A Lattice QCD study of the $\rho$ resonance

Abstract

We present a lattice QCD study of the $\rho$ resonance with $N_f=2+1$ clover fermions at a pion mass of approximately $320$ MeV and lattice size $3.6$ fm. We consider two processes involving the $\rho$. The first process is elastic scattering of two pions in P-wave with isospin $1$. Using the Lüscher method we determine the scattering phase shift, from which we obtain the $\rho$ resonance mass and decay width $\Gamma (\rho \to \pi \pi )$. The second process is the radiative transition $\pi \gamma \to \pi \pi$, where we follow the Briceño-Hansen-Walker-Loud approach to determine the transition amplitude in the invariant mass region near the $\rho$ resonance and for both space- and time-like photon momentum. This allows us to determine the coupling between the $\rho$, the pion and the photon, and the resulting $\rho$ radiative decay width.

Talk presented at CIPANP2018. 8 pages, LaTeX, 3 figures