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Electric dipole moment of $^{225}$Ra due to P- and T-violating weak interactions

We report rigorous calculations of electric dipole moment (EDM) in $^{225}$Ra due to parity and time-reversal violating tensor-pseudotensor (T-PT) and nuclear Schiff moment (NSM) interactions between the electrons and nucleus by employing the relativistic all order coupled-cluster (RCC) methods at various levels of approximation. The most accurate EDM ($d_A$) results are obtained as $d_A=-10.04\times 10^{-20} C_T <σ_n>|e|cm$ and $d_A^{NSM}=-6.79 \times 10^{-17} S (|e|fm^3)^{-1} |e|cm$ with $C_T$ and $S$ are the T-PT coupling constant and NSM respectively. Due to exhaustive treatment of the electron correlation effects in these calculations, the EDM results for the corresponding T-PT and NSM interactions reduce by about 45\% and 23\%, respectively, from the previously known values. Nonetheless they are still found to be 2-3 times larger than the $^{199}$Hg results. Validity of the RCC results are countenanced by comparing our calculations at the zeroth order Dirac-Fock method and all order random-phase approximation with the other groups. In view of the current experimental progress in the $^{225}$Ra EDM measurement, our high accuracy calculations are very useful to yield limits on $C_T$ and $S$ in this atom. Thusly, it is possible to realize more accurate limits on the electron-quark T-PT interaction and $θ_{QCD}$ parameter of particle physics in future.