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Left-handed Z′ and Z FCNC quark couplings facing new b → sμ + μ − data

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Abstract

In view of the recent improved data on B s,d → μ + μ − and B d → K * μ + μ − we revisit two simple New Physics (NP) scenarios analyzed by us last year in which new FCNC currents in b → sμ + μ − transitions are mediated either entirely by a neutral heavy gauge boson Z ′ with purely left-handed complex couplings \( \Delta_L^{qb}\left( {{Z^{\prime }}} \right)\left( {q=d,s} \right) \) and real couplings to muons \( \Delta_A^{{\mu \overline{\mu}}}\left( {{Z^{\prime }}} \right) \) and \( \Delta_V^{{\mu \overline{\mu}}}\left( {Z\prime } \right) \) or the SM Z boson with left-handed complex couplings \( \Delta_L^{qb }(Z) \). We demonstrate how the reduced couplings, the couplings in question divided by M Z′ or M Z, can be determined by future ΔF = 2 and b → sμ + μ − observables up to sign ambiguities. The latter do not affect the correlations between various observables that can test these NP scenarios. We present the results as functions of \( {C_{{{B_q}}}}={{{\varDelta Mq}} \left/ {{{{{\left( {\varDelta Mq} \right)}}_{\mathrm{SM}}}}} \right.},{S_{{\psi \phi }}} \) and \( {S_{{\psi {K_S}}}} \) which should be precisely determined in this decade. We calculate the violation of the CMFV relation between \( \mathcal{B}\left( {{B_{s,d }}\to {\mu^{+}}{\mu^{-}}} \right) \) and ΔM s,d in these scenarios. We find that the data on B s,d → μ + μ − from CMS and LHCb can be reproduced in both scenarios but in the case of Z, ΔM s and S ψϕ have to be very close to their SM values. As far as B d → K * μ + μ − anomalies are concerned the Z′ scenario can significantly soften these anomalies while the Z boson fails badly 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 \( C_9^{\mathrm{NP}} \) implies uniquely an enhancement of ΔM s with respect to its SM value, while a complex \( C_9^{\mathrm{NP}} \) allows for both enhancement and suppression of ΔM s and simultaneously novel CP-violating effects. Correlations between b → sμ + μ − and \( b\to s\nu \overline{\nu} \) observables in these scenarios are emphasized. We also discuss briefly scenarios in which the Z′ boson has right-handed FCNC couplings. In this context we point out a number of correlations between angular observables measured in B d → K * μ + μ − that arise in the absence of new CP-violating phases in scenarios with only left-handed or right-handed couplings or scenarios in which left-handed and right-handed couplings are equal to each other or differ by sign.

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  1. TUM-IAS, Lichtenbergstr. 2a, D-85748, Garching, Germany

    Andrzej J. Buras & Jennifer Girrbach

  2. Physik Department, TUM, D-85748, Garching, Germany

    Andrzej J. Buras & Jennifer Girrbach

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Buras, A.J., Girrbach, J. Left-handed Z′ and Z FCNC quark couplings facing new b → sμ + μ − data. J. High Energ. Phys. 2013, 9 (2013). https://doi.org/10.1007/JHEP12(2013)009

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