Flavor-changing radiative decay of thetquark

We study the loop-induced flavor-changing decay $t\to c+\gamma$ in a nonlinear $R_{\xi }$ gauge for the standard model with three and four generations and in models with two Higgs doublets. We find that this decay could be relevant only in a scenario with two Higgs doublets and the mass of the fourth-generation $b^{\prime }$ quark larger than $m_t$. Under these conditions, the flavor-changing electromagnetic decays $T_q^{*}\to D_q\gamma (T_q\to D_q^{*}\gamma )$ may surpass the standard electromagnetic transition $T_q^{*}\to T_q\gamma$.