Probing Low-Mass Vector Bosons with Parity Nonconservation and Nuclear Anapole Moment Measurements in Atoms and Molecules

In the presence of $P$-violating interactions, the exchange of vector bosons between electrons and nucleons induces parity-nonconserving (PNC) effects in atoms and molecules, while the exchange of vector bosons between nucleons induces anapole moments of nuclei. We perform calculations of such vector-mediated PNC effects in Cs, ${\mathrm{Ba}}^{+}$, Yb, Tl, Fr, and ${\mathrm{Ra}}^{+}$ using the same relativistic many-body approaches as in earlier calculations of standard-model PNC effects, but with the long-range operator of the weak interaction. We calculate nuclear anapole moments due to vector-boson exchange using a simple nuclear model. From measured and predicted (within the standard model) values for the PNC amplitudes in Cs, Yb, and Tl, as well as the nuclear anapole moment of ${}^{133}\mathrm{Cs}$, we constrain the $P$-violating vector-pseudovector nucleon-electron and nucleon-proton interactions mediated by a generic vector boson of arbitrary mass. Our limits improve on existing bounds from other experiments by many orders of magnitude over a very large range of vector-boson masses.

Figure 1

Limits on the $P$-violating vector-pseudovector nucleon-electron (top panel) and nucleon-proton (bottom panel) interactions mediated by a generic vector boson of mass $m_{Z^{\prime }}$, as defined in Eq. (1). The regions in grey correspond to regions of parameters excluded by this Letter from consideration of atomic parity nonconservation experiments. The regions in darker grey correspond to existing constraints from torsion-pendulum and magnetometry experiments [44, 45, 46].