QCD corrections to decay distributions of neutral Higgs bosons with (in)definiteCPparity

We compute the order ${\alpha }_s$ QCD corrections to the density matrix for the decay of a neutral Higgs boson $\phi$ with (in)definite $\mathrm{CP}$ parity into a quark-antiquark pair and the QED corrections for the decay into a pair of charged leptons. We classify and calculate single spin asymmetries and spin-spin correlations which are generated by the scalar and pseudoscalar Yukawa couplings. These spin effects can be traced in $\phi \to {\tau }^{-}{\tau }^{+}$ and, for heavy Higgs bosons, in $\phi \to t\overline{t}$. We also calculate resulting correlations among the final states and estimate, for the respective decay modes, the number of events needed to measure the Yukawa couplings with these correlations at the 3$\sigma$ level.