  Fundamental physical constants are determined from a collection of precision
measurements of elementary particles, atoms and molecules. This is usually done
under the assumption of the Standard Model~(SM) of particle physics. Allowing
for light new physics~(NP) beyond the SM modifies the extraction of fundamental
physical constants. Consequently, setting NP bounds using these data, and at
the same time assuming the CODATA recommended values for the fundamental
physical constants, is not reliable. As we show in this Letter, both SM and NP
parameters can be simultaneously determined in a consistent way from a global
fit. For light vectors with QED-like couplings, such as the dark photon, we
provide a prescription that recovers the degeneracy with the photon in the
massless limit, and requires calculations only at leading order in the small
new physics couplings. At present, the data show tensions partially related to
the proton charge radius determination. We show that these can be alleviated by
including contributions from a light scalar with flavor non-universal
couplings.
