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

Allowed via a charged-current weak decay. The quark emits a virtual $W^{-}$ in $b\to u{W}^{-\ast }$, followed by $W^{-\ast }\to e^{-}{\bar{\nu }}_e$. The relevant terms are the quark and lepton weak charged currents, with amplitude proportional to the CKM matrix element $V_{ub}$. At low energy their product gives a four-fermion interaction of the form $({\bar{u}}_L{\gamma }^{\mu }{b}_L)({\bar{e}}_L{\gamma }_{\mu }{\nu }_{eL})$ plus its conjugate.