Constraints on new vector boson mediated electron-nucleus interactions from spectroscopy of polar diatomic molecules

A measurement of parity violation in the hyperfine structure of $^{138}$Ba$^{19}$F [E. Altunta\c{s} et al. Phys. Rev. Lett. 120, 142501 (2018)] is reinterpreted with electronic structure calculations in terms of beyond Standard Model vector boson mediated electron-nucleus interactions. Our results set constraints on previously unexplored, new boson mediated axial vector-vector nucleus-electron interactions. Similar bounds are obtained by analyzing the atomic parity violation experiment with $^{133}$Cs. Moreover, we show that future experiments with cold heavy diatomic molecules like $^{225}$RaF can improve the present sensitivity to axial vector-vector nucleus-electron and nucleon-nucleus interactions by up to five orders of magnitudes.