Sensitivity of the YbOH molecule to $\mathcal{P}$,$\mathcal{T}$-odd effects in the external electric field

Electron electric dipole moment (eEDM) search using lasercoolable triatomics like YbOH is one of the most sensitive probes for physics beyond the Standard Model. The eEDM-induced energy shift is proportional to polarization ($P$) of the molecule. Similarly to diatomics with $\Omega-$doubling structure it was assumed that for triatomics with $l-$doubling structure, related to the vibrational angular momentum, $P$ can easily be saturated to almost 100\% value with moderate external electric field. We developed the method for calculation of properties of triatomic molecules and applied it to calculation of $P$ of $^{174}$YbOH in the first excited $v=1$ bending mode. Calculations showed that the most of the levels reach less than 50\% efficiency. We showed that this fact is related to the Hund's case $b$ coupling scheme of YbOH. As coupling scheme (for $\Omega=1/2$ molecules) approaches $a$ (or $c$) case polarization increases up to 100\% value. Results of our calculations should be used for correct extracting of eEDM value from YbOH experiment and similar calculations are required for other molecules.