Two-gluon one-photon vertex in a magnetic field and its explicit one-loop approximation in the intermediate field strength regime

TL;DR

This paper derives the structure of the two-gluon one-photon vertex in a magnetic field, computes its one-loop approximation in an intermediate regime, and discusses implications for photon emission in heavy-ion collisions.

Contribution

It provides the first explicit one-loop calculation of the two-gluon one-photon vertex in a magnetic field considering symmetry constraints and intermediate field strengths.

Findings

Vertex has three tensor structures consistent with symmetries.

Photon emission is favored in the plane transverse to the magnetic field.

Results may explain enhanced photon elliptic flow in heavy-ion collisions.

Abstract

We find the general structure for the two-gluon one-photon vertex in the presence of a constant magnetic field. We show that, when accounting for the symmetries satisfied by the strong and electromagnetic interactions under parity, charge conjugation and gluon interchange, and for gluons and photons on mass-shell, there exist only three possible tensor structures that span the vertex. These correspond to external products of the polarization vectors for each of the particles in the vertex. We also explicitly compute the one-loop approximation to this vertex in the intermediate field strength regime, which is the most appropriate one to describe possible effects of the presence of a magnetic field to enhance photon emission during pre-equilibrium in peripheral relativistic heavy-ion collisions. We show that the most favored direction for the photon to propagate is in the plane transverse to the field, which is consistent with a positive contribution to $\nu_2$ and may help to understand the larger than expected elliptic flow coefficient measured in this kind of reactions.