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In view of the recent improved data on B_{s,d}->mu^+ mu^- and B_d->K^*mu^+mu^- we revisit two simple NP scenarios in which new FCNC currents in b->s mu^+ mu^- transitions are mediated either entirely by a neutral heavy gauge boson Z' with purely LH complex couplings Delta_L^{qb}(Z') (q=d,s) and couplings to muons Delta_A^{mu mu}(Z') and Delta_V^{mu mu}(Z') or the SM Z boson with LH complex couplings Delta_L^{qb}(Z).
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