MHV Rules for Higgs Plus Multi-Gluon Amplitudes

TL;DR

This paper develops a new set of MHV rules for calculating Higgs boson plus multi-gluon scattering amplitudes using a generalized scalar graph approach, simplifying computations in the heavy top quark limit.

Contribution

It introduces MHV and anti-MHV vertices for Higgs plus gluons, extending the scalar graph method to non-supersymmetric one-loop amplitudes in the heavy top mass limit.

Findings

Reproduces known analytic formulas for Higgs + up to 5 gluons

Provides shorter, more efficient amplitude expressions

Extends MHV rules to non-supersymmetric Higgs-gluon interactions

Abstract

We use tree-level perturbation theory to show how non-supersymmetric one-loop scattering amplitudes for a Higgs boson plus an arbitrary number of partons can be constructed, in the limit of a heavy top quark, from a generalization of the scalar graph approach of Cachazo, Svrcek and Witten. The Higgs boson couples to gluons through a top quark loop which generates, for large top mass, a dimension-5 operator H tr G^2. This effective interaction leads to amplitudes which cannot be described by the standard MHV rules; for example, amplitudes where all of the gluons have positive helicity. We split the effective interaction into the sum of two terms, one holomorphic (selfdual) and one anti-holomorphic (anti-selfdual). The holomorphic interactions give a new set of MHV vertices -- identical in form to those of pure gauge theory, except for momentum conservation -- that can be combined with pure gauge theory MHV vertices to produce a tower of amplitudes with more than two negative helicities. Similarly, the anti-holomorphic interactions give anti-MHV vertices that can be combined with pure gauge theory anti-MHV vertices to produce a tower of amplitudes with more than two positive helicities. A Higgs boson amplitude is the sum of one MHV-tower amplitude and one anti-MHV-tower amplitude. We present all MHV-tower amplitudes with up to four negative-helicity gluons and any number of positive-helicity gluons (NNMHV). These rules reproduce all of the available analytic formulae for Higgs + n-gluon scattering (n<=5) at tree level, in some cases yielding considerably shorter expressions.