Enhanced parity and time-reversal-symmetry violation in diatomic molecules: LaO, LaS, and LuO

High-precision measurements of symmetry violations in molecules are a promising route to test the standard model of particle physics. In particular, the violation of parity $(P)$ and time-reversal $(T)$ symmetry is enhanced in the LaS, LaO, and LuO molecules due to the small energy differences between states of opposite parity (0.2 ${\mathrm{cm}}^{\ensuremath{-}1}$ or less) in the electronic ground state. We calculate the molecular enhancement for the relevant symmetry-violating interactions in these molecules, i.e., the $P,T$-violating electron electric dipole moment ${W}_{\mathrm{d}}$, scalar-pseudoscalar nucleon-electron interaction ${W}_{\mathrm{s}}$, and nuclear magnetic quadrupole moment ${W}_{\mathrm{M}}$, and for the nuclear-spin-dependent $P$-violating anapole moment ${W}_{\mathrm{A}}$. We use the relativistic four-component coupled-cluster method and perform a systematic study to estimate the associated uncertainties in our approach. We find that the individual contribution of each computational parameter to the total uncertainty in a system is approximately the same for all the calculated enhancement factors, summing up to a total uncertainty of $\ensuremath{\sim}6$%. Furthermore, we use simple nuclear models to estimate the magnitude of the anapole moment and the magnetic quadrupole moment, from which we calculate the matrix elements probed in experiments and the sensitivity to beyond-the -standard-model physics in terms of higher-energy $P,T$-violating coupling constants, respectively.