Double virtual corrections for gluon scattering at NNLO

Abstract

We use the antenna subtraction method to isolate the double virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In previous papers, we derived the subtraction terms that rendered (a) the double real radiation tree-level process finite in the single and double unresolved regions of phase space and (b) the mixed single real radiation one-loop process both finite and well behaved in the unresolved regions of phase space. Here, we show how to construct the double virtual subtraction term using antenna functions with both initial-and final-state partons which remove the explicit infrared poles present in the two-loop amplitude. As an explicit example, we write down the subtraction term for the four-gluon two-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space leaving a finite remainder that can be safely evaluated numerically in four-dimensions.

Antenna subtraction at NNLO with hadronic initial states: double real initial-initial configurations

“…Finally, we notice that the integrated initial-initial antenna functions F 12 and F 13 derived here appear in the integrated subtraction terms of the all-gluon contribution to two-jet production. They contribute to the cancellation of all infrared poles when combined with all other integrated subtraction terms and with the virtual two-loop matrix elements [126]. This pole cancellation has been verified [126] and can be regarded as a strong check on the correctness of our results presented here for these integrated antennae F 12 and F 13 .…”

“…A very promising approach could be the combination of subtraction with sector decomposition [40][41][42], which was recently applied in the calculation of NNLO corrections to the quark-induced processes in top quark pair production [98,99]. This paper is structured as follows: in section 2, we briefly summarise the application of the antenna subtraction formalism to hadronic collisions, which was developed in [79][80][81]84]. The antenna functions required for double real radiation and their associated phase space mappings are described in section 3 while the phase space integration is described in section 4.…”

“…Case (e) can always be described [81] by soft antenna functions in final-final kinematics, that were derived in [50][51][52][53][54]. In case (b), tree-level four-parton antennae are needed.…”

“…Potential applications, where two-loop matrix elements have already been derived, are: two-jet production [112][113][114][115][116][117][118][119][120], vector-boson-plus-jet production [121][122][123] and Higgs-boson-plus-jet production [124]. Important steps have already been taken in the calculation of two-jet production at NNLO, where the unintegrated subtraction terms for purely gluonic processes have already been derived and tested for the double real radiation at tree-level [80] and the single real radiation at one-loop [81], and in the incorporation of processes with quarks into this calculation [125]. Finally, we notice that the integrated initial-initial antenna functions F 12 and F 13 derived here appear in the integrated subtraction terms of the all-gluon contribution to two-jet production.…”

CT10 next-to-next-to-leading order global analysis of QCD

“…NNLO matrix elements are unknown for several other processes in the global analysis. Most notably, the key input theoretical cross section for inclusive jet production in p p ð−Þ collisions is still evaluated at NLO, although some of the NNLO radiative contributions have already been computed [22,23]. 1 Various NNLO PDF sets have been published in the literature [24][25][26][27][28][29] that make use of NNLO matrix elements when available.…”