10.2 Problems
557
10.98 Sketch the Feynman diagrams and replace the symbols l with the correct
leptons or anti-leptons in the following:
[University of Cambridge, Tripos 2004]
(i) l + n → e
−
+ p
(ii) τ
−
→ μ
−
+ + ¯
l
(iii) B
0
→ D
−
+ μ
+
+ l
[The quark content of B
0 is bd and D
− is cd]
10.99 Draw the lowest order Feynman diagram for the following decays
(a) Δ
0
→ pπ
−
(b) Ω
−
→ ΛK
−
10.100 (a) Draw the lowest order Feynman diagram for e
+ e
−
→ ν μ ν μ
(b) Draw the lowest order Feynman diagram for D
0
→ K
−
π
+ and estimate
the ratio of the transition rates.
[Quark contents (masses in MeV/c
2 ):Δ
+
= uud (1, 232), Ω
−
= sss(1, 672),
Ξ
0
= uss(1, 315), p = uud (938), n = udd (940), π
0
=
1
√
2
uu + dd
(135),
π
+
= ud(140), D
0
= cu(1, 865), K
−
= ¯
us(494)]
[Adapted from University of Cambridge, Tripos 2004]
10.101 Draw the lowest order Feynman diagram for the following processes:
(a) e
−
− e
− elastic scattering (Moller scattering)
(b) e
+ e
−
→ e
+ e
− (Bhabha scattering)
10.102 Draw the lowest order Feynman diagram at the quark level for the following
decays
(a) Λ → p + e
−
+ ν e
(b) D
−
→ K
0
+ π
−
10.103 Draw the Feynman diagrams at the quark level for the reactions:
(a) π
−
+ p → K
0
+ Λ
(b) e
+
+ e
−
→ B 0 + B
0 , where B is a meson containing a b-quark.
10.104 Draw the lowest order Feynman diagram for the decay K
−
→ μ
−
+ ν μ +γ
and hence deduce the form of the overall effective coupling.
10.105 Explain with the aid of Feynman diagrams, why the decay D
0
→ K
−
+ π
+
can occur as a charged-current weak interaction at lowest order, but the
decay D
+
→ K
0
+ π
+ cannot.
10.106 Why is the mean lifetime of the charged pion much longer than that of the
neutral pion? Draw Feynman diagram to illustrate your answer.
10.107 Draw Feynman diagrams for
(a) Bremsstrahlung
(b) pair production.
10.108 Draw Feynman diagrams for
(a) photo electric effect
(b) Compton scattering