Confronting $B$ anomalies with atomic physics.

We consider a simple implementation of a minimal $Z^\prime$ model in the context of the anomalies in the $B$ decays. With the assumption of the primary contribution being due to the electron, implications from the recent measurements on the weak charge of proton $Q_W^p$ and the Caesium atom $Q_W^{Cs}$ are studied. The conclusion is characterized by different limiting behaviour depending on the chirality of the lepton current. The constraints are then compared with those coming from direct searches. This observation is crucial in determining the exact nature of the solution to the anomaly. The bounds on the simplified models from atomic physics are then compared with those from direct searches. We demonstrate that a minor improvement in the atomic physics measurements can be comparable with the bounds from direct searches with possibly better sensitivities for the heavier masses ($ \gtrsim 3.9$ TeV). We finally comment on the collider prospect for observing states beyond the realm of resonant production at LHC.