Rare decays of $B$ mesons play a crucial role in understanding and exploring the intricacies of physics beyond the standard model. Various experimental results as well as theoretical investigations involving rare $B$ meson decays have motivated us to investigate the rare decay, $B\to \omega {\mu }^{+}{\mu }^{-}$, proceeding through the quark transition $b\to d{\ell }^{+}{\ell }^{-}$ in standard model and nonuniversal $Z^{\prime }$ model. We have incorporated the new physics (NP) couplings of the $Z^{\prime }$ boson with quarks from $B_d-\overline{B_d}$ mixing. We have estimated the NP leptonic couplings from the experimental values of branching fractions of other $b\to d{\ell }^{+}{\ell }^{-}$ decays. With these NP couplings, we have estimated the branching ratio, forward-backward asymmetry, and lepton polarization asymmetries. We have observed significant deviation from standard model predictions, especially for the branching fraction and forward-backward asymmetry.

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• Flavor changing neutral currents
• Hypothetical particle physics models
• Particle decays
• Particle phenomena