Three-loop O(αs2GFMt2) corrections to Higgs production and decay at e+e− colliders Original Research Article

We evaluate the next-to-leading-order QCD corrections of O(αs2GFMt2) to the Standard-Model ℓ+ℓ−H, ZZH, and W+W−H couplings in the heavy-top-quark limit. Exploiting these results together with knowledge of Δπ to the same order, we analyze a variety of production and decay processes of low-mass Higgs bosons at e+e− colliders. Specifically, we consider H → ℓ+ℓ−, H → ℓ+ℓ−ℓ′+ℓ′−, e+e− → ZH, Z → ffH, and e+e− → ffH, with f = ℓ, ν. We work in the electroweak on-shell scheme formulated with GF and employ both the on-shell and MS definitions of the top-quark mass in QCD. As expected, the scheme and scale dependences are greatly reduced when the next-to-leading-order corrections are taken into account. In the on-shell scheme of top-quark mass renormalization, the O(αs2GFMt2) corrections act in the same direction as the O(αsGFMt2) ones and further increase the screening of the O(GFMt2) terms. The coefficients of (αs/π)2 range from −6.847 for the ZZH coupling to −16.201 for the ℓ+ℓ−H coupling. This is in line with the value −14.594 recently found for Δπ.