Study of the pion-mass dependence of $ρ$-meson properties in lattice QCD

Abstract

We collect spectra extracted in the $I=\ell=1$ $ππ$ sector provided by various lattice QCD collaborations and study the $m_π$ dependence of $ρ$-meson properties using Hamiltonian Effective Field Theory (HEFT). In this unified analysis, the coupling constant and cutoff mass, characterizing the $ρ- ππ$ vertex, are both found to be weakly dependent on $m_π$, while the mass of the bare $ρ$, associated with a simple quark-model state, shows a linear dependence on $m_π^2$. Both the lattice results and experimental data can be described well. Drawing on HEFT's ability to describe the pion mass dependence of resonances in a single formalism, we map the dependence of the phase shift as a function of $m_π$, and expose interesting discrepancies in contemporary lattice QCD results.