MHV Rules for Higgs Plus Multi-Parton Amplitudes

TL;DR

This work extends the CSW/MHV framework to Higgs boson processes with arbitrary numbers of gluons and quarks by leveraging a dimension-5 HGG effective operator and splitting the interaction into self-dual and anti-self-dual parts. It introduces two helicity towers (phi with MHV vertices and phi-dagger with anti-MHV vertices) and derives new Higgs–fermion MHV/NMHV vertices via pseudo-supersymmetry, enabling compact analytic expressions for Higgs plus multi-parton amplitudes. The authors validate their formulas against known results for up to five partons and provide a recursive formulation to construct non-MHV amplitudes with fermions and scalars, including explicit NN-MHV cases. These results offer efficient, compact tree-level predictions relevant for Higgs phenomenology at the LHC in the large m_t limit, and they establish a scalable approach to Higgs + multi-parton amplitudes through recursion and double-tower MHV structures.

Abstract

We present MHV-rules for constructing perturbative amplitudes for a Higgs boson and an arbitrary number of partons. We give explicit expressions for amplitudes involving a Higgs and three negative helicity partons and any number of positive helicity partons - the NMHV amplitudes. We also present a recursive formulation of MHV rules that incorporates the Higgs, quarks and gluons. The recursion relations are valid for all non-MHV amplitudes. The general results agree numerically with all of the available Higgs + n-parton amplitudes and in some cases provide considerably shorter expressions.

Figures (11)

• Figure 1: The structure of Higgs plus multi-gluon amplitudes obtained by combining the MHV tower for $\phi+n$ gluons and the anti-MHV tower of $\phi^\dagger +n$ gluon amplitudes.
• Figure 2: The structure of Higgs plus multi-gluon plus quark-antiquark pair amplitudes obtained by combining the MHV tower for $\phi+q\bar{q}+n$ gluons and the anti-MHV tower of $\phi^\dagger +q\bar{q}+n$ gluon amplitudes.
• Figure 3: The structure of Higgs plus multi-gluon plus two quark-antiquark pair amplitudes obtained by combining the MHV tower for $\phi+q\bar{q}+Q\bar{Q} +n$ gluons and the anti-MHV tower of $\phi^\dagger +q\bar{q}+Q\bar{Q}+n$ gluon amplitudes.
• Figure 4: MHV vertices for $\phi$ and one quark pair. The quark line is represented by the red dot-dashed line where $\pm\lambda_1$ are the helicities of the quark and anti-quark. The negative helicity gluon is represented as a solid black line.
• Figure 5: Skeleton diagram showing the labelling of the positive helicity gluons in NMHV amplitudes. The gluons are shown as dotted lines with labels showing the bounding $g^+$ lines in each MHV vertex.