Theoretical study of heavy-atom molecules to search for physics beyond the Standard model

The goal of the report is to review our latest studies for heavy-atom diatomics - ThO, RaO, RaF, PbF - which are of practical interest to search the T, P-odd effects. Particular attention is devoted to the $H^{3}\Delta_{1\, }$ state of ThO [1, 2]. Combination of the spin precession measurement of ThO [3] with the calculated E$_{eff}$ (ThO) [1] leads to the most rigid limit on $e$EDM:, \textbar d$_{e}$\textbar \textless 8.7 $\times$ 10$^{-29}$e$\cdot$cm. This is more than one order of magnitude better than other limits obtained. The knowledge of the g-factor dependence on electric fields is important for understanding possible systematic effects. Our study of the g-factors for $H^{3}\Delta_{1\, }$has shown that the J $=$ 2 rotational state should be even more robust against a number of systematic errors compared to J $=$ 1 [2]. [1] L. V. Skripnikov, A. N. Petrov, and A. V. Titov, JCP Communication, \textbf{139}, 221103 (2013) [2] A.N. Petrov, L.V. Skripnikov, A.V. Titov, N.R. Hutzler, P.W. Hess, \quad B.R. O'Leary, B. Spaun, D. DeMille, G. Gabrielse, and J.M. Doyle, \textit{Phys. Rev. A} \textbf{89}, 062505 (2014) [3] J. Baron, W. C. Campbell, D. DeMille, \textit{et al.} (ACME Collab.), \textit{Science} \textbf{343}, 269 (2014)