Infrared Structure of $e^+e^- \to 2$ jets at NNLO

TL;DR

This paper develops and analytically analyzes an NNLO subtraction framework for two-jet production in $e^+e^-$ annihilation, addressing double real and single real radiation with subtraction terms tied to full four-parton and one-loop three-parton matrix elements. By decomposing NNLO contributions into two-, three-, and four-parton final states, it derives and integrates the corresponding infrared subtraction terms, and matches the pole structure to Catani's infrared factorization formula along with the one-loop soft gluon current. The authors demonstrate explicit cancellation of all infrared poles across all partonic channels and recover the known NNLO correction to the hadronic $R$-ratio, thus validating the subtraction scheme and its analytic master-integral backbone. The work provides key insights and a practical route toward general NNLO jet calculations and subtraction formalisms applicable to higher jet multiplicities and different collider environments.

Abstract

The production of two jets is the simplest exclusive quantum chromodynamics process in electron-positron annihilation. Using this process, we examine the structure of next-to-next-to-leading order (NNLO) corrections to jet production observables. We derive a subtraction formalism including double real radiation at tree level and single real radiation at one loop. For two-jet production, these subtraction terms coincide with the full matrix elements, thus highlighting the phase space structure of the subtraction procedure. We then analytically compute the infrared singularities arising from each partonic channel. For the purely virtual (two-parton) NNLO corrections, these take the well known form predicted by Catani's infrared factorization formula. We demonstrate that individual terms in the infrared factorization formula can be identified with infrared singular terms from three- and four-parton final states, leaving only single poles and a contribution from the one-loop soft gluon current, which subsequently cancels between the three- and four-parton final states. Summing over all different final states, we observe an explicit cancellation of all infrared poles and recover the known two-loop correction to the hadronic $R$-ratio.