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.

11 pages, 1 figure

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