Higgs boson decays to a fermion pair and a polarized $Z$ boson at NLO accuracy

Abstract: In this paper, we investigate the Higgs boson decay process $H\to f\bar{f}Z\to f\bar{f}\mu^-\mu^+$, where $f$ denotes any light fermions, at the next-to-leading order (NLO) accuracy. The calculation is performed within the framework of single-pole approximation, in which the contributions of different polarization states of the $Z$ boson are considered separately. Numerical results show that, by taking appropriate cut, the non-resonant background is negligible, and the NLO corrections are $1\%$--$4\%$ of the LO contributions. We also find that the inclusion of NLO corrections can greatly reduce the dependence on the electroweak coupling scheme, and enhance the prediction reliability. We formulate a method for the extraction of the pseudo-observable $\Gamma^{H\to ffZ}$ from the $f\bar{f}\mu^-\mu^+$ signal.