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

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 $\ln (m_l^2\mathrm{/}{\mathrm{\Lambda }}^2)(m_l^2\mathrm{/}{\mathrm{\Lambda }}^2{)}^n$ and $(m_l^2\mathrm{/}{\mathrm{\Lambda }}^2{)}^n$ to the decay amplitude is performed, where $m_l$ is the lepton mass and $\mathrm{\Lambda }\approx m_{\rho }$ is the characteristic scale of the $P\to {\gamma }^{\ast }{\gamma }^{\ast }$ 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.