Complete structure dependent analysis of the decay $P\to l^{+}{l}^{-}$

Abstract

We use the Mellin-Barnes representation in order to improve the theoretical estimate of mass corrections to the width of light pseudoscalar meson decays into a lepton pair, $P\to l^{+}{l}^{-}$ . The full resummation of the terms $(M^2/\hat{I}{›}^2{)}^n,$ $(m^2/M^2{)}^n$and $(m^2/\hat{I}{›}^2{)}^n$ to the decay amplitude is performed, where $m$ is the lepton mass, $M$ is the meson mass and $\hat{I}›\approx m_{\ddot{I}}$ is the characteristic scale of the $P\to γ^{\ast}γ^{\ast}$ form factor. The total effect of mass corrections is quite important for $\hat{I}\cdot (\hat{I}{\cdot }^{\prime })$ decays. We also comment on the estimation of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment in the chiral perturbation theory.

11 pages, 1 figure