Effects of an extra Z' gauge boson on the top quark decay t → cγ gamma

The effects of an extra ${Z}^{\ensuremath{'}}$ gauge boson with family nonuniversal fermion couplings on the rare top quark decay $t\ensuremath{\rightarrow}c\ensuremath{\gamma}$ are first examined in a model-independent way and then in the minimal 331 model. It is found that the respective branching fraction is at most of the order of ${10}^{\ensuremath{-}8}$ for ${m}_{{Z}^{\ensuremath{'}}}=500$ GeV and dramatically decreases for a heavier ${Z}^{\ensuremath{'}}$ boson. This results is in sharp contrast with a previous evaluation of this decay in the context of topcolor-assisted technicolor models, which found that $B(t\ensuremath{\rightarrow}c\ensuremath{\gamma})\ensuremath{\simeq}{10}^{\ensuremath{-}6}$ for ${m}_{{Z}^{\ensuremath{'}}}=1$ TeV.