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One-loop helicity amplitudes for H -> gluons: the all-minus configuration

S. D. Badger, E. W. N. Glover

TL;DR

The paper tackles the one-loop Higgs-to-gluons amplitude in the large top-mass limit for the all-minus helicity configuration. It employs twistor-inspired, on-shell/MHV methods and a selfdual/anti-selfdual decomposition via the complex field φ to separate and simplify SD/ASD contributions, enabling a closed-form cut-constructible part and a rational part for four gluons. The cut-constructible result is expressed in terms of scalar integral functions (Tri, F^{1m}, F^{2me}) and the tree-level φ-amplitude, with the pure φ† CC contribution vanishing; the rational part is computed explicitly for four gluons and fixed by collinear behavior. Consistency checks include infrared pole structure, collinear factorization, and soft-Higgs limits, demonstrating the robustness of the on-shell approach and outlining how to extend to arbitrary multiplicities and other helicity configurations.

Abstract

We use twistor inspired rules to compute the one-loop amplitude for a Higgs boson coupling to any number of negative helicity gluons in the large top mass limit.

One-loop helicity amplitudes for H -> gluons: the all-minus configuration

TL;DR

The paper tackles the one-loop Higgs-to-gluons amplitude in the large top-mass limit for the all-minus helicity configuration. It employs twistor-inspired, on-shell/MHV methods and a selfdual/anti-selfdual decomposition via the complex field φ to separate and simplify SD/ASD contributions, enabling a closed-form cut-constructible part and a rational part for four gluons. The cut-constructible result is expressed in terms of scalar integral functions (Tri, F^{1m}, F^{2me}) and the tree-level φ-amplitude, with the pure φ† CC contribution vanishing; the rational part is computed explicitly for four gluons and fixed by collinear behavior. Consistency checks include infrared pole structure, collinear factorization, and soft-Higgs limits, demonstrating the robustness of the on-shell approach and outlining how to extend to arbitrary multiplicities and other helicity configurations.

Abstract

We use twistor inspired rules to compute the one-loop amplitude for a Higgs boson coupling to any number of negative helicity gluons in the large top mass limit.

Paper Structure

This paper contains 12 sections, 29 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Higgs Model
  3. Tree-level results
  4. The one-loop all-minus amplitude
  5. The cut constructible contribution
  6. The non cut-constructible contribution
  7. Checks of the result
  8. Infrared poles
  9. Collinear limit
  10. Soft Higgs limit
  11. Outlook
  12. Acknowledgements

Figures (3)

  • Figure 1: The three classes of diagram contributing to the cut constructible part of the one-loop all-minus amplitude $A^{(1)}(\phi;1^-,\ldots,n^-)$.
  • Figure 2: Schematic of contribution from Fig 1(a).
  • Figure 3: Schematic of the collinear limit of the all-minus one-loop amplitude. Open circles represent loops, while shaded circles represent trees.