Effects of an extra $Z'$ gauge boson on the top quark decay $t --> c   \gamma$
  The effects of an extra $Z'$ gauge boson with family nonuniversal fermion couplings on the rare top quark decay $t --> c $gamma$ 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 $10^{-8}$ for $m_{Z'}=500$ GeV and dramatically decreases for a heavier $Z'$ 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 $B(t --> c \gamma)\sim 10^{-6}$ for $m_{Z'}=1$ TeV. 
A. Cordero-Cid, G. Tavares-Velasco, J. J. Toscano