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

*L. Leskovec, C. Alexandrou, G. Koutsou, S. Meinel, J. Negele, S. Paul, M. Petschlies, A. Pochinsky, G. Rendon, S. Syritsyn*

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf

**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 $\pi \pi \to \pi \gamma^{\ast}$, 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 Lüscher method, the scattering phase shift is used in

conjunction with the $1\to2$ transition matrix element formalism of Brice\~no,

Hansen and Walker-Loud \cite{Briceno:2014uqa} to compute the

$\pi\pi\to\pi\gamma^{\ast}$ amplitude at several values of the momentum

transfer and $\pi\pi$ invariant mass.