The $Zb\bar{b}$ vertex in a left-right model

Abstract

We consider the one-loop corrections to the $Zb\bar{b}$ 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 $Zb\bar{b}$ vertex in the SM from the same vertex in the LRM. We effect a proper renormalization of the $Zb\bar{b}$ 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 $Zb\bar{b}$ 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 $SU(2{)}_R$.

57 pages, 8 figures; v2: added section 3, figure 2 and three references; v3: matches published version