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We study the effect of non-universal $Z'$ boson on the rare leptonic decaymodes of $B_s^*$ mesons, mediated by $b arrow sll$ quark transition. Rare Bdecays are sensitive to various new physics operators. As B mesons arecomposite particles, such decay modes of the excited states are ideal forprobing new physics beyond the standard model. We have constrained our modelparameters from $B_(s,d)-$ {B bar(s,d)}$ mixing data to predict the leptonpolarization asymmetry of $B_(s,d)^*$ arrow ${\mu}^+ {\mu}^-$ channel. It isfound that this asymmetry deviates from its SM prediction along with the$Z'$effect

Lepton polarization asymmetry in $B_(s,d)^*$ arrow ${\mu}^+ {\mu}^-$ with new Z' couplings