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We investigate the exclusive rare semileptonic decays $ B_c \toD_{s}^{(*)}\,(\ell \ell, \nu \bar{\nu})$ induced by neutral current transition$b \to s (\ell \ell,\nu \bar{\nu})$ in the presence of non-universal$Z^{\prime}$, scalar and vector leptoquark new physics models. We constrain thenew physics parameter space by using the latest experimental measurements of$R_{K^{(*)}}$, $P_5^{\prime}$, $\mathcal{B}(B_s \to \phi \mu^+ \mu^-)$ and$\mathcal{B}(B_s \to \mu^+ \mu^-)$. Throughout the analysis, we choose to workwith the particular new physics scenario $C_9 ^{\mu \mu}(NP)=-C_{10} ^{\mu\mu}(NP)$ where both $Z^{\prime}$, $S_{1/3}^3$ and $U_{-2/3}^3$ leptoquarkssatisfy the condition. Using these new coupling parameters we scrutinize theseveral physical observables such as differential branching fraction, theforward backward asymmetry, the lepton polarization asymmetry, the angularobservable $P^{\prime}_5$ and the lepton flavor universal sensitive observablesincluding the ratio of branching ratio $R_{D_s^{(*)}}$ and the few $Q$parameters in the $B_c \to D_s^{(*)}\,\mu ^+ \mu ^-$ and $B_c \to D_s^{(*)}\,\nu \bar{\nu}$ decay processes.

physical review. d/physical review. d.

Combined analysis of $B_c \to D_s^{(*)}\,\mu ^+ \mu ^-$ and $B_c \to  D_s^{(*)}\, \nu \bar{\nu}$ decays within $Z^{\prime}$ and leptoquark new  physics models