Two real parton contributions to non-singlet kernels for exclusive QCD DGLAP evolution

Abstract

Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integrated over the phase space in order to provide solid numerical control of the MC codes and for the discussion of the differences between the standard $\overline{MS}$ factorization and Monte Carlo implementation at the level of inclusive NLO evolution kernels. Presented results cover the class of non-singlet diagrams entering into NLO kernels. The classic work of Curci-Furmanski-Pertonzio was used as a guide in the calculations.

34 pages, 3 figures

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• Implementing NLO DGLAP evolution in Parton Showers
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• What is a parton shower?
• Inclusion of the QCD next-to-leading order corrections in the quark-gluon Monte Carlo shower
• The role of colour flows in matrix element computations and Monte Carlo simulations
• Disentangling soft and collinear effects in QCD parton showers
• Transverse-momentum-dependent quark splitting functions in $k_T$-factorization: real contributions
• Transverse momentum dependent splitting functions at work: quark-to-gluon splitting
• A general algorithm to build real-radiation antenna functions for higher-order calculations
• On the dependence of QCD splitting functions on the choice of the evolution variable
• Parton distribution functions in the context of parton showers
• On regularizing the infrared singularities in QCD NLO splitting functions with the new Principal Value prescription
• Fully NLO Parton Shower in QCD
• Two-loop anomalous dimensions for small-$R$ jet versus hadronic fragmentation functions