  This is the second of a pair of articles on scattering of glue by glue, in
which we give the light-cone gauge calculation of the one-loop on-shell
helicity conserving scattering amplitudes for gluon-gluon scattering
(neglecting quark loops). The 1/p^+ factors in the gluon propagator are
regulated by replacing p^+ integrals with discretized sums omitting the p^+=0
terms in each sum. We also employ a novel ultraviolet regulator that is
convenient for the light-cone worldsheet description of planar Feynman
diagrams. The helicity conserving scattering amplitudes are divergent in the
infra-red. The infrared divergences in the elastic one-loop amplitude are shown
to cancel, in their contribution to cross sections, against ones in the cross
section for unseen bremsstrahlung gluons. We include here the explicit
calculation of the latter, because it assumes an unfamiliar form due to the
peculiar way discretization of p^+ regulates infrared divergences. In resolving
the infrared divergences we employ a covariant definition of jets, which allows
a transparent demonstration of the Lorentz invariance of our final results.
Because we use an explicit cutoff of the ultraviolet divergences in exactly 4
space-time dimensions, we must introduce explicit counterterms to achieve this
final covariant result. These counter-terms are polynomials in the external
momenta of the precise order dictated by power-counting. We discuss the
modifications they entail for the light-cone worldsheet action that reproduces
the ``bare'' planar diagrams of the gluonic sector of QCD. The simplest way to
do this is to interpret the QCD string as moving in six space-time dimensions.
