Subatomic Physics

15.10. References 499
(b) Apply the results of part (a) to the splitting of the light pseudoscalar
and vector mesons of Table 15.1. How well does the application work
here?
(c) If the spin–orbit potential is proportional to the inverse square of the
quark masses, repeat (a) for the splitting of the 3 P2, 3 P1, and 3 P0 states.
Can you explain the discrepancy with experiment?
15.23. (a) For a harmonic oscillator how does the energy splitting between S-states
depend on the mass of the bound particle?
(b) Repeat (a) for a Coulomb (1/r) potential.
(c) Compare these energy spacings to those for charmonium and bottomium.
15.24. Table 15.2 indicates that the masses of the up and down quarks differ by
about 6MeV/c 2 . Show that, to lowest order in mu − md, this mass difference
contributes to the mass difference of the neutron and proton, but not to that
of the π + and π 0 .
15.25. (a) Show that there is no symmetric total spin-1/2 wavefunction in spin
space for three quarks of spin 1/2.
(b) Repeat part (a) for an antisymmetric wavefunction.
15.26. (a) If the mass differences between the light pseudoscalar and vector mesons
is due to a difference in the forces between nonstrange quarks, a strange
and a nonstrange quark, and between strange quarks, determine the
nature of the difference.
(b) Apply (a) to the low lying 1/2 + and 3/2 + baryons.
15.27. Determine the boundary conditions in the MIT bag model if color is to be
confined inside a bag of radius R, and if the quarks are free to move inside
the bag.
15.28. Explain how saturation of the lowest mass baryon states by three quarks and
mesons by qq is evidence for color.
15.29. Show that the mean square radii of the K 0 and K 0 with a simple nonrelativistic
central quark–antiquark potential are such that 〈r(K 0 ) 2 〉 is negative
and 〈r(K 0 ) 2 〉 is positive.