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Quark-Gluon Antenna Functions from Neutralino Decay

A. Gehrmann--De Ridder, T. Gehrmann, E. W. N. Glover

TL;DR

The paper addresses the subtraction of infrared singularities in NNLO QCD jet observables by deriving quark-gluon antenna functions from an effective Lagrangian describing neutralino decay into a gluino and a gluon. It demonstrates that the infrared structure of these neutralino-decay matrix elements reproduces the known NLO and NNLO quark-gluon antenna behavior, including explicit integrated antenna pieces and their Catani/I^(1)/H^(2) pole structure. This provides a systematic, physically grounded route to all antenna functions from physical matrix elements and suggests extensions to gluon-gluon antennas via Higgs-like couplings and to production/scattering through analytic continuation. The results lay groundwork for analytic NNLO subtraction terms and broader applicability of antenna methods in high-precision QCD calculations.

Abstract

The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. One commonly used method at next-to-leading order (NLO) is based on the antenna factorization of colour-ordered matrix elements, and uses antenna functions to subtract the real radiation singularities. Up to now, NLO antenna functions could be derived in a systematic manner only for hard quark-antiquark pairs, while the gluon-gluon and quark-gluon antenna functions were constructed from their limiting behaviour. In this paper, we show that antenna functions for hard quark-gluon pairs can be systematically derived from an effective Lagrangian describing heavy neutralino decay. The infrared structure of the colour-ordered neutralino decay matrix elements at NLO and NNLO is shown to agree with the structure observed for parton radiation off a quark-gluon antenna.

Quark-Gluon Antenna Functions from Neutralino Decay

TL;DR

The paper addresses the subtraction of infrared singularities in NNLO QCD jet observables by deriving quark-gluon antenna functions from an effective Lagrangian describing neutralino decay into a gluino and a gluon. It demonstrates that the infrared structure of these neutralino-decay matrix elements reproduces the known NLO and NNLO quark-gluon antenna behavior, including explicit integrated antenna pieces and their Catani/I^(1)/H^(2) pole structure. This provides a systematic, physically grounded route to all antenna functions from physical matrix elements and suggests extensions to gluon-gluon antennas via Higgs-like couplings and to production/scattering through analytic continuation. The results lay groundwork for analytic NNLO subtraction terms and broader applicability of antenna methods in high-precision QCD calculations.

Abstract

The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. One commonly used method at next-to-leading order (NLO) is based on the antenna factorization of colour-ordered matrix elements, and uses antenna functions to subtract the real radiation singularities. Up to now, NLO antenna functions could be derived in a systematic manner only for hard quark-antiquark pairs, while the gluon-gluon and quark-gluon antenna functions were constructed from their limiting behaviour. In this paper, we show that antenna functions for hard quark-gluon pairs can be systematically derived from an effective Lagrangian describing heavy neutralino decay. The infrared structure of the colour-ordered neutralino decay matrix elements at NLO and NNLO is shown to agree with the structure observed for parton radiation off a quark-gluon antenna.

Paper Structure

This paper contains 6 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Effective Lagrangian and Feynman rules
  3. Colour-ordered amplitudes in neutralino decay
  4. NLO antenna functions
  5. Structure of NNLO antenna functions
  6. Conclusions and Outlook

Figures (2)

  • Figure 1: Colour flow contained in tree level decay $\tilde{\chi} \to \tilde{g} g$. Double (single) lines denote adjoint (fundamental) colour indices.
  • Figure 2: Colour flow contained in the colour ordered amplitude $M_{\tilde{g} g g g}^0 (p_1,p_i,p_j,p_k)$ contributing to the tree level decay $\tilde{\chi} \to \tilde{g} g gg$.