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

The rare $b \to s \ell^+\ell^-$ 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.