Implication of the running mass of theρ0meson for the dilepton mass spectrum and theμ+μ−/e+e−ratio inK+→π+l+l−decays

Abstract

We make an attempt to resolve the discrepancy of the observed ${e}^{+}{e}^{\ensuremath{-}}$ mass spectrum in the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{e}^{+}{e}^{\ensuremath{-}}$ decay with that predicted by meson dominance. To this end we investigate the properties of the ${\ensuremath{\rho}}^{0}$ propagator. We use dispersion relations to evaluate the running mass ${m}_{\ensuremath{\rho}}^{2}(t)$ of the ${\ensuremath{\rho}}^{0}$ resonance without adjustable parameters. To improve the convergence of the dispersion integral, the momentum dependence of strong vertices is taken from the flux-tube-breaking model of Kokoski and Isgur. The obtained behavior of ${m}_{\ensuremath{\rho}}^{2}(t)$ at small momentum squared t makes the ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{e}^{+}{e}^{\ensuremath{-}}$ form factor rise faster with increasing t than in the original meson dominance calculation and more in agreement with the published data. As a consequence, the meson dominance prediction of the ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{/e}^{+}{e}^{\ensuremath{-}}$ ratio changes slightly, from 0.224 to 0.236. We do not see any possibility to accommodate into the meson dominance approach an even steeper ${e}^{+}{e}^{\ensuremath{-}}$ spectrum, indicated by the preliminary data of the E865 Collaboration at BNL AGS.