On mass corrections to the decays P \to l^+l^-

TL;DR

This paper employs Mellin-Barnes techniques to accurately resum mass correction terms in light pseudoscalar meson decays into lepton pairs, refining theoretical predictions especially for muon channels.

Contribution

It introduces a full resummation method for mass correction terms in $P o l^+l^-$ decays using Mellin-Barnes representation, improving previous estimates.

Findings

Mass corrections are negligible for $e^+e^-$ channel.

Mass corrections are of a few percent for $u$ channel.

Resummation provides more precise decay width estimates.

Abstract

We use the Mellin-Barnes representation in order to improve the theoretical estimate of mass corrections to the width of light pseudoscalar meson decay into a lepton pair, $P\to l^+l^-$ . The full resummation of the terms $\ln(m_l^2/\Lambda^2)(m_l^2/\Lambda^2)^n$ and $(m_l^2/\Lambda^2)^n$ to the decay amplitude is performed, where $m_l$ is the lepton mass and $\Lambda\approx m_\rho$ is the characteristic scale of the $P\to\gamma^*\gamma^*$ form factor. The total effect of mass corrections for the $e^+e^-$ channel is negligible and for the $\mu^+\mu^-$ channel its order is of a few per cent.