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Search for parity and time reversal violating effects in HgH: Relativistic coupled-cluster study

The high effective electric field ($E_\mathrm{eff}$) experienced by the unpaired electron in an atom or a molecule is one of the key ingredients in the success of electron electric dipole moment (eEDM) experiment and its precise calculation require a very accurate theory. We, therefore, employed the Z-vector method in the relativistic coupled-cluster framework and found that HgH has a very large $E_\mathrm{eff}$ value (123.2 GV/cm) which makes it a potential candidate for the next generation eEDM experiment. Our study also reveals that it has a large scalar-pseudoscalar ${\mathcal{P,T}}$-violating interaction constant, $W_\mathrm{s}$ = 284.2 kHz. To judge the accuracy of the obtained results we have calculated parallel and perpendicular magnetic HFS constants and compared with the available experimental values. The results of our calculation are found to be in nice agreement with the experimental values. Therefore, by looking at the HFS results we can say that both $E_\mathrm{eff}$ and $W_\mathrm{s}$ values are also very accurate. Further, We have derived the relationship between these quantities and the ratio which will help to get model independent value of eEDM and S-PS interaction constant.