Exclusive $c\to u\gamma$ transitions of $B_c$ meson

We study the rare decays of the $B_c$ meson induced by the flavour changing neutral current $c\to u\gamma$ transition. In the Standard Model they are strongly suppressed by the Glashow-Iliopoulos-Maiani mechanism, therefore they are sensitive to new physics. The difficulty is to get rid of long-distance contributions. We study such effects in radiative $B_c$ transitions both to $B^{\ast }$ and to the axial-vector $B_1^{\mathrm{\prime }}$ meson.