  Recent observations suggest that $\gamma$-ray bursts (GRBs) and their
afterglows are produced by jets of highly relativistic cannonballs (CBs),
emitted in supernova (SN) explosions. The CBs, reheated by their collision with
the shell, emit radiation that is collimated along their direction of motion
and Doppler-boosted to the typical few-hundred keV energy of the GRB.
Accompanying the GRB, there should be an intense burst of neutrinos of a few
hundreds of GeV energy, made by the decay of charged pions produced in the
collisions of the CBs with the SN shell . The neutrino beam carries almost all
of the emitted energy, but is much narrower than the GRB beam and should only
be detected in coincidence with the small fraction of GRBs whose CBs are moving
very close to the line of sight. The neutral pions made in the transparent
outskirts of the SN shell decay into energetic $\gamma$-rays (EGRs) of energy
of ${\cal{O}}$(100) GeV. The EGR beam, whose energy fluence is comparable to
that of the companion GRB, is as wide as the GRB beam and should be observable,
in coincidence with GRBs, with existing or planned detectors. We derive in
detail these predictions of the CB model.
