Subatomic Physics

380 The Weak Interaction
11.30. * Consider the strangeness-changing weak current of hadrons, for instance,
in the case Λ 0 → p in semi-leptonic processes. Such a current satisfies the
selection rule
∆S =∆Q,
where ∆S is the change of strangeness and ∆Q the change in charge.
(a) Give a few additional currents that have been observed and that satisfy
this selection rule.
(b) Have currents with ∆S = −∆Q been observed? (The quantum numbers
S and Q always refer to the hadrons.)
11.31. Discuss the isospin selection rules that are satisfied by the weak interaction
(a) In nonstrange decays, and
(b) In decays involving a change of strangeness.
(c) What experiments can be used to test these selection rules?
11.32. Discuss the evidence for and against the existence of neutral currents.
11.33. Show that the maximum cross section for a point interaction is given by the
so-called unitary limit
σmax =4π� 2 /p 2 ,
where p is the c.m. momentum.
11.34. What experiments can be carried out to test the absence of ∆S ≥ 2weak
currents?
11.35. Show that the reaction νµe → νµe is forbidden if only charged currents exist.
11.36. Determine and briefly discuss one or more tests of the conserved vector current
hypothesis.
11.37. Use the lifetime for the beta decay of 14 O and Eq. (11.9) to determine the
beta decay lifetime of the positive pion (see Tables 11.1 and 11.2). Compare
with experiment.
11.38. How can the decay Λ 0 → nπ 0 occur despite the absence of strangenesschanging
neutral currents?
11.39. Use Eq. 11.80 to show that m2,m1 �= me,mµ.
11.40. Find the probability Pνe that an electron neutrino is still an electron neutrino
after time t, rather than having turned into a muon neutrino, as in Eq. (11.82).