Physics 556/714 Problem Set #5
due beginning of class Thurday Oct 16
1. Griffiths problem 4.21: "Show that eips z/2 =i
s
z
"
2. Griffiths problem 4.35: "Is the neutrino an eigenstate of P?"
3. Griffiths problem 4.36: "Using the information in Table 4.6"
4. Griffiths problem 4.37: "The dominant decays of the
h
meson are"
5. Consider a particle/antiparticle pair of spin zero bosons.
a) What is the charge conjugation of such a pair?
b) Verify that C and P are each conserved in the strong decay r0®
p
+
p
-
c) What can you say about the charge conjugation of a particle/antiparticle pair
of vector (spin 1) bosons? Support your claim with reference to Clebsch-
Gordon coefficients.
6. Consider the sequential decay
D
0®
K
*0
p
0 with
K
*0 ®
K
+
p
-.
a) What are the spins of all the particles involved?
b) In the rest frame of the D0, what is the orbital angular momentum l,m of the
K
*0
p
0 system, measured with z axis along the
K
*0 momentum direction?
c) In the rest frame of the
K
*0 what is the orbital angular momentum l,m of the
K
+
p
- system, measured with z' axis along the
K
+ momentum direction?
d) What is the distribution of angle q between the
K
+ direction measured in the
K
*0
rest frame and the
K
*0 direction measured in the D0 rest frame?
714 students please also do the following:
7. What possible values of spin, parity and charge conjugation (JPC) are possible for
a) a meson made up of a quark-antiquark pair?
b) a boson made up of two gluons?
(In this case it may help you to know that the two-gluon color singlet state is
symmetric under color exchange.)
c) Are there any JPC states that result from the combination of two gluons but are not
possible from the combination of quark-antiquark? If so, these states would be
said to have “exotic quantum numbers”, and their discovery would be strong
evidence for the existence of “glueballs”.