  Having in mind the pre-equilibrium stage in peripheral heavy-ion collisions
as a possible scenario for the production of electromagnetic radiation, we
compute the two-gluon one-photon vertex in the presence of an intense magnetic
field at one-loop order. The quarks in the loop are taken such that two of them
occupy the lowest Landau level, with the third one occupying the first exited
Landau level. When the field strength is the largest of the energy (squared)
scales, the tensor basis describing this vertex corresponds to two of the three
vector particles polarized in the longitudinal direction whereas the third one
is polarized in the transverse direction. However, when the photon energy is of
order or larger than the field strength, the explicit one-loop computation
contains extra tensor structures that spoil the properties of the basis,
compared to the case when the field strength is the largest of the energy
scales, which signals that the calculation is incomplete. Nevertheless, by
projecting the result onto the would-be basis, we show that the squared
amplitude for processes involving two gluons and one photon exhibits the
expected properties such as a preferred in-plane photon emission and a slightly
decreasing strength for an increasing magnetic field strength. We comment on
possible venues to improve the one-loop calculation that include accounting for
progressive occupation of the three quarks of the lowest and first excited
Landau levels such that, still working in the large field limit, a more
complete description can be achieved when the photon energy increases.
