Sterile neutrinos in leptonic and semileptonic decays

We address the impact of a modified $W \ell \nu$ coupling on a wide range of observables, such as $\tau$ leptonic and mesonic decays, leptonic decays of pseudoscalar mesons, as well as semileptonic meson decays. In particular, we concentrate on deviations from lepton flavour universality, focusing on the ratios $R_{P} = \Gamma (P \to \ell \nu) / \Gamma (P \to \ell' \nu)$, with $P=K, \pi, D, D_s$, $R(D)={\Gamma (B^+ \to D \tau^+ \nu)}/{\Gamma (B^+ \to D\ell^+ \nu)}$, $R \tau={\Gamma (\tau\to \mu\nu\nu)}/{\Gamma (\tau\to e\nu\nu)}$, $R^{\ell \tau}_P=\Gamma(\tau\to P\nu)/\Gamma(P\to \ell \nu)$, and $\text{BR}(B \to \tau \nu)$. We further consider leptonic gauge boson decays, such as $W\to \ell \nu $ and $Z \to \nu \nu$. For all the above observables, we provide the corresponding complete analytical expressions, derived for the case of massive neutrinos. Working in the framework of the Standard Model extended by additional sterile fermions, which mix with the active (left-handed) neutrinos, we numerically study the impact of active-sterile mixings on the above mentioned observables.