Parity-nonconserving (PNC) effects in atoms produced by $Z$-boson exchange between the electron and the nucleus grow rapidly with the nuclear charge $Z$. If a hypothetical additional $Z^{\prime }$ boson is light, however, its contribution does not exhibit the same strong enhancement with $Z$. As a result, the ratio of the low-mass $Z^{\prime }$ contribution to the Standard Model $Z$-boson contribution increases rapidly with decreasing $Z$, in fact faster than $1/Z^2$. Hydrogen has a further important advantage: its theoretical description is substantially cleaner than that of heavy atoms, allowing a more accurate interpretation of experimental results. For these two reasons, hydrogen and deuterium PNC experiments may provide an especially favorable setting in which to disentangle a possible $Z^{\prime }$ contribution from the Standard Model background. In this paper we calculate the ratio of the $Z^{\prime }$-boson contribution, for arbitrary $Z^{\prime }$ mass, to the Standard Model $Z$-boson contribution to parity violation in hydrogen and deuterium, including both nuclear-spin-independent and nuclear-spin-dependent interactions.

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• Signatures with new bosons
• Atoms