A Lattice QCD study of the $\rho$ resonance

TL;DR

This paper uses lattice QCD simulations to study the $ ho$ resonance, determining its mass, decay width, and radiative decay properties through pion scattering and photon interactions.

Contribution

It introduces a combined lattice QCD approach to analyze both $ ho$ resonance properties and its radiative decay, extending previous methods.

Findings

Determined the $ ho$ resonance mass and decay width from pion scattering phase shifts.

Calculated the $ ho$ radiative decay width and the $ ho$-pion-photon coupling.

Applied the L"uscher and Brice ilde{n}o-Hansen-Walker-Loud methods in a lattice QCD context.

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 L\"uscher 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 Brice\~no-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.