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Considering the gluon condensate corrections, the form factors relevant tothe semileptonic rare $B_c \rar D,D_s(J^{P}=0^{-}) l^{+}l^{-}$ with$l=\tau,\mu,e$ and $B_c \rar D,D_s(J^{P}=0^{-})\nu\bar{\nu}$ transitions arecalculated in the framework of the three point QCD sum rules. The heavy quarkeffective theory limit of the form factors are computed. The branching fractionof these decays are also evaluated and compared with the predictions of therelativistic constituent quark model. Analyzing of such type transitions couldgive useful information about the strong interactions inside the pseudoscalar$D_{s}$ meson and its structure.

Analysis of the rare semileptonic $B_c \rar P(D,D_s) l^{+}l^{-}/\nu\bar{\nu}$ decays within QCD sum rules