Z′→gggdecay in left-right symmetric models with three and four fermion families

Abstract

We study the ${Z}^{\ensuremath{'}}\ensuremath{\rightarrow}\overline{q}q,ggg$ decays in the context of a manifest left-right symmetric gauge theory with three and four generations. The ${Z}^{\ensuremath{'}}$ couplings to quarks are fixed essentially by the parameters of the standard model and we obtain $\ensuremath{\Gamma}({Z}^{\ensuremath{'}}\ensuremath{\rightarrow}q\overline{q})\ensuremath{\approx}14\text{ }\text{ }\mathrm{GeV}$ for ${M}_{{Z}^{\ensuremath{'}}}\ensuremath{\approx}1\text{ }\text{ }\mathrm{TeV}$. For the ${Z}^{\ensuremath{'}}\ensuremath{\rightarrow}ggg$ decay and three families we obtain a branching ratio $\mathrm{BR}({Z}^{\ensuremath{'}}\ensuremath{\rightarrow}ggg)=\frac{\ensuremath{\Gamma}({Z}^{\ensuremath{'}}\ensuremath{\rightarrow}ggg)}{\ensuremath{\Gamma}({Z}^{\ensuremath{'}}\ensuremath{\rightarrow}q\overline{q})}=1.2\ensuremath{-}2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ for ${m}_{{Z}^{\ensuremath{'}}}=700--1500\text{ }\text{ }\mathrm{GeV}$. The fourth generation produces an enhancement in the branching ratio for ${Z}^{\ensuremath{'}}$ masses close to the ${\overline{b}}^{\ensuremath{'}}{b}^{\ensuremath{'}}$ threshold and a dip for ${Z}^{\ensuremath{'}}$ masses close to the ${\overline{t}}^{\ensuremath{'}}{t}^{\ensuremath{'}}$ threshold. Using the values of the fourth-generation quark masses allowed by electroweak precision data, we obtain a branching ratio $\mathrm{BR}({Z}^{\ensuremath{'}}\ensuremath{\rightarrow}ggg)=(1\ensuremath{-}6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ for ${m}_{{Z}^{\ensuremath{'}}}=(700--1500)\text{ }\text{ }\mathrm{GeV}$.