MHV rules for Higgs plus multi-gluon amplitudes

Dixon, L.J.; Glover, E.W.N.; Khoze, V.V.

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 mt, a dimension-5 operator Htr GμνGμν. 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.

Citation

Dixon, L., Glover, E., & Khoze, V. (2004). MHV rules for Higgs plus multi-gluon amplitudes. Journal of High Energy Physics, 2004(12), https://doi.org/10.1088/1126-6708/2004/12/015

• Journal Article Type: Article
• Publication Date: Dec 1, 2004
• Deposit Date: May 8, 2008
• Publicly Available Date: May 8, 2008
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2004
• Issue: 12
• DOI: https://doi.org/10.1088/1126-6708/2004/12/015
• Keywords: QCD, Higgs physics, Jets, Hadronic colliders.