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We study the exclusive semileptonic rare $B_c^+ \to D^+ \nu \bar{\nu}$ decayin the framework of light-cone quark model. The transition form factors$f_{+}(q^2)$ and $f_{T}(q^2)$ are evaluated in the time-like region using theanalytic continuation method in $q^{+} = 0$ frame. The analytic solutions ofthese form factors are compared with the results obtained from the double poleparametric form. The branching ratio for $B_c^+ \to D^+ \nu \bar{\nu}$ decay iscalculated and compared with the other theoretical model predictions. Thepredicted results in this model can be tested at the LHCb experiments in nearfuture which will help in testing the unitarity of CKM quark mixing matrix,thus, providing an insight into the phenomenon of CP violation.

Study of rare semileptonic $B_c^+ \to D^+ \nu \bar{\nu}$ decay in the light-cone quark model