Charged pions and kaons weak leptonic decays at finite density

Abstract

The weak leptonic decays $\pi^\pm\to\mu^\pm\nu_{\mu}(\bar{\nu}_{\mu}), \pi^\pm\to e^\pm\nu_e(\bar{\nu}_{e}), K^\pm\to\mu^\pm\nu_{\mu}(\bar{\nu}_{\mu})$ and $K^\pm\to e^\pm \nu_e(\bar{\nu}_{e})$ are investigated within the framework of the SU(3) Nambu-Jona-Lasinio model, in the vacuum and in quark matter in $\beta$ equilibrium. It is found that, at low densities, the decay rates of the charge multiplets, that are decoupled in this kind of flavor asymmetric matter, are affected differently. As the density increases, these decay rates become closer and show a tendency to vanish. This shows that weak interactions are strongly influenced by the medium as a consequence of restoration of chiral symmetry.