Exploring new physics in the FCNC $B_c\to D_s\nu \bar{\nu }$ channel

The rare $b\to s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ transition is a well-explored transition, particularly for new physics beyond the standard model. Similar to this transition, another flavor changing neutral current transition $b\to s\nu \bar{\nu }$ involving a dineutrino pair also plays an important role in the search for new physics. The $B\to K\nu \bar{\nu }$ mode is one such dineutrino channel that has been analyzed in many works both within the standard model and beyond standard model framework. In this paper, we investigate the $B_c\to D_s\nu \bar{\nu }$ decay channel which proceeds via the $b\to s\nu \bar{\nu }$ transition. We consider an effective Hamiltonian framework involving new physics currents. To explore these currents further, we also analyse the decay mode within the $V_2$ leptoquark model. In our analysis, we use the form factors that have been obtained in lattice QCD calculations. We then make predictions of the $B_c\to D_s\nu \bar{\nu }$ branching fraction both within the standard model and beyond.