Axion-mediated electron-nucleus and electron-electron interactions in the barium monofluoride molecule

The effects induced by the time-reversal ($\mathcal{T}$) and spatial parity ($\mathcal{P}$)-violating electron-nucleus and electron-electron interactions mediated by the axionlike particles (ALPs) in the BaF molecule were estimated. Molecular parameters characterizing these interactions were calculated across a wide range of ALP masses. In the case of the electron-nuclear interaction, the effect of the extended nucleus was studied and shown to be significant for heavy ALPs. Based on the calculated molecular parameters, we obtained a link between the $\mathcal{T},\mathcal{P}$-violating energy shift which can be measured in the ongoing experiment designed to search for the electron electric dipole moment using the BaF molecule (A. Boeschoten et al., arXiV:2303.06402) and the products of coupling constants of the ALP-electron or ALP-electron and ALP-nucleus interactions.

Figure 1

Derived constraints on (a) $|{\overline{g}}_N^s{g}_e^p|$ and on (b) $|g_e^s{g}_e^p|$ products (dashed green line and blue region) corresponding to the $e\mathrm{EDM}$ limitation $|d_{\mathrm{e}}|=5.0\times {10}^{-30}e\mathrm{cm}$ expected in the planned experiment on BaF [12]. At the graph scale, the constraints almost coincide with the current limitations on $|{\overline{g}}_N^s{g}_e^p|$ and $|g_e^s{g}_e^p|$ obtained in the ${\mathrm{HfF}}^{+}$ experiment [10, 32]. Constraint on $|{\overline{g}}_N^s{g}_e^p|$ from macroscopic experiments (black line and violet region) were compiled in Ref. [28] using the results of Refs. [59, 61, 62, 63, 64, 65, 66]. The macroscopic constraints of $|g_e^s{g}_e^p|$ were estimated in Ref. [28] by reevaluating the published constraints on $|{\overline{g}}_N^s{g}_e^p|$.