Energizing gamma ray bursts via $Z^\prime$ mediated neutrino heating

The pair annihilation of neutrinos $(\nu\overline{\nu}\rightarrow e^+e^-)$ can energize violent stellar explosions such as gamma ray bursts (GRBs). The energy in this neutrino heating mechanism can be further enhanced by modifying the background spacetime over that of Newtonian spacetime. However, one cannot attain the maximum GRB energy $(\sim 10^{52}~\rm{erg})$ in either the Newtonian background or Schwarzschild and Hartle-Thorne background. On the other hand, using modified gravity theories or the Quintessence field as background geometries, the maximum GRB energy can be reached. In this paper, we consider extending the standard model by an extra $U(1)_{\rm{B-L}}$ gauge group and augmenting the energy deposition by neutrino pair annihilation process including contributions mediated by the $Z^\prime$ gauge boson belonging to this model. From the observed energy of GRB, we obtain constraints on $U(1)_{\rm{B-L}}$ gauge coupling in different background spacetimes. We find that the bounds on gauge coupling in modified gravity theories and quintessence background are stronger than those coming from the neutrino-electron scattering experiments in the limit of small gauge boson masses. Future GRB observations with better accuracy can further strengthen these bounds.