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Left-handed Z' and Z FCNC quark couplings facing new b -> s mu^+ mu^- data

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). We demonstrate how these couplings can be determined by future Delta F=2 and b->s mu^+ mu^- observables. The correlations between various observables can test these NP scenarios. We present the results as functions of Delta M_q/Delta M_q^SM, S_{psi phi} and S_{psi K_S} which should be precisely determined in this decade. We calculate the violation of the CMFV relation between BR(B_{s,d}-> mu^+ mu^-) and Delta M_{s,d} in these scenarios. We find that the data on B_{s,d}->mu^+ mu^- from CMS and LHCb can be reproduced in both scenarios but in the case of Z, Delta M_s and S_{psi phi} have to be very close to their SM values. As far as B_d->K^*mu^+mu^- anomalies are concerned the Z' scenario can significantly soften these anomalies while the Z boson fails because of the small vector coupling to muons. We also point out that recent proposals of explaining these anomalies with the help of a real Wilson coefficient C^NP_9 implies uniquely an enhancement of Delta M_s with respect to its SM value, while a complex C^NP_9 allows for both enhancement and suppression of Delta M_s and simultaneously novel CP-violating effects. We also discuss briefly scenarios in which the Z' boson has RH FCNC couplings. In this context we point out a number of correlations between angular observables measured in B_d->K^*mu^+ mu^- that arise in the absence of new CP-violating phases in scenarios with only LH or RH couplings or scenarios in which LH and RH couplings are equal to each other or differ by sign.