The simplest extension of the Standard Model (SM) that generally introduces new sources of flavour violation and CP violation as well as right-handed (RH) currents is the addition of a U (1) gauge symmetry to the SM gauge group. If the corresponding heavy gauge boson (Z ) mediates FCNC processes in the quark sector at tree-level, these new physics (NP) contributions imply a pattern of deviations from SM expectations for FCNC processes that depends only on the couplings of Z to fermions and on its mass. This implies stringent correlations between ∆F = 2 and ∆F = 1 observables which govern the landscape of the allowed parameter space for Z -models. Anticipating the Flavour Precision Era (FPE) ahead of us we illustrate this by searching for allowed oases in this landscape assuming significantly smaller uncertainties in CKM and hadronic parameters than presently available. To this end we analyze ∆F = 2 observables in K 0 −K 0 and B 0 s,d −B 0 s,d systems and rare K and B decays including both left-handed and right-handed Z -couplings to quarks in various combinations. We identify a number of correlations between various flavour observables that could test and distinguish these different Z scenarios. The important role of b → s + − and b → sνν transitions in these studies is emphasized. Imposing the existing flavour constraints, a rich pattern of deviations from the SM expectations in B s,d and K meson systems emerges provided M Z ≤ 3 TeV. While for M Z ≥ 5 TeV Z effects in rare B s,d decays are found typically below 10% and hard to measure even in the FPE, K → πνν and K L → π 0 + − decays provide an important portal to scales beyond those explored by the LHC. We apply our formalism to NP scenarios with induced flavour changing neutral Z-couplings to quarks. We find that in the case of B d and K decays such Z-couplings still allow for sizable departures from the SM. On the other hand in the B s system, constraints on b → s + − transitions basically eliminate NP effects from such couplings.

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.

The decay B s → µ + µ − is one of the milestones of the flavor program at the LHC. We reappraise its Standard Model prediction. First, by analyzing the theoretical rate in the light of its main parametric dependence, we highlight the importance of a complete evaluation of higher-order electroweak corrections, at present known only in the large-m t limit, and leaving sizable dependence on the definition of electroweak parameters. Using insights from a complete calculation of such corrections for K → πνν decays, we find a scheme in which NLO electroweak corrections are likely to be negligible. Second, we address the issue of the correspondence between the initial and the final state detected by the experiments, and those used in the theoretical prediction. Particular attention is devoted to the effect of the soft radiation, that has not been discussed for this mode in the previous literature, and that can lead to O(10%) corrections to the decay rate. The "non-radiative" branching ratio (that is equivalent to the branching ratio fully inclusive of bremsstrahlung radiation) is estimated to be (3.23 ± 0.27) × 10 −9 for the flavor eigenstate, with the main uncertainty resulting from the value of f Bs , followed by the uncertainty due to higher order electroweak corrections. Applying the same strategy to B d → µ + µ − , we find for its non-radiative branching ratio (1.07 ± 0.10) × 10 −10 .