65
Solutions to Problems in
Chapter 15: The Standard Model
15.1. The Gell-Mann-Nishijima relation gives the particle charge, Q, as
For the mesons given in Table 15.6 the value of B is always zero. Other values are calculated from the quark
properties in table 15.1. These are summarized as follows:
meson
3
T
S
C
B
T
Q
uc
–1/2
0
+1
0
0
0
uc
+1/2
0
–1
0
0
0
dc
+1/2
0
+1
0
0
+1
–1/2
0
–1
0
0
–1
0
+1
+1
0
0
+1
0
–1
–1
0
0
–1
0
0
0
0
0
0
+1/2
0
0
+1
0
+1
–1/2
0
0
+1
0
0
+1/2
0
0
–1
0
0
0
–1
0
+1
0
0
0
0
0
0
0
0
15.2. Using the values of T3 for the following quarks
quark
T3
u
+1/2
d
66
particle
quarks
3
T
–
u
d
–1
15.3. Referring to Table 15.6 for particle properties we can construct the following diagram.
15.4. The diagram for the exchange of a positive pion is
u
c
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For the exchange of a negative pion the diagram is
15.5. The Feynman diagrams for the three decay processes are as shown below.