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 M S 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.

Parton distribution functions in the context of parton showers

“…Since we include parton masses in the dynamics of initial state splittings, we need evolution kernels for parton evolution that have non-trivial mass dependence. This view is in accord with the work of Jadach, Kusina, Placzek, Skrzypek and Slawinska [16,17], who connect parton shower splittings with the parton distribution function kernels with the aim of extending parton shower splittings to next-to-leading order in α s , albeit for massless partons. In this paper, we work only at lowest order, but include masses.…”

On regularizing the infrared singularities in QCD NLO splitting functions with the new Principal Value prescription

“…The simplest way is to use the Principal Value (PV) prescription [5,6,9,10]. The other option is the Mandelstam-Leibbrandt (ML) prescription [11,12], which is better justified from the field-theoretical point of view, but leads to more complicated calculations, especially for the real-emission-graphs [9]. Other methods of avoiding the problem of spurious singularities can be found in [13,14].…”

NLO Corrections to Hard Process in Parton Shower MC --- {\sf KrkNLO} Method

“…The non-singlet 2-real kernels were presented in Ref. [23]. A simplified and faster scheme was reported (with numerical tests) in Ref.…”