Rare Semileptonic $$b \rightarrow d \mu ^+ \mu ^- $$ Transitions and Effects of $$Z^\prime $$ in the 331 Model

Abstract

We study the rare semileptonic \(B \rightarrow \rho \mu ^+ \mu ^-\) decay mediated by \(b \rightarrow d \mu ^+ \mu ^- \) transition. Differential branching ratio, longitudinal lepton polarization and forward-backward asymmetry of \(B \rightarrow \rho \mu ^+ \mu ^-\) are analyzed within the Standard Model in the low \(q^2\) region. We study the effects of \(Z^\prime \) in the 331 or \(SU_{C}(3)\times SU_{L}(3)\times U_{X}(1)\) model on this decay mode by varying the model parameter \(\beta \) at \(M_{Z^\prime }=1,~ 3 \mathrm{TeV}\). The couplings of \(Z^\prime \) are constrained by flavor observables of \(B_\mathrm{d}-\bar{B}_\mathrm{d}\) mixing. We find that the observables of interest are sensitive to \(Z^\prime \) effects and we observe deviations from the SM for some values of \(\beta \).