In this work we have studied the top quark decay $t\rightarrow c\gamma$ mediated by a neutral gauge boson $V$ which produces flavour changing couplings at tree level. Such a boson can be induced in some theories beyond the Standard Model with an extended gauge group. $t\rightarrow c\gamma$ decay is induced by one loop and the amplitude is generated by three Feynman diagrams in the unitary norm: two bubble diagrams and one triangle diagram. We used the Feynman parametrization method to calculate the one loop integrals and we considered the dimensional regularization method in order to isolate the ultraviolet divergences and verify their cancellation. We have used tensorial integrals to obtain analytic expressions that contains parametric integrals for the $A_{L}$ and $A_{R}$ coefficients which are related to the $ \sigma^{\mu\nu} q_\mu P_L$ and $ \sigma^{\mu\nu} q_\mu P_R$ terms. We considered the $Z^{\prime}$ gauge boson contribution predicted in models with extended $U(1)^{\prime}$ gauge symmetry. Finally we computed the branching ratio numerical analysis $BR(t\rightarrow c\gamma)$ as a function of $Z^{\prime}$ boson mass in the range of 500 GeV $< m_{Z^{\prime}} < $ 1000 GeV.Contribution of a new neutral gauge boson $Z^{\prime}$ to the top quark decay $t\rightarrow c\gamma$ in extended gauge sector models

Theory/Pheno