The Milagrito collaboration recently reported evidence for emission of very
high energy gamma-rays in the TeV range from one of the BATSE GRBs, GRB
970417a. Here I discuss possible interpretations of this result. Taking into
account the intergalactic absorption of TeV gamma-rays by the cosmic infrared
background, I found that the detection rate (one per 54 GRBs observed by the
Milagrito) and energy fluence can be consistently explained with the redshift
of this GRB at z \sim 0.7 and the isotropic total energy in the TeV range,
E_{TeV, iso} >~ 10^{54} erg. This energy scale is not unreasonably large, but
interestingly similar to the maximum total GRB energy observed to date, in the
sub-MeV range for GRB 990123. On the other hand, the energy emitted in the
ordinary sub-MeV range becomes E_{MeV, iso} \sim 10^{51} erg for the GRB
970417a, which is much smaller than the total energy in the TeV range by a
factor of about 10^3. I show that the proton-synchrotron model of GRBs provides
a possible explanation for these observational results. I also discuss some
observational signatures expected in the future experiments from this model.Comment: 6 pages, 2 figures, Accepted by ApJ Letter
