Running mass of the rho0 meson's implication for the dilepton mass spectrum and the mu+mu-/e+e- branching ratio in the K+ --> pi+l+l- decays

TL;DR

This paper investigates the rho0 meson's running mass using dispersion relations to better match the observed e+e- spectrum in K+ decays, slightly adjusting the mu+mu-/e+e- branching ratio prediction.

Contribution

It introduces a dispersion relation approach to evaluate the rho0 propagator's running mass without adjustable parameters, improving meson dominance predictions for decay spectra.

Findings

The rho0 mass squared varies with momentum, affecting decay form factors.

The predicted mu+mu-/e+e- branching ratio increases from 0.224 to 0.236.

The approach cannot account for the steeper e+e- spectrum seen in preliminary data.

Abstract

We make an attempt to resolve the discrepancy of the observed e+e- mass spectrum in the K+ --> pi+e+e- decay with that predicted by meson dominance. To this end we investigate the properties of the rho0 propagator. We use dispersion relations to evaluate the running mass squared m_rho^2(t) of the rho0 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_rho^2(t) at small momentum squared t makes the K+ --> pi+e+e- 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 mu+mu-/e+e- branching 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- spectrum, indicated by the preliminary data of the E865 collaboration at BNL AGS.