544
10 Particle Physics – II
matrix element, the general form being (q
2
+ m
2 )
−1 , where m is the mass of the
exchanged particle and q is the four-momentum transfer.
In general, the same end result is obtained from a number of Feynman diagrams.
The transition matrix element includes the superposition of amplitudes of all such
diagrams.
For the weak interaction the exchanged particle is a massive boson, W
± or Z
0 ,
indicated by a wavy or broken line. For the strong interaction, the exchanged particle
is a gluon indicated by a spring.
10.2 Problems
10.2.1 Conservation Laws
10.1 Are the following particle interactions allowed by the conservation
rules? If so, state which force is involved and draw a Feynman diagram for
the process.
[University of Aberystwyth 2003]
(i) μ
−
→ e
−
+ ν μ + ν e
(ii) Λ → π
+
+ π
−
(iii) ν e + n → p + e
−
(iv) π
0
→ τ
+
+ τ
−
(v) e
+
+ e
−
→ μ
+
+ μ
−
10.2 Indicate, with an explanation, whether the following interactions proceed
through the strong, electromagnetic or weak interactions, or whether they
do not occur.
(i) π
−
→ μ
−
+ ν μ
(ii) τ
−
→ μ
−
+ ν τ
(iii) Σ
0
→ Λ + γ
(iv) p → n + e
+
+ ν e
(v) π
−
+ p → π
0
+ Σ
0
(vi) π
−
+ p → K
0
+ Σ
0
(vii) e
+
+ e
−
→ μ
+
+ μ
−
10.3 Consider the decay of K
0 meson of momentum P 0 into π
+ and π
− of
momenta p + and p − in the opposite direction such that p + = 2 p − . Determine p 0 .
[Mass of K
0 is 498 MeV/c
2 ; mass of π
± is 140 MeV/c
2 ]
10.4 Indicate, with an explanation, whether the following interactions proceed
through the strong, electromagnetic or weak interactions, or whether they
do not occur.
(i) Ξ
−
→ Σ
−
+ π
0
(ii) τ
−
→ e
−
+ ν e + ν τ
(iii) τ
+
→ μ
+
+ γ