  We calculate running coupling corrections for the lowest-order gluon
production cross section in high energy hadronic and nuclear scattering using
the BLM scale-setting prescription. At leading order there are three powers of
fixed coupling; in our final answer, these three couplings are replaced by
seven factors of running coupling: five in the numerator and two in the
denominator, forming a `septumvirate' of running couplings, analogous to the
`triumvirate' of running couplings found earlier for the small-x BFKL/BK/JIMWLK
evolution equations. It is interesting to note that the two running couplings
in the denominator of the `septumvirate' run with complex-valued momentum
scales, which are complex conjugates of each other, such that the production
cross section is indeed real. We use our lowest-order result to conjecture how
running coupling corrections may enter the full fixed-coupling
k_T-factorization formula for gluon production which includes non-linear
small-x evolution.
