We report the results of our theoretical study and analysis of earlier experimental data for the g-factor tensor components of the ground $^2Pi_{1/2}$ state of free PbF radical. The values obtained both within the relativistic coupled-cluster method
combined with the generalized relativistic effective core potential approach and with our fit of the experimental data from [R.J. Mawhorter, B.S. Murphy, A.L. Baum, T.J. Sears, T. Yang, P.M. Rupasinghe, C.P. McRaven, N.E. Shafer-Ray, L.D. Alphei, J.-U. Grabow, Phys. Rev. A 84, 022508 (2011); A. Baum, B.S. thesis, Pomona College, 2011]. The obtained results agree very well with each other but contradict the previous fit performed in the cited works. Our final prediction for g-factors is $G_{parallel}= 0.081(5)$, $G_{perp}=-0.27(1)$.
The current limit on the electrons electric dipole moment, $|d_mathrm{e}|<8.7times 10^{-29} e {cdotp} {rm cm}$ (90% confidence), was set using the molecule thorium monoxide (ThO) in the $J=1$ rotational level of its $H ^3Delta_1$ electronic state [Sc
ience $bf 343$, 269 (2014)]. This state in ThO is very robust against systematic errors related to magnetic fields or geometric phases, due in part to its $Omega$-doublet structure. These systematics can be further suppressed by operating the experiment under conditions where the $g$-factor difference between the $Omega$-doublets is minimized. We consider the $g$-factors of the ThO $H^3Delta_1$ state both experimentally and theoretically, including dependence on $Omega$-doublets, rotational level, and external electric field. The calculated and measured values are in good agreement. We find that the $g$-factor difference between $Omega$-doublets is smaller in $J=2$ than in $J=1$, and reaches zero at an experimentally accessible electric field. This means that the $H,J=2$ state should be even more robust against a number of systematic errors compared to $H,J=1$.
