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

TL;DR

This paper computes two-loop all-plus helicity amplitudes for a self-dual Higgs boson with gluons, using unitarity cuts and finite field methods, providing compact analytic expressions.

Contribution

It introduces a novel approach combining unitarity cuts and finite field tensor reduction to derive explicit two-loop amplitudes in the all-plus sector.

Findings

Explicit two-loop amplitudes expressed with polylogarithms and rational functions.

Method effectively handles rational ambiguities via finite field tensor reduction.

Results facilitate precise calculations in Higgs-gluon interactions.

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.