  A neutrino-dominated accretion flow (NDAF) around a rotating stellar-mass
black hole (BH) is one of the plausible candidates for the central engine of
gamma-ray bursts (GRBs). Two mechanisms, i.e., Blandford-Znajek (BZ) mechanism
and neutrino annihilation process, are generally considered to power GRBs.
Using the analytic solutions from Xue et al. (2013) and ignoring the effects of
the magnetic field configuration, we estimate the BZ and neutrino annihilation
luminosities as the functions of the disk masses and BH spin parameters to
contrast the observational jet luminosities of GRBs. The results show that,
although the neutrino annihilation processes could account for most of GRBs,
the BZ mechanism is more effective, especially for long-duration GRBs.
Actually, if the energy of afterglows and flares of GRBs is included, the
distinction between these two mechanisms is more significant. Furthermore,
massive disk mass and high BH spin are beneficial to power high luminosities of
GRBs. Finally, we discuss possible physical mechanisms to enhance the disk mass
or the neutrino emission rate of NDAFs and relevant difference between these
two mechanisms.
