Light- and strange-quark mass dependence of the $\rho(770)$ meson revisited

TL;DR

This paper analyzes how the properties of the $ ho(770)$ meson depend on light and strange quark masses using lattice data and unitarized Chiral Perturbation Theory, providing new insights and predictions for different quark mass trajectories.

Contribution

It offers the first detailed study of strangeness dependence of $ ho(770)$ meson properties and refines Low Energy Constants in unitarized Chiral Perturbation Theory.

Findings

Predictions for $ ho(770)$ properties with lighter strange-quark masses.

Precise determination of Low Energy Constants in the theoretical framework.

Analysis of the discrepancy between two- and three-flavor lattice results.

Abstract

Recent lattice data on $\pi\pi$-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the $\rho(770)$ meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the $\rho(770)$ meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the $\rho(770)$ meson is studied.