Three-jet cross sections to next-to-leading order

TL;DR

To address the need for precise predictions of three-jet production at next-to-leading order, the paper extends the subtraction method for infrared singularities by adopting angle and energy variables and a jet measurement function. It provides complete analytic results for soft and collinear integrals, and details how to organize real and virtual contributions so that all divergences cancel analytically, enabling efficient numerical implementation. The approach generalizes to n-jet production and applies to e+e and photon-hadron collisions, offering robust tools for precision QCD and alpha_s extraction. Overall, this work delivers a practical, general framework for NLO three-jet cross sections and enhances the reliability of hadronic jet phenomenology.

Abstract

One- and two-jet inclusive quantities in hadron collisions have already been calculated to next-to-leading order accuracy, using both the subtraction and the cone method. Since the one-loop corrections have recently been obtained for all five-parton amplitudes, three-jet inclusive quantities can also be predicted to next-to-leading order. The subtraction method presented in the literature is based on a systematic use of boost-invariant kinematical variables, and therefore its application to three-jet production is quite cumbersome. In this paper we re-analyze the subtraction method and point out the advantage of using angle and energy variables. This leads to simpler results and it has complete generality, extending its validity to $n$-jet production. The formalism is also applicable to $n$-jet production in $e^+e^-$ annihilation and in photon-hadron collisions. All the analytical results necessary to construct an efficient numerical program for next-to-leading order three-jet inclusive quantities in hadroproduction are given explicitly. As new analytical result, we also report the collinear limits of all the two-to-four processes.