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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


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 L├╝scher 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.