Two-loop five-point massless QCD amplitudes within the integration-by-parts approach

Herschel A Chawdhry,Matthew A Lim,Alexander Mitov

doi:10.1103/physrevd.99.076011

Abstract

We solve the integration-by-parts (IBP) identities needed for the computation of any planar two-loop five-point massless amplitude in QCD. We also derive some new results for the most complicated non-planar topology with irreducible numerators of power as high as six. We do this by applying a new strategy for solving the IBP identities which scales better for problems with a large number of scales and/or master integrals. Our results are a proof of principle that the remaining non-planar contributions for all two-loop five-point massless QCD amplitudes can be computed in analytic form.

Highlights

Gauge theories, whose predictivity is dependent on calculations of scattering amplitudes at higher perturbative orders, have been hugely successful in describing natural phenomena
The focus of this work is on perturbative quantum chromodynamics (QCD) which can be viewed as a prototype for a generic unbroken nonsupersymmetric gauge theory
We demonstrate that supplementing this strategy with the standard Laporta algorithm is sufficient to solve the IBP identities needed to compute the complete set of planar two-loop five-point amplitudes in massless QCD in analytic form

Summary

Introduction

Gauge theories, whose predictivity is dependent on calculations of scattering amplitudes at higher perturbative orders, have been hugely successful in describing natural phenomena. The focus of this work is on perturbative quantum chromodynamics (QCD) which can be viewed as a prototype for a generic unbroken nonsupersymmetric gauge theory. QCD is special because multiloop QCD amplitudes are the backbone of theoretical predictions for precision collider observables like the ones measured at the Large Hadron Collider. Four-point massless amplitudes are fully known through two loops (partially three) [12,13,14,15,16,17] while five-point ones are fully known at one loop (partly two [18,19,20,21,22,23,24,25,26]). The ultimate goal of this work is to extend the two-loop frontier to the complete set of five-point massless QCD amplitudes

Objectives

Results

Conclusion