A global analysis of $b \to s \ell \ell$ data in heavy and light $Z'$ models

Abstract

We perform a model-independent global fit to all $b \to s \ell \ell$ data in the light of recent measurements of the lepton flavour universality violating (LFUV) observables $R_{K_S^0}$ and $R_{K^{*+}}$ as well as the updated measurements of observables in $B_s \to \phi \mu^+ \mu^-$ decay, by the LHCb collaboration. We obtain new physics (NP) solutions to the current anomalies in the data, assuming NP in the muon sector only. We find that the 1D NP scenarios $C_9^{\rm NP} <0 $ and $C_{9}^{\rm NP}=-C_{10}^{\rm NP}$ continue to be the most favoured ones. However, the significance of the then favoured scenario $C_{9}^{\rm NP}=-C'_{9}$ has reduced and the updated data now marginally prefers $C_{10}^{\rm NP}$ scenario over $C_{9}^{\rm NP}=-C'_{9}$. The 2D scenarios $(C_9^{\rm NP}, C_{10}^{\prime} )$, $(C_9^{\rm NP}, C_{9}^{\prime} )$ and $(C_9^{\rm NP}, C_{10}^{\rm NP} )$, continue to be favoured by the data in the listed order. We also analyse generic TeV scale $Z'$ models which can generate the favored 1D scenarios, $C_9^{\rm NP} $ and $C_9^{\rm NP} = -C_{10}^{\rm NP}$ along with the 2D NP scenarios $(C_9^{\rm NP}, C_{9}^{\prime} )$ and $(C_9^{\rm NP}, C_{10}^{\rm NP} )$. Using the additional constraints from $B_s -\bar{B_s}$ mixing and neutrino trident data, we find that all four models provide an equally good fit to the data. Further, we consider a model with a 25 MeV $Z'$ that couples to muons and has a $q^2$ dependent $b - s$ coupling. We also study the implications of the current data on the LFUV observable $R_{\phi}$, $Q_{4,5}$ along with $R_{K^{(*)}}$ in the high $q^2$. We find that a precise measurements of these observables can provide a good discrimination between a few favored model-independent solutions, and have a potential to disentangle different heavy and light $Z'$ scenarios considered in this work.