Large hadron collider constraints on some simple $$Z^\prime $$ models for $$b\rightarrow s \mu ^+\mu ^-$$ anomalies

We examine current Large Hadron Collider constraints on some simple $$Z^\prime $$ Z ′ models that significantly improve on Standard Model fits to $$b\rightarrow s \mu ^+\mu ^-$$ b → s μ + μ - transition data. The models that we consider are the ‘third family baryon number minus second family lepton number’ ($${B_3-L_2}$$ B 3 - L 2 ) model and the ‘third family hypercharge’ model and variants. The constraints are applied on parameter regions of each model that fit the $$b\rightarrow s \mu ^+\mu ^-$$ b → s μ + μ - transition data and come from high-mass Drell–Yan di-muons and measurements of Standard Model processes. This latter set of observables place particularly strong bounds upon the parameter space of the $${B_3-L_2}$$ B 3 - L 2 model when the mass of the $$Z^\prime $$ Z ′ boson is less than 300 GeV.