  We have computed the hard dilepton production rate from a weakly magnetized
deconfined QCD medium within one-loop photon self-energy by considering one
hard and one thermomagnetic resummed quark propagator in the loop. In the
presence of the magnetic field, the resummed propagator leads to four
quasiparticle modes. The production of hard dileptons consists of rates when
all four quasiquarks originating from the poles of the propagator individually
annihilate with a hard quark coming from a bare propagator in the loop. Besides
these, there are also contributions from a mixture of pole and Landau cut part.
In weak field approximation, the magnetic field appears as a perturbative
correction to the thermal contribution. Since the calculation is very involved,
for a first effort as well as for simplicity, we obtained the rate up to first
order in the magnetic field, i.e., ${\cal O}[(eB)]$, which causes a marginal
improvement over that in the absence of magnetic field.
