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

TL;DR

This paper improves the theoretical calculation of light pseudoscalar meson decays into lepton pairs by resumming mass correction terms, highlighting significant effects for eta and eta' decays and discussing implications for muon g-2.

Contribution

It introduces a Mellin-Barnes based method to fully resum mass corrections in decay amplitude calculations, enhancing precision over previous approximations.

Findings

Mass corrections significantly affect eta and eta' decay widths.

Resummation method provides more accurate decay amplitude estimates.

Comments on hadronic light-by-light scattering impact on muon g-2.

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.