Photon production from gluon splitting and fusion induced by a magnetic field in heavy-ion collisions

In heavy-ion collisions, an excess in photon production, together with a larger than expected positive elliptic flow, has been observed, a phenomenon commonly referred to as the direct photon puzzle. In this work we study the mechanism of photon production arising from gluon splitting and fusion during the pre-equilibrium stage in the presence of magnetic fields in peripheral heavy-ion collisions. We begin by analyzing the general tensor structure of the two-gluon one-photon vertex, computing it at the one-loop level for magnetic fields of arbitrary strength without resorting to additional approximations. Using these expressions, we calculate the contribution of gluon fusion and splitting to the photon yield, revealing that splitting dominates over fusion at low photon energies. Our results are compared with experimental data from the PHENIX collaboration. Finally, we incorporate a longitudinal anisotropy into the initial gluon distribution and find that it does not significantly alter the photon yield compared to an isotropic distribution.