Higgs boson decay to top quarks atO(αs2)

Three-loop corrections to the scalar and pseudoscalar current correlator are calculated. By applying the large momentum, expansion mass terms up to order ${(m}^2{/q}^2{)}^4$ are evaluated analytically. As an application $O\left({\alpha }_s^2\right)$ corrections to the decay of a scalar and pseudoscalar Higgs boson into top quarks are considered. It is shown that for a Higgs mass not far above the $t\overline{t}$ threshold these higher order mass corrections are necessary to get reliable results.