$R_{K^{(\ast )}}$ and related $b\to s\mathrm{\ell }\bar{\mathrm{\ell }}$ anomalies in minimal flavor violation framework with $Z^{\mathrm{\prime }}$ boson

A recent LHCb measurement of the ratio $R_{K^{\ast }}$ of $B\to K^{\ast }\mu \bar{\mu }$ to $B\to K^{\ast }e\bar{e}$ branching fractions has produced results in mild tension with the standard model (SM). This adds to the known anomalies also induced by the $b\to s\mathrm{\ell }\bar{\mathrm{\ell }}$ transitions, resulting in a confidence level now as high as 4$\sigma$. We analyze whether the parameter space preferred by all the $b\to s\ell\bar\ell$anomaliesiscompatiblewithaheavy$Z’$ boson assumed to have nonuniversal couplings to SM fermions dictated by the principle of minimal flavor violation (MFV). We deal with the MFV couplings of the $Z^{\mathrm{\prime }}$ to leptons in the context of the type-I seesaw scenario for generating neutrino masses. The flavor-violating $Z^{\mathrm{\prime }}$ interactions are subject to stringent constraints from other processes, especially $B$-$\bar{B}$ mixing, charged lepton decays ${\mathrm{\ell }}_i\to {\mathrm{\ell }}_j{\mathrm{\ell }}_k{\bar{\mathrm{\ell }}}_l$ occurring at tree level, and the loop induced $\mu \to e\gamma$. We perform scans for parameter regions allowed by various data and predict the ranges for a number of observables. Some of the predictions, such as the branching fractions of lepton-flavor violating $\tau \to 3\mu$, $B\to Ke\mu$, $K_L\to e\mu$, and $Z\to \mathrm{\ell }{\mathrm{\ell }}^{\mathrm{\prime }}$, are not far below their experimental bounds and therefore could be probed by searches in the near future. The viable parameter space depends strongly on the neutrino mass hierarchy, with a preference for the inverted one.