High-precision tests of fundamental symmetries are looking for the parity- ($\mathcal{P}$), time-reversal- ($\mathcal{T}$) violating electric dipole moment of the electron (eEDM) as proof of physics beyond the Standard Model. Particularly, in polyatomic molecules, the complex vibrational and rotational structure gives the possibility to reach high enhancement of the $\mathcal{P},\mathcal{T}$-odd effects in moderate electric fields, and with the possibility of increasing the statistical sensitivity by using laser cooling. In this work, we calculate the $\mathcal{P},\mathcal{T}$-odd molecular enhancement factor of the eEDM ($W_{\mathrm{d}}$) and of the scalar-pseudoscalar interaction ($W_{\mathrm{s}}$) necessary for the interpretation of future experiments on the promising candidates ${\mathrm{BaCH}}_3$ and ${\mathrm{YbCH}}_3$. We employ high-accuracy relativistic coupled cluster methods and systematically evaluate the uncertainties of our computational approach. Compared to other Ba- and Yb-containing molecules, ${\mathrm{BaCH}}_3$ and ${\mathrm{YbCH}}_3$ exhibit larger $W_{\mathrm{d}}$ and $W_{\mathrm{s}}$ associated to the increased covalent character of the $M$–C bond. The calculated values are $3.22\pm 0.12\times {10}^{24}\frac{h\text{Hz}}{e\text{cm}}$ and $13.80\pm 0.35\times {10}^{24}\frac{h\text{Hz}}{e\text{cm}}$ for $W_{\mathrm{d}}$, and $8.42\pm 0.29h\mathrm{kHz}$ and $50.16\pm 1.27h\mathrm{kHz}$ for $W_{\mathrm{s}}$, in ${\mathrm{BaCH}}_3$ and ${\mathrm{YbCH}}_3$, respectively. The robust, accurate, and cost-effective computational scheme reported in this work makes our results suitable for extracting the relevant fundamental properties from future measurements and also can be used to explore other polyatomic molecules sensitive to various violations of fundamental symmetries.

• Received 8 August 2022
• Accepted 1 November 2022

DOI:https://doi.org/10.1103/PhysRevA.106.052811