MHV Rules for Higgs Plus Multi-Gluon Amplitudes
- SLAC
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{sup 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 {le} 5) at tree level, in some cases yielding considerably shorter expressions.
- Research Organization:
- Stanford Linear Accelerator Center (SLAC), Menlo Park, CA
- Sponsoring Organization:
- SC
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 839591
- Report Number(s):
- SLAC-PUB-10839
- Country of Publication:
- United States
- Language:
- English
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