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In the presence of P-violating interactions, the exchange of vector bosonsbetween electrons and nucleons induces parity-nonconserving (PNC) effects inatoms and molecules, while the exchange of vector bosons between nucleonsinduces anapole moments of nuclei. We perform calculations of suchvector-mediated PNC effects in Cs, Ba$^+$, Yb, Tl, Fr and Ra$^+$ using the samerelativistic many-body approaches as in earlier calculations of standard-modelPNC effects, but with the long-range operator of the weak interaction. Wecalculate nuclear anapole moments due to vector boson exchange using a simplenuclear model. From measured and predicted (within the standard model) valuesfor the PNC amplitudes in Cs, Yb and Tl, as well as the nuclear anapole momentof $^{133}$Cs, we constrain the P-violating vector-pseudovectornucleon-electron and nucleon-proton interactions mediated by a generic vectorboson of arbitrary mass. Our limits improve on existing bounds from otherexperiments by many orders of magnitude over a very large range of vector-bosonmasses.

Probing low-mass vector bosons with parity nonconservation and nuclear anapole moment measurements in atoms and molecules