Antenna subtraction with hadronic initial states

Abstract

The antenna subtraction method for the computation of higher order corrections to jet observables and exclusive cross sections at collider experiments is extended to include hadronic initial states. In addition to the already known antenna subtraction with both radiators in the final state (final-final antennae), we introduce antenna subtractions with one or two radiators in the initial state (initial-final or initial-initial antennae). For those, we derive the phase space factorization and discuss the allowed phase space mappings at NLO and NNLO. We present integrated forms for all antenna functions relevant to NLO calculations, and describe the construction of the full antenna subtraction terms at NLO on two examples. The extension of the formalism to NNLO is outlined.

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

“…Likewise, the jet algorithm acts on the (m + 1)-final state momenta that remain after the mapping has been applied. In this case, the phase space in (2.22) can be factorised into the convolution of an (m + 1)-particle phase space, involving only the redefined momenta, with a 2-particle phase space [71]. For the special case i = 1, it reads, 25) where C(ǫ) is given in (2.10).…”

“…For the initial-initial configuration the phase space in (2.28) factorises into the convolution of an (m + 1)-particle phase space, involving only redefined momenta, with the phase space of parton j [71] so that when i = 1 and k = 2,…”

“…The formalism has been fully worked out for initial state hadrons at NLO [71] and further developed at NNLO [72][73][74]. Within this method, the subtraction terms are constructed from so-called antenna functions which describe all unresolved partonic radiation (soft and collinear) between a hard pair of radiator partons.…”