The Zbb¯ vertex in a left–right model

Abstract

We consider the one-loop corrections to the Zbb¯ vertex in a CP-conserving left–right model (LRM), viz. a model with gauge group SU(2)L×SU(2)R×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 Zbb¯ vertex in the SM from the same vertex in the LRM. We effect a proper renormalization of the Zbb¯ 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 Zbb¯ 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 ≲50 GeV. This is true even when we allow for markedly different gauge coupling constants of SU(2)L and SU(2)R.