The infrared behavior of one-loop gluon amplitudes at next-to-next-to-leading order

Abstract

For the case of n-jet production at next-to-next-to-leading order in the QCD coupling, in the infrared divergent corners of phase space where particles are collinear or soft, one must evaluate (n + 1)-parton final-state one-loop amplitudes through O(ǫ 2 ), where ǫ is the dimensional regularization parameter. For the case of gluons, we present to all orders in ǫ the required universal functions which describe the behavior of one-loop amplitudes in the soft and collinear regions of phase space. An explicit example is discussed for three-parton production in multi-Regge kinematics that has applications to the next-to-leading logarithmic corrections to the BFKL equation.

Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO

“…At the same order, one-loop corrections to simple collinear [38] and simple soft [14] emissions need to be accounted for. The behaviour in all these limits is understood in detail, and served as a construction principle for subtraction methods at NNLO [15][16][17].…”

One-loop splitting amplitudes in gauge theory

“…The explicit forms of the splitting amplitudes at one-loop through O(ǫ 0 ) (in dimensional regularization, with D = 4 − 2ǫ) have previously been extracted by taking the collinear limit explicitly in various five-point amplitudes [5,6], or from an analysis of one-loop integrals [7]. In addition, Bern, Del Duca, and Schmidt [8] have recently given an expression for the gluon splitting amplitude to all orders in the dimensional regulator ǫ.…”

A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission

“…(2.14) remains valid, with the same expansion parameter, no matter in which RS the bare amplitudes are computed if we perform the substitution [12] β The IR part of the RS dependence can be decomposed into universal finite terms and non-universal contributions at O(ε) [14]. The finite terms are completely factorized, 17) while the O(ε) contributions do not contribute to dσ NNLO m+1 in the four-dimensional limit. The transition coefficients that relate the amplitudes in the RS's depend only on the flavour of the external partons and were first computed in ref.…”