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 $(M^{2}/\Lambda^{2}) ^{n},$ $(m^{2}/M^{2}) ^{n}$and $(m^{2}/\Lambda^{2}) ^{n}$ to the decay amplitude is performed, where $m$ is the lepton mass, $M$ is the meson mass and $\Lambda\approx m_{\rho}$ is the characteristic scale of the $P\to \gamma^{\ast}\gamma^{\ast}$ form factor. The total effect of mass corrections is quite important for $\eta(\eta^{\prime})$ 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.