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AutoDipole - Automated generation of dipole subtraction terms -

K. Hasegawa, S. Moch, P. Uwer

TL;DR

AutoDipole automates the generation of Catani-Seymour dipole subtraction terms for NLO QCD by using a Mathematica-driven code generator that outputs optimized Fortran code interfacing with MadGraph/HELAS to evaluate color- and spin-correlated Born amplitudes. It supports massless and massive partons and provides automated checks of soft/collinear limits, along with extensive validation against existing results. The approach yields a modular, extensible framework capable of handling high-multiplicity final states and facilitating future extensions to NNLO, fragmentation, and BSM scenarios. The practical impact is a streamlined, reliable pipeline for NLO QCD calculations with robust IR subtraction, improving accuracy and efficiency for LHC phenomenology.

Abstract

We present an automated generation of the subtraction terms for next-to-leading order QCD calculations in the Catani-Seymour dipole formalism. For a given scattering process with n external particles our Mathematica package generates all dipole terms, allowing for both massless and massive dipoles. The numerical evaluation of the subtraction terms proceeds with MadGraph, which provides Fortran code for the necessary scattering amplitudes. Checks of the numerical stability are discussed.

AutoDipole - Automated generation of dipole subtraction terms -

TL;DR

AutoDipole automates the generation of Catani-Seymour dipole subtraction terms for NLO QCD by using a Mathematica-driven code generator that outputs optimized Fortran code interfacing with MadGraph/HELAS to evaluate color- and spin-correlated Born amplitudes. It supports massless and massive partons and provides automated checks of soft/collinear limits, along with extensive validation against existing results. The approach yields a modular, extensible framework capable of handling high-multiplicity final states and facilitating future extensions to NNLO, fragmentation, and BSM scenarios. The practical impact is a streamlined, reliable pipeline for NLO QCD calculations with robust IR subtraction, improving accuracy and efficiency for LHC phenomenology.

Abstract

We present an automated generation of the subtraction terms for next-to-leading order QCD calculations in the Catani-Seymour dipole formalism. For a given scattering process with n external particles our Mathematica package generates all dipole terms, allowing for both massless and massive dipoles. The numerical evaluation of the subtraction terms proceeds with MadGraph, which provides Fortran code for the necessary scattering amplitudes. Checks of the numerical stability are discussed.

Paper Structure

This paper contains 17 sections, 57 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Review of the Catani-Seymour subtraction formalism
  3. The AutoDipole package
  4. Structure of the code
  5. Algorithm of dipole generation
  6. The color linked Born amplitude squared
  7. Spin correlations for gluon emitters
  8. Checking the soft and collinear limits
  9. Running AutoDipole
  10. Install
  11. A short example
  12. General usage
  13. Examples
  14. Conclusion
  15. Creation order of subtraction terms
  16. ...and 2 more sections

Figures (4)

  • Figure 1: The directory structure of the AutoDipole package.
  • Figure 2: The flowchart of the execution of AutoDipole.
  • Figure 3: The four categories of dipoles (Dipole 1, ..., 4), the seven possible splittings and their order of creation in AutoDipole, see Table \ref{['tab:creation-order-dip']} for details.
  • Figure 4: The order of creation of the integrated dipoles in AutoDipole with insertion of the I-operator (left) and of the ${\hbox{\bf P}}$- and ${\hbox{\bf K}}$-operators (right), see Tables \ref{['tab:creation-order-I']} and \ref{['tab:creation-order-pandk']} for details.