Tau radiative decays in the light front quark model

Abstract

We study the decays of ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{P}^{\ensuremath{-}}\ensuremath{\gamma}(P={\ensuremath{\pi}}^{\ensuremath{-}}{,K}^{\ensuremath{-}})$ in the light front quark model. We calculate the form factors and use them to evaluate the decay widths. We find that, in the standard model, the decay widths are $1.62\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}(3.86\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}){\ensuremath{\Gamma}}_{{\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\ensuremath{\pi}}^{\ensuremath{-}}}$ and $1.91\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}(5.38\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}){\ensuremath{\Gamma}}_{{\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{K}^{\ensuremath{-}}}$ with the cuts of ${E}_{\ensuremath{\gamma}}=50(400)\mathrm{MeV}$ and ${t}_{0}=800(1200)\mathrm{MeV}$ for ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\gamma}$ and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{K}^{\ensuremath{-}}\ensuremath{\gamma},$ respectively. We also show that, with including the radiative decay widths, the experimental rate for ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}{P}^{\ensuremath{-}}$ can be explained.