  We consider the one-loop corrections to the $Z b \bar b$ vertex in a
$CP$-conserving left--right model (LRM), $viz$. a model with gauge group
$SU(2)_L \times SU(2)_R \times U(1)$. We allow the gauge coupling constants of
$SU(2)_L$ and $SU(2)_R$ to be different. The spontaneous symmetry breaking is
accomplished only by doublets and/or singlets of $SU(2)_L$ and $SU(2)_R$. The
lightest massive neutral gauge boson of our LRM is assumed to have the same
Yukawa couplings to bottom-quark pairs as the $Z$ of the Standard Model (SM);
this assumption has the advantage that, then, the infrared divergences
automatically cancel down in the subtraction of the $Z b \bar b$ vertex in the
SM from the same vertex in the LRM. We effect a proper renormalization of the
$Z b \bar b$ vertex and check explicitly both its gauge invariance and the
cancellation of all the ultraviolet divergences. We find out that a LRM with
the above assumptions cannot achieve a better fit to the $Z b \bar b$ vertex
than a multi-Higgs extension of the SM, $viz$. both models can only achieve a
decent fit when one admits scalar particles with very low masses $\lesssim 50$
GeV. This is true even when we allow for markedly different gauge coupling
constants of $SU(2)_L$ and $SU(2)_R$.
