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

We collect spectra extracted in the $I=\mathrm{\ell }=1$ $\pi \pi$ sector provided by various lattice QCD collaborations and study the $m_{\pi }$ dependence of $\rho$-meson properties using Hamiltonian Effective Field Theory (HEFT). In this unified analysis, the coupling constant and cutoff mass, characterizing the $\rho -\pi \pi$ vertex, are both found to be weakly dependent on $m_{\pi }$, while the mass of the bare $\rho$, associated with a simple quark-model state, shows a linear dependence on $m_{\pi }^2$. 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 $m_{\pi }$, and expose interesting discrepancies in contemporary lattice QCD results.