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The parton-level Monte Carlo generator MATRIX performs fully differential computations at the next-to-next-to-leading order (NNLO) QCD; it is based on a number of different computations and tools from various people and groups [6,10-15].
The loop-induced gg contribution entering at the NNLO is available for the diphoton production process.
On the other hand, the use of this criterion by the theoretical investigations at NNLO is necessary to ensure an Infra-Red (IR) safe definition of the cross-section since no fragmentation functions are included.
Tramontano, "Associated ZH production at hadron colliders: the fully differential NNLO QCD calculation," Physics Letters B, vol.
All calculations in this work are performed using the JETPHOX with including all diagrams up to the LO and NLO order of QED and QCD coupling, respectively, defined in the [bar.MS] renormalization scheme (it is worth pointing out in this context that since the NNLO calculations  have not yet been incorporated into any readily available codes like JETPHOX, the NLO results are still interesting).
The large scale variations indicate that the NNLO calculations are needed to make more realistic theoretical predictions.
We found that the scale uncertainty can reach 20% in some regions so the NNLO calculations are needed to make more realistic theoretical predictions.
Theoretical prediction of Z boson is available up to next-to-next-to-leading order (NNLO) in perturbative QCD and to next-to-leading order (NLO) for EW processes.
Particularly, HERAPDF2.0 prediction at NNLO best describes the measurement.
Guzzi, "NNLO logarithmic expansions and exact solutions of the DGLAP equations from x-space: new algorithms for precision studies at the LHC," Nuclear Physics B, vol.
Yndurain, "Improved calculation of F2 in electroproduction and xF3 in neutrino scattering to NNLO and determination of as" Nuclear Physics B, vol.
Guzzi, "Precision studies of the NNLO DGLAP evolution at the LHC with Candia," Computer Physics Communications, vol.
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