Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 47 / 4 / b / iv / Solution

Absent in the minimal Standard Model. The single charged-lepton Yukawa matrix supplies both the fermion mass matrix and the Higgs coupling, so the same left/right rotations diagonalize both. There is no off-diagonal $h\tau \mu$ vertex. With massless neutrinos, the separate charged-lepton family numbers prevent this transition perturbatively. If neutrino masses and mixing are added, loop-induced charged-lepton flavour violation can occur but is extremely suppressed; a sizeable rate would require an additional source of flavour violation. Part (c) provides one such source.