On the interplay of constraints from Bs,D, and K meson mixing in Z′ models with implications for b→sνν¯ transitions

Within Z′ models, neutral meson mixing severely constrains beyond the Standard Model (SM) effects in flavour changing neutral current (FCNC) processes. However, in certain regions of the Z′ parameter space, the contributions to meson mixing observables become negligibly small even for large Z′ couplings. While this a priori allows for significant new physics (NP) effects in FCNC decays, we discuss how large Z′ couplings in one neutral meson sector can generate effects in meson mixing observables of other neutral mesons, through correlations stemming from SU(2)L gauge invariance and through Renormalization Group (RG) effects in the SM Effective Field Theory (SMEFT). This is illustrated with the example of Bs0-B¯s0 mixing, which in the presence of both left- and right-handed Z′bs couplings ΔLbs and ΔRbs remains SM-like for ΔRbs≈0.1ΔLbs. We show that in this case, large Z′bs couplings generate effects in D and K meson mixing observables, but that the D and K mixing constraints and the relation between ΔRbs and ΔLbs are fully compatible with a lepton flavour universality (LFU) conserving explanation of the most recent b→sℓ+ℓ- experimental data without violating other constraints like e+e-→ℓ+ℓ- scattering. Assuming LFU, invariance under the SU(2)L gauge symmetry leads then to correlated effects in b→sνν¯ observables presently studied intensively by the Belle II experiment, which allow to probe the Z′ parameter space that is opened up by the vanishing NP contributions to Bs0-B¯s0 mixing. In this scenario the suppression of B→K(K∗)μ+μ- branching ratios implies uniquely enhancements of B→K(K∗)νν¯ branching ratios up to 20%.