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Multi-parton Cross Sections at Hadron Colliders

Costas G. Papadopoulos, Malgorzata Worek

TL;DR

The paper develops an efficient, leading-order framework for multi-parton cross sections at hadron colliders by combining Dyson-Schwinger recursion for helicity amplitudes with Monte Carlo colour summation in the colour-flow basis. It demonstrates that the computational cost scales as $3^n$ instead of the factorial growth of Feynman-diagram methods, and validates the approach with extensive numerical results at LHC energies, showing fast performance and accurate cross sections and distributions. The methodology yields colour-flow information compatible with parton showers, enabling practical integration with shower/hadronization codes. This work significantly improves the tractability of high-multiplicity final states in QCD and related processes at hadron colliders.

Abstract

We present an alternative method to calculate cross sections for multi-parton scattering processes in the Standard Model at leading order. The helicity amplitudes are computed using recursion relations in the number of particles, based on Dyson-Schwinger equations whereas the summation over colour and helicity configurations is performed by Monte Carlo methods. The computational cost of our algorithm grows asymptotically as 3^n, where n is the number of particles involved in the process, as opposed to the n!-growth of the Feynman diagram approach. Typical results for the total cross section, differential distributions of invariant masses and transverse momenta of partons are presented and cross checked by explicit summation over colours.

Multi-parton Cross Sections at Hadron Colliders

TL;DR

The paper develops an efficient, leading-order framework for multi-parton cross sections at hadron colliders by combining Dyson-Schwinger recursion for helicity amplitudes with Monte Carlo colour summation in the colour-flow basis. It demonstrates that the computational cost scales as instead of the factorial growth of Feynman-diagram methods, and validates the approach with extensive numerical results at LHC energies, showing fast performance and accurate cross sections and distributions. The methodology yields colour-flow information compatible with parton showers, enabling practical integration with shower/hadronization codes. This work significantly improves the tractability of high-multiplicity final states in QCD and related processes at hadron colliders.

Abstract

We present an alternative method to calculate cross sections for multi-parton scattering processes in the Standard Model at leading order. The helicity amplitudes are computed using recursion relations in the number of particles, based on Dyson-Schwinger equations whereas the summation over colour and helicity configurations is performed by Monte Carlo methods. The computational cost of our algorithm grows asymptotically as 3^n, where n is the number of particles involved in the process, as opposed to the n!-growth of the Feynman diagram approach. Typical results for the total cross section, differential distributions of invariant masses and transverse momenta of partons are presented and cross checked by explicit summation over colours.

Paper Structure

This paper contains 6 sections, 89 equations, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Dual amplitudes and colour decomposition
  3. The colour flow decomposition
  4. Dyson-Schwinger recursion relations
  5. Organisation of the calculation
  6. Numerical Results

Figures (11)

  • Figure 1: Colour flows for the three gluon vertex.
  • Figure 2: Colour flows for the four gluon vertex.
  • Figure 3: Colour flows for the $q\bar{q}g$ vertex.
  • Figure 4: Recursive equation for an off mass shell gluon of momentum P.
  • Figure 5: Recursive equation for an off mass shell quark of momentum P.
  • ...and 6 more figures