Atomic precision tests and light scalar couplings

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. For a range of masses these constraints are not as stringent as those from fifth force experiments or optical astrophysical and laboratory measurements. However, they have the advantage that they are universal, applying to all scalars, even those that hide their effects dynamically from fifth force searches, such as the chameleon and Galileon models. 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.