  The one-loop effective action for the scalar field part of a non-Abelian
gauge theory based on a general gauge group of the form $G\times U(1)$, where
the gauge group $G$ is arbitrary, is calculated. A complex scalar field, both
Abelian and non-Abelian gauge fields and Dirac fermions coupled to gauge and
scalar fields are included. A general mass term for the Dirac fields that
includes a pseudoscalar term as well as both scalar and pseudoscalar Yukawa
couplings is considered. The background field method is used in its manifestly
gauge condition independent and gauge invariant form to isolate the divergent
part of the one-loop effective action and to calculate the associated
renormalisation group functions. Terms in the renormalised effective action up
to and including those quadratic in the curvature are calculated using
renormalisation group methods. The background scalar field is not assumed to be
constant, so the second order derivative terms in the effective action can be
calculated, and the gravitational background is kept arbitrary. The difference
between the gauge condition independent approach and the more standard approach
where gauge condition dependent results are found is demonstrated by explicit
calculations. The anomaly that can arise if the pseudoscalar mass term for the
fermions is transformed away from the classical theory is noted.
