Probing $c\to u\gamma$ in $B_c\to B_u^*\gamma$ decay

Flavour changing neutral current (FCNC) transitions $c\to u\gamma$ and $c\to ul^+l^-$ are very rare in the standard model and present an interesting probe for the physics beyond it. We study long distance contamination to these short distance processes in different hadron decays. As the most suitable probe for $c\to u\gamma$ transition we propose $B_c\to B_u^*\gamma$ decay. Its detection at the branching ratio well above $10^{-8}$ would signal new physics. The $c\to ul^+l^-$ transition may be probed at high $m_{ll}$ in $D\to \pi l^+l^-$. The decays $D\to V\gamma$ and $D\to Vl^+l^-$ ($V$ is a light vector meson) are less suitable, since they are dominated by the long distance effects.