Malaphoric $Z^{\prime }$ models for $b\to s{\ell }^{+}{\ell }^{-}$ anomalies

Abstract

We study some phenomenological effects of kinetic mixing between the hypercharge field and a new $U(1)$ gauge field in specific $Z^{\prime }$ models that ameliorate the tensions between measurements and Standard Model predictions in $b\to s{\ell }^{+}{\ell }^{-}$ decays. To this end, we rederive the dimension-6 SMEFT coefficients resulting from integrating out the kinetically-mixed (`malaphoric') $Z^{\prime }$ field. The kinetic mixing provides a family-universal component to the couplings of the $Z^{\prime }$ field, which can improve fits to lepton flavour universality observables. We show how kinetic mixing improves the best fit of the $B_3-L_2$ model to $b\to s$ data by 7.0 units of ${\chi }^2$ while remaining compatible with other relevant data sets such as electroweak precision observables and measurements of $e^{+}{e}^{-}\to {\ell }^{+}{\ell }^{-}$ at LEP2.

Comments: 20 pages, 4 figures, fixed small bug in numeric part, added comments