Study of the pion-mass dependence of $\ddot{I}$-meson properties in lattice QCD

Abstract

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

24 pages, 16 figures