A study of the radiative transition $\pi \pi \to \pi \gamma^{*}$ with lattice QCD

TL;DR

This paper uses lattice QCD to study the radiative transition    , focusing on the  resonance and employing advanced finite-volume methods to compute transition amplitudes.

Contribution

It introduces a lattice QCD approach to calculate radiative transitions involving unstable particles, expanding beyond previous stable-hadron limitations.

Findings

Determined  resonance parameters using the Lfcscher method.

Computed   transition amplitudes at various momentum transfers.

Demonstrated the application of the Brice, Hansen, and Walker-Loud formalism for unstable states.

Abstract

Lattice QCD calculations of radiative transitions between hadrons have in the past been limited to processes of hadrons stable under the strong interaction. Recently developed methods for $1\to2$ transition matrix elements in a finite volume now enable the determination of radiative decay rates of strongly unstable particles. Our lattice QCD study focuses on the process $\pi \pi \to \pi \gamma^{*}$, where the $\rho$ meson is present as an enhancement in the cross-section. We use $2+1$ flavors of clover fermions at a pion mass of approximately $320$ MeV and a lattice size of approximately $3.6$ fm. The required $2$-point and $3$-point correlation functions are constructed from a set of forward, sequential and stochastic light quark propagators. In addition to determining the $\rho$ meson resonance parameters via the L\"uscher method, the scattering phase shift is used in conjunction with the $1\to2$ transition matrix element formalism of Brice\~no, Hansen and Walker-Loud to compute the $\pi\pi\to\pi\gamma^{*}$ amplitude at several values of the momentum transfer and $\pi\pi$ invariant mass.