On mass corrections to the decays P \to l^+l^-
Abstract
Description
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 $\ln(m_l^2/Λ^2)(m_l^2/Λ^2)^n$ and $(m_l^2/Λ^2)^n$ to the decay amplitude is performed, where $m_l$ is the lepton mass and $Λ\approx m_ρ$ is the characteristic scale of the $P\toγ^*γ^*$ form factor. The total effect of mass corrections for the $e^+e^-$ channel is negligible and for the $μ^+μ^-$ channel its order is of a few per cent.
10 pages, 1 figure; one figure is added
10 pages, 1 figure; one figure is added