  Due to the extreme large magnetic field produced in the initial stage of
non-central heavy-ion collision, the dynamical process of gluon decay into
heavy quark pair will take place under an external field rather than in vacuum.
Unlike in the vacuum case, where the process is forbidden by energy momentum
conservation, under the external field, a process emerges considering the
background energy which recovers the conservation. We calculate the gluon decay
rate at leading order under a uniform magnetic field.
