calculate the magnetic moment of the proton and
neutron
Quarks are Dirac particles with different
magnetic moments because of different charges and
masses.
Use Isospin symmetry mu ? md ? m
We could substitute and compare with the known
absolute values, except that we dont really know
the appropriate quark mass. How about a ratio?
Predicted
Measured