Physics - Semileptonic decays

This script takes two mesons and calculates the branching fraction of semileptonic decay (via \(e\nu\) emission) from one meson to the other, taking the mass, quark contents and lifetime of the mesons into account. The expression for the partial width of a semileptonic decay of a pseudoscalar meson, \(P\), to another psuedoscalar meson, \(Q\), and leptons \(e\nu\) is given by:

\[ \Gamma(P\to Qe\nu) = \frac{G_F^2|V_{qq}|^2\Delta^5}{30\pi^3} \]

where:

\[ \Delta = \frac{M_P^2-M_Q^2}{2M_P} \]

and \(|V_{qq}|\) is the relevant CKM matrix element.

This is then turned into a branching fraction by taking the ratio with the total width:

\[ \mathcal{B}(P\to Qe\nu) = \frac{\Gamma(P\to Qe\nu)}{\Gamma(P)} = \frac{\Gamma(P\to Qe\nu)\tau_P}{\hbar} \]

where \(\tau_P\) is the lifetime of the meson, \(P\).