Antenna subtraction for gluon scattering at NNLO

Abstract

We use the antenna subtraction method to isolate the double real radiation infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. The antenna subtraction framework has been successfully applied to the calculation of NNLO corrections to the 3-jet cross section and related event shape distributions in electron-positron annihilation. Here we consider processes with two coloured particles in the initial state, and in particular two-jet production at hadron colliders such as the Large Hadron Collider (LHC). We construct a subtraction term that describes the single and double unresolved contributions from the six-gluon tree-level process using antenna functions with initial state partons and show numerically that the subtraction term correctly approximates the matrix elements in the various single and double unresolved configurations.

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

“…The diagrams belonging to the sets ii) and iii) form part of the NLO corrections to top-pair-plus-jet production and have been calculated by several groups [49][50][51][52]. Aside from the calculation of the required Feynman diagrams, a full NNLO calculation of the top-quark pair production cross section is particularly challenging because it entails the development of a NNLO subtraction method, which could be used in processes with massive partons [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69].…”

“…Their implementation requires the application of a NNLO subtraction method. The methods presently available [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67] do not provide yet the full counterterms for a 2 → 2 hadronic process involving massive partons. Two subtraction methods for the NNLO calculation of the top-quark pair production cross section were outlined recently [68,69].…”

Real-virtual corrections for gluon scattering at NNLO

“…The key property of J (n) m is that the jet observable is collinear and infrared safe. In a previous paper [75], we have discussed the NNLO contribution coming from processes where two additional partons are radiated -the double real contribution dσ RR N N LO and its subtraction term dσ S N N LO . dσ RR N N LO involves the (m + 4)-parton process at tree level and is given by,…”

“…Most antennae fit into this class including, for example, the quark-antiquark antenna A 0 4 , the quark-gluon subantenna D 0 4,a [58] and the gluon-gluon subantenna F 0 4,a [75]. Upon integration, the X 0 3 × X 0 3 terms produce integrated antenna that cancel against the explicit poles present in X 1 3 that will be discussed in Section 2.2.2.…”

“…Suppressing the labels of the partons in the initial state of the hard scattering, the general form for the subtraction terms for an m-particle final state at NNLO is given by [21] Note that because integration of the subtraction term dσ S N N LO gives contributions to both the (m+1)-and m-parton final states, we have explicitly decomposed the integrated double real subtraction term into a piece that is integrated over one unresolved particle phase space and a piece that is integrated over the phase space of two unresolved particles, In a previous paper [75], the subtraction term dσ S N N LO corresponding to the leading colour pure gluon contribution to dijet production at hadron colliders was derived. The subtraction term was shown to reproduce the singular behaviour present in dσ RR N N LO in all of the single and double unresolved limits.…”