Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints

Abstract

We present the two-loop amplitudes for a self-dual Higgs boson with up to four positive helicity gluons in the heavy top-quark limit. Because the tree amplitudes in the all-plus sector vanish, we can construct simple representations of the polylogarithmic parts of the two-loop amplitudes using four-dimensional unitarity cuts into rational one-loop and tree amplitudes. The remaining rational function ambiguity is extracted from a tensor integral reduction over finite fields. The final expressions are presented using polylogarithms up to weight two and compact rational functions of spinor-helicity products.

Comments: 31 pages, 7 figures, 1 table, ancillaries at https://zenodo.org/records/17592605 -- v2: publish v2