Two-flavor Simulations of the $ρ(770)$ and the Role of the $K\bar K$ Channel

Abstract: The $\rho (770)$ meson is the most extensively studied resonance in lattice QCD simulations in two ($N_f=2$) and three ($N_f=2+1$) flavor formulations. We analyze $N_f=2$ lattice scattering data using unitarized Chiral Perturbation Theory, allowing not only for the extrapolation in mass but also in flavor, $N_f=2\to N_f=2+1$. The flavor extrapolation requires information from a global fit to $\pi\pi$ and $\pi K$ phase shifts from experiment. While the chiral extrapolation of $N_f=2$ lattice data leads to masses of the $\rho(770)$ meson far below the experimental one, we find that the missing $K\bar{K}$ channel is able to explain this discrepancy.