The $Z b \bar b$ vertex in a left-right model

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 effected only by doublets and/or singlets of $SU(2)_L$ and $SU(2)_R$. We assume that the lightest massive neutral gauge boson has the same couplings, at the tree level, as in the Standard Model (SM); then, the infrared divergences 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.