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Towards LHC phenomenology at the loop level: A new method for one-loop amplitudes

T. Binoth, M. Ciccolini, G. Heinrich

TL;DR

The paper addresses the challenge of incorporating one-loop corrections for multi-particle final states in LHC phenomenology by introducing a semi-numerical reduction scheme. It combines an analytic tensor-reduction framework with a robust numerical evaluation of basis integrals via sector decomposition and contour deformation to handle problematic phase-space regions, while cleanly isolating infrared poles. The approach yields stable, compact results for complex processes, demonstrated on gg -> W*W* backgrounds and gg -> gamma gamma g amplitudes, illustrating improved reliability for NLO predictions in high-multiplicity final states. This methodology enhances the practicality of precise LHC calculations by balancing analytical control with numerical stability across broad kinematic regimes.

Abstract

A precise understanding of LHC phenomenology requires the inclusion of one-loop corrections for multi-particle final states. In this talk we describe a semi-numerical method to compute one-loop amplitudes with many external particles and present first applications.

Towards LHC phenomenology at the loop level: A new method for one-loop amplitudes

TL;DR

The paper addresses the challenge of incorporating one-loop corrections for multi-particle final states in LHC phenomenology by introducing a semi-numerical reduction scheme. It combines an analytic tensor-reduction framework with a robust numerical evaluation of basis integrals via sector decomposition and contour deformation to handle problematic phase-space regions, while cleanly isolating infrared poles. The approach yields stable, compact results for complex processes, demonstrated on gg -> W*W* backgrounds and gg -> gamma gamma g amplitudes, illustrating improved reliability for NLO predictions in high-multiplicity final states. This methodology enhances the practicality of precise LHC calculations by balancing analytical control with numerical stability across broad kinematic regimes.

Abstract

A precise understanding of LHC phenomenology requires the inclusion of one-loop corrections for multi-particle final states. In this talk we describe a semi-numerical method to compute one-loop amplitudes with many external particles and present first applications.

Paper Structure

This paper contains 5 sections, 16 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Reduction formalism
  3. Numerical evaluation of basis integrals
  4. Applications
  5. Summary

Figures (2)

  • Figure 1: Schematical evaluation of basic box functions. $\Lambda$ is a user-defined parameter serving as a switch between analytic/numerical representations.
  • Figure 2: Invariant mass distribution of the charged lepton pair for $gg\to W^*W^*\to l\bar{\nu}\,\bar{l}'\nu'$. The two sets of curves are the LHC prediction with (lower) and without (upper) standard cuts. The effect of the third generation massive quark loop leads to a slight enhancement (full) compared to the case with two massless generations (dashed). For parameter choices see Binoth:2005ua.