B-anomalies from flavorful U(1)$$'$$ extensions, safely

Abstract$$U(1)^\prime $$ U ( 1 ) ′ extensions of the standard model with generation-dependent couplings to quarks and leptons are investigated as an explanation of anomalies in rare B-decays, with an emphasis on stability and predictivity up to the Planck scale. To these ends, we introduce three generations of vector-like standard model singlet fermions, an enlarged, flavorful scalar sector, and, possibly, right-handed neutrinos, all suitably charged under the $$U(1)^\prime $$ U ( 1 ) ′ gauge interaction. We identify several gauge-anomaly free benchmarks consistent with $$B_s$$ B s -mixing constraints, with hints for electron-muon universality violation, and the global $$b \rightarrow s$$ b → s fit. We further investigate the complete two-loop running of gauge, Yukawa and quartic couplings up to the Planck scale to constrain low-energy parameters and enhance the predictive power. A characteristic of models is that the $$Z^\prime $$ Z ′ with TeV-ish mass predominantly decays to invisibles, i.e. new fermions or neutrinos. $$Z^\prime $$ Z ′ -production can be studied at a future muon collider. While benchmarks feature predominantly left-handed couplings $$C_9^{\mu }$$ C 9 μ and $$C_{10}^{\mu }$$ C 10 μ , right-handed ones can be accommodated as well.