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

TL;DR

This study analyzes how the properties of the $ ho$-meson depend on pion mass using lattice QCD data and Hamiltonian Effective Field Theory, revealing weak dependence of coupling and cutoff, and a linear dependence of the bare $ ho$ mass on $m_.

Contribution

It introduces a unified HEFT-based framework to describe the pion mass dependence of $ ho$-meson properties across various lattice QCD results and experimental data.

Findings

Coupling constant and cutoff mass are weakly dependent on $m_$.

Bare $ ho$ mass shows linear dependence on $m_^2$.

Discrepancies in lattice QCD results are highlighted.

Abstract

We collect spectra extracted in the $I=\ell=1$ $\pi\pi$ 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.