Radiative corrections toπl2decays

Abstract

Radiative corrections to ${\mathrm{\ensuremath{\pi}}}_{\mathit{l}2}$ (l=e or \ensuremath{\mu}) decays are examined. Higher order electroweak leading logarithms short-distance QCD corrections, and structure dependent effects are incorporated. The results are employed to (1) test e-\ensuremath{\mu} universality in \ensuremath{\Gamma}(\ensuremath{\pi}\ensuremath{\rightarrow}e\ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{e}}$(\ensuremath{\gamma}))/\ensuremath{\Gamma}(\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathrm{\ensuremath{\mu}}}$(\ensuremath{\gamma})), (2) extract an ${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}$ which is used to check the Goldberger-Treiman relation and PCAC-anomaly prediction for \ensuremath{\Gamma}(${\mathrm{\ensuremath{\pi}}}^{0}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}), and (3) determine the tau partial decay rate \ensuremath{\Gamma}(\ensuremath{\tau}\ensuremath{\rightarrow}\ensuremath{\pi}${\ensuremath{\nu}}_{\mathrm{\ensuremath{\tau}}}$(\ensuremath{\gamma})).