On the Interplay of Constraints from $B_s$, $D$, and $K$ Meson Mixing in $Z^{\prime }$ Models with Implications for $b\to s\nu \bar{\nu }$ Transitions

Abstract

Within $Z^{\prime }$ 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 $Z^{\prime }$ parameter space, the contributions to meson mixing observables become negligibly small even for large $Z^{\prime }$ couplings. While this a priori allows for significant new physics (NP) effects in FCNC decays, we discuss how large $Z^{\prime }$ couplings in one neutral meson sector can generate effects in meson mixing observables of other neutral mesons, through correlations stemming from ${\text{SU(2)}}_L$ gauge invariance and through Renormalization Group (RG) effects in the SM Effective Field Theory (SMEFT). This is illustrated with the example of $B_s^0-{\bar{B}}_s^0$ mixing, which in the presence of both left- and right-handed $Z^{\prime }bs$ couplings ${\Delta }_L^{bs}$ and ${\Delta }_R^{bs}$ remains SM-like for ${\Delta }_R^{bs}\approx 0.1{\Delta }_L^{bs}$. We show that in this case, large $Z^{\prime }bs$ couplings generate effects in $D$ and $K$ meson mixing observables, but that the $D$ and $K$ mixing constraints and the relation between ${\Delta }_R^{bs}$ and ${\Delta }_L^{bs}$ are fully compatible with a lepton flavour universality (LFU) conserving explanation of the most recent $b\to s{\ell }^{+}{\ell }^{-}$ experimental data without violating other constraints like $e^{+}{e}^{-}\to {\ell }^{+}{\ell }^{-}$ scattering. Assuming LFU, invariance under the ${\text{SU(2)}}_L$ gauge symmetry leads then to correlated effects in $b\to s\nu \bar{\nu }$ observables presently studied intensively by the Belle II experiment, which allow to probe the $Z^{\prime }$ parameter space that is opened up by the vanishing NP contributions to $B_s^0-{\bar{B}}_s^0$ mixing. In this scenario the suppression of $B\to K(K^{\ast }){\mu }^{+}{\mu }^{-}$ branching ratios implies uniquely enhancements of $B\to K(K^{\ast })\nu \bar{\nu }$ branching ratios up to $20\%$.

Comments: 63 pages, 6 figures, 2 tables. v2: matches the journal version