  Using a real-time implementation of the self-consistent $GW$ method, we
theoretically investigate the photo-induced changes in the electronic structure
of the quasi two-dimensional semi-metal BaNiS$_2$. This material features four
Dirac cones in the unit cell and our simulation of the time- and
momentum-resolved nonequilibrium spectral function reveals a flattening of the
Dirac bands after a photo-doping pulse with a 1.5 eV laser. The simulation
results are consistent with the recently reported experimental data on
photo-doped BaNiS$_2$ and ZrSiSe, another Dirac semi-metal. A detailed analysis
of the numerical data allows us to attribute the nonequilibrium modifications
of the Dirac bands to (i) an increased effective temperature after the
photo-excitation, which affects the screening properties of the system, and
(ii) to nontrivial band shifts in the photo-doped state, which are mainly
induced by the Fock term.
