Atomic Precision Tests and Light Scalar Couplings

Abstract

We calculate the shift in the atomic energy levels induced by the presence of a scalar field which couples to matter and photons. We find that a combination of atomic measurements can be used to probe both these couplings independently. A new and stringent bound on the matter coupling springs from the precise measurement of the 1s to 2s energy level difference in the hydrogen atom, while the coupling to photons is essentially constrained by the Lamb shift. Combining these constraints with current particle physics bounds we find that the contribution of a scalar field to the recently claimed discrepancy in the proton radius measured using electronic and muonic atoms is negligible.