331 models facing new b → sμ + μ − data

Abstract

Abstract:We investigate how the 331 models, based on the gauge group SU(3) C × SU(3) L ×U(1) X face new data on B s,d → µ + µ − and B d → K * (K)µ + µ − taking into account present constraints from ∆F = 2 observables, low energy precision measurements, LEP-II and the LHC data. In these models new sources of flavour and CP violation originate dominantly through flavour violating interactions of ordinary quarks and leptons with a new heavy Z gauge boson. The strength of the relevant couplings is governed by four new parameters in the quark sector and the parameter β which in these models determines the charges of new heavy fermions and gauge bosons. We study the implications of these models for β = ±n/ √ 3 with n = 1, 2, 3. The case β = − √ 3 leading to Landau singularities for M Z ≈ 4 T eV can be ruled out when the present constraints on Z couplings, in particular from LEP-II, are taken into account. For n = 1, 2 interesting results are found for M Z < 4 T eV with largest NP effects for β < 0 in B d → K * µ + µ − and the ones in B s,d → µ + µ − for β > 0. As Re(C NP 9 ) can reach the values −0.8 and −0.4 for n = 2 and n = 1, respectively the B d → K * µ + µ − anomalies can be softened with the size depending on ∆M s /(∆M s ) SM and the CP-asymmetry S ψφ . A correlation between Re(C NP 9 ) and B(B s → µ + µ − ), identified for β < 0, implies for negative Re(C NP 9 ) uniquely suppression of B(B s → µ + µ − ) relative to its SM value which is favoured by the data. In turn also S ψφ < S SM ψφ is favoured with S ψφ having dominantly opposite sign to S SM ψφ and closer to its central experimental value. Another triple correlation is the one between Re(C NP 9 ), B(B s → µ + µ − ) and B(B d → Kµ + µ − ). NP effects in b → sνν transitions, K + → π + νν and K L → π 0 νν turn out to be small. We find that the absence of B d → K * µ + µ − anomalies in the future data and confirmation of the suppression of B(B s → µ + µ − ) relative to its SM value would favour β = 1/ √ 3 and M Z ≈ 3 T eV . Assuming lepton universality, we find an upper bound |C NP 9 | ≤ 1.1(1.4) from LEP-II data for all Z models with only left-handed flavour violating couplings to quarks when NP contributions to ∆M s at the level of 10%(15%) are allowed.

On the impact of power corrections in the prediction of B → K *μ+μ− observables

“…Several later studies have reached similar conclusions from B → K * µ + µ − data, using different observables [8] and/or statistical methods [9], with possible interpretations in terms of Z models 1 [7,8,[18][19][20][21]. Interestingly, a recent lattice study of B → K * µ + µ − and B s → φµ + µ − form factors [22,23] confirms the same trend using different observables (branching ratios rather than angular observables) and in a different kinematic regime (low rather than large hadronic recoil).…”

Flavour anomalies after the R K ∗ measurement

“…Models featuring extra Z to explain the anomalies are very popular, see the partial list of references [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Typically these models contain a Z with mass M Z savagely coupled to …”

An explicit Z ′-boson explanation of the B → K ∗ μ + μ − anomaly

“…A big "thank you" goes to Andrzej Buras for pointing out errors in various equations in section 9 of the first version of this manuscript (see also [60]). The research of R. G. is supported by an STFC Postgraduate Studentship and F. G. acknowledges support by the Swiss National Foundation under contract SNF 200021-143781.…”