Role of the strange quark in the rho(770) meson

TL;DR

This paper investigates how the strange quark influences the rho(770) meson mass by analyzing lattice QCD data with Unitary Chiral Perturbation Theory, highlighting the significant impact of the missing Kar{K} channel.

Contribution

It demonstrates the substantial effect of the strange quark via the Kar{K} channel on the rho meson mass in lattice simulations, providing chiral extrapolations for N_f=2+1 data.

Findings

The absence of strange quarks lowers the rho mass in two-flavor lattice data.

Including the Kar{K} channel raises the phase shift and the rho mass.

Chiral extrapolations for N_f=2+1 simulations are consistent with experimental data.

Abstract

Recently, the GWU lattice group has evaluated high-precision phase-shift data for $\pi\pi$ scattering in the $I = 1$, $J = 1$ channel. Unitary Chiral Perturbation Theory describes these data well around the resonance region and for different pion masses. Moreover, it allows to extrapolate to the physical point and estimate the effect of the missing $K\bar{K}$ channel in the two-flavor lattice calculation. The absence of the strange quark in the lattice data leads to a lower $\rho$ mass, and the analysis with U$\chi$PT shows that the $K \bar{K}$ channel indeed pushes the $\pi\pi$-scattering phase shift upward, having a surprisingly large effect on the $\rho$-mass. The inelasticity is shown to be compatible with the experimental data. The analysis is then extended to all available two-flavor lattice simulations and similar mass shifts are observed. Chiral extrapolations of $N_f = 2 + 1$ lattice simulations for the $\rho(770)$ are also reported.