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A compact representation of the 2 photon 3 gluon amplitude

T. Binoth, J. Ph. Guillet, F. Mahmoudi

TL;DR

The paper computes the one-loop amplitude for γγggg → 0, a background contribution to Higgs searches at the LHC, by decomposing the helicity amplitudes and converting to a field-strength tensor basis organized by an irreducible function basis. This approach yields compact, numerically stable expressions with explicit Ward identities and Bose symmetry, avoiding complex phases in the final results. Two independent algebraic implementations validate the results, and the method is shown to be scalable to more complex multi-leg amplitudes. The work has direct relevance for Higgs-background modeling in γγ + jet channels and offers a robust framework for future amplitude calculations in collider phenomenology.

Abstract

A compact representation of the loop amplitude gamma gamma ggg -> 0 is presented. The result has been obtained by using helicity methods and sorting with respect to an irreducible function basis. We show how to convert spinor representations into a field strength representation of the amplitude. The amplitude defines a background contribution for Higgs boson searches at the LHC in the channel H -> gamma gamma + jet which was earlier extracted indirectly from the one-loop representation of the 5-gluon amplitude.

A compact representation of the 2 photon 3 gluon amplitude

TL;DR

The paper computes the one-loop amplitude for γγggg → 0, a background contribution to Higgs searches at the LHC, by decomposing the helicity amplitudes and converting to a field-strength tensor basis organized by an irreducible function basis. This approach yields compact, numerically stable expressions with explicit Ward identities and Bose symmetry, avoiding complex phases in the final results. Two independent algebraic implementations validate the results, and the method is shown to be scalable to more complex multi-leg amplitudes. The work has direct relevance for Higgs-background modeling in γγ + jet channels and offers a robust framework for future amplitude calculations in collider phenomenology.

Abstract

A compact representation of the loop amplitude gamma gamma ggg -> 0 is presented. The result has been obtained by using helicity methods and sorting with respect to an irreducible function basis. We show how to convert spinor representations into a field strength representation of the amplitude. The amplitude defines a background contribution for Higgs boson searches at the LHC in the channel H -> gamma gamma + jet which was earlier extracted indirectly from the one-loop representation of the 5-gluon amplitude.

Paper Structure

This paper contains 14 sections, 44 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Algebraic methods
  3. Preliminaries
  4. Spinor helicity methods
  5. Basic analytical structures
  6. Rules for field strength objects
  7. Result
  8. ${\cal A}^{+++++}$
  9. ${\cal A}^{-++++}$
  10. ${\cal A}^{++++-}$
  11. ${\cal A}^{--+++}$
  12. ${\cal A}^{+++--}$
  13. ${\cal A}^{-+++-}$
  14. Summary

Figures (2)

  • Figure 1: The two basic topologies of the $\gamma\gamma ggg$ amplitude. All the other graphs are obtained by reordering of photons and gluons.
  • Figure 2: The scalar graph topologies of the $\gamma\gamma ggg$ amplitude.