Past exam of the particle physics course of the University of Oxford / 2018 / 3 / b

The two indistinguishable paths to the same final state must be added as probability amplitudes:Taking the squared modulus gives the time-dependent decay rate, with the common final-state phase-space normalization absorbed into the probability amplitudes:The cross term is the interference between direct decay and decay after flavour conversion. For reference, diagonal propagation gives $g_{\pm }=(e_{\ell }\pm e_h)/2$, where $e_j=e^{-i{m}_{j}t-{\Gamma }_{j}t/2}$ and $t$ is proper time. The unfactored expression remains usable if $A_f=0$, when the ratio $\lambda$ itself is undefined.