Radiative decay of $Z^{\prime }$ boson

In the framework of the extended $SU(2{)}_h\times SU(2{)}_l$ model we study the radiative decay of an extra gauge boson $Z^{\prime }$, $Z^{\prime }\to \gamma Z$. The data analysis results of the CDF collaboration at the Fermilab Tevatron allow one to establish not only the lower bound of the decay probability $Z^{\prime }\to \gamma Z$ normalized to Drell-Yan process $Z^{\prime }\to {\mu }^{+}{\mu }^{-}$, $R(Z^{\prime }\to \gamma Z/{\mu }^{+}{\mu }^{-})>1.4\times {10}^{-5}{cot}^2\varphi$, but also to estimate the mixing angle $\xi$ between the states $Z^{\prime }$ and $Z$, $|\xi |<5\times {10}^{-2}$, taking into account the additional mixing angle $\varphi$ related to the extended gauge group $SU(2{)}_h\times SU(2{)}_l$. The comparison with the decays $Z^{\prime }\to {\tau }^{+}{\tau }^{-}$ and $Z^{\prime }\to \overline{b}b$, $Z^{\prime }\to \overline{t}t$ based on the LEP data is also presented.

Figure 1

Decay width $\Gamma (Z^{\prime }\to \gamma Z)$ as a function of $M_{Z^{\prime }}$ with the contribution due to only $b$- and $t$-quarks in the loop and taking into account the additional contribution extended by the quarks of the fourth generation.

Figure 2

The ratio $R(Z^{\prime }\to \gamma Z/\overline{l}l)$ as a function of the mass $M_{Z^{\prime }}$ in the $\tau$-lepton channel ($l=\tau$) taking into account the contribution from only $b$- and $t$-quarks and with the additional loop containing the quarks of the fourth generation.