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

TL;DR

This paper calculates one-loop corrections to the Zbbar vertex in a CP-conserving left-right model with different SU(2) gauge couplings, finding it cannot outperform multi-Higgs models in fitting experimental data unless very light scalars are introduced.

Contribution

It provides a detailed renormalization and gauge invariance check of the Zbbar vertex in a left-right model with asymmetric gauge couplings, highlighting limitations in fitting experimental data.

Findings

Left-right model cannot surpass multi-Higgs models in fitting Zbbar data.

Decent fit requires scalar particles with masses below 50 GeV.

Different SU(2) gauge couplings do not improve fit quality.

Abstract

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 $SU(2)_R$.