Hidden physics in pion and some other meson decays

Abstract

It has been commonly assumed that pseudoscalar contributions to the leptonic decay of charged mesons, like pions and kaons, is strongly constrained due to the helicity suppression present in the ratio $R_{l/l^{\prime }}=\Gamma (P\to l\nu [\gamma ])/\Gamma (P\to l^{\prime }\nu [\gamma ])$, where $P$ are the charged pseudoscalar meson and $l,l^{\prime }=e,\mu ,\tau$. Here we show that if the effective couplings are proportional to the corresponding charged lepton masses (and also the PMNS matrix), the constraints from $R_{l/l^{\prime }}$ are entirely avoided, and a rather new large allowed region is permitted in the parameter space. In the case of the electron, we found a non-trivial region in the range $10^{-4}\lesssim (G^{\eta }/G_F)\lesssim 10^{-3}$, where $G^{\eta }$ is the effective pseudoscalar coupling associated with a novel charged scalar field, $\eta$, and $G_F$ is the Fermi constant. Furthermore, we show that this dependence of the pseudoscalar couplings on the charged lepton masses can naturally be associated with a critical class beyond the standard model physics, namely models without (leptonic) flavor-changing neutral currents in the scalar sector. The most known examples are the models that satisfy the so-called Glashow-Weinberg-Paschos theorem. Finally, we also point out that, in those cases, the decay rate is degenerated with the Standard Model prediction, possibly hiding the new physics effects in those decays.

Comments: 21 pages, 4 figures