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We analyze the semileptonic (B_c -> B_u* l+ l-) decay in the frame work of the Standard Model. We calculate the (B_c) to (B_u*) transition form factors in QCD sum rules. Analytical expressions for the spectral densities and gluon condensates are presented. The branching ratio of the (B_c -> B_u* l+ l-) decay is calculated, and it is obtained that this decay can be detectable at forthcoming LHC machines.

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