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In this paper, we analyze different decay observables of semileptonic $ B_c$decays into $(D_(s,d)^((*))){\mu}^+ {\mu}^-$ such as branching ratio,forward-backward asymmetry, polarization fraction and lepton polarizationasymmetry in the non-universal Z' model. We have also studied the dependence ofbranching fraction to the new model parameters. Here, we have found that thevalues of different decay parameters increase in the Z' model, which provides apossible way out for the search of new physics as well as the unknown phenomenaof charm B meson.

Investigation of rare semileptonic $ B_c$ decays into $(D_(s,d)^((*))){\mu}^+ {\mu}^-$ decays with non-universal $ Z'$ effect