Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering

TL;DR

This paper computes two-loop QCD helicity amplitudes for (2+1)-jet production in deep inelastic scattering, providing analytic expressions and numerical evaluation methods crucial for precision collider physics.

Contribution

It derives the two-loop helicity amplitudes for key partonic processes in deep inelastic scattering, extending known results via analytic continuation and detailed harmonic polylogarithm expressions.

Findings

Analytic expressions for finite parts of amplitudes in terms of harmonic polylogarithms.

Explicit variable transformations for numerical evaluation in different kinematic regions.

Separation of infrared divergent and finite contributions using Catani's formula.

Abstract

We derive the two-loop QCD helicity amplitudes for the processes $l q \to l qg$ ($l \bar q \to l \bar q g$) and $l g \to l q\bar q$, which are the partonic reactions yielding $(2+1)$-jet final states in deep inelastic lepton nucleon scattering. The amplitudes are obtained by analytic continuation of the known helicity amplitudes for $e^+e^- \to q\bar q g$. We separate the infrared divergent and finite parts of the amplitudes using Catani's infrared factorization formula. The analytic results for the finite parts of the amplitudes are expressed in terms of one- and two-dimensional harmonic polylogarithms. To evaluate these functions numerically, we list in detail the non-trivial (and kinematic region dependent) variable transformations one needs to perform.