  The baryon asymmetry of the universe may be explained by rotations of the QCD
axion in field space and baryon number violating processes. We consider the
minimal extension of the Standard Model by a non-Abelian gauge interaction,
$SU(2)_R$, whose sphaleron process violates baryon number. Assuming that axion
dark matter is also created from the axion rotation by the kinetic misalignment
mechanism, the mass scale of the $SU(2)_R$ gauge boson is fixed as a function
of the QCD axion decay constant, and vise versa. Significant portion of the
parameter space has already been excluded by new gauge boson searches, and the
high-luminocity LHC will further probe the viable parameter space.
