Studying the $\rho$ resonance parameters with staggered fermions

Abstract

We deliver a lattice study of $\rho$ resonance parameters with p-wave $\pi \pi$ scattering phases, which are extracted by finite-size methods at one center-of-mass frame and four moving frames for six MILC lattice ensembles with pion masses ranging from $346$ to $176$ MeV. The effective range formula is applied to describe the scattering phases as a function of the energy covering the resonance region, this allows us to extract $\rho$ resonance parameters and to investigate the quark-mass dependence. Lattice studies with three flavors of the Asqtad-improved staggered fermions enable us to use the moving-wall source technique on large lattice spatial dimensions ($L=64$) and small light $u/d$ quarks. Numerical computations are carried out at two lattice spacings, $a\approx 0.12$ and $0.09$ fm.