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

Abstract

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.

53 pages, 20 figures; one additional figure, references and few explanations added; conclusions unchanged; to appear in JHEP

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