Inclusion of the QCD next-to-leading order corrections in the quark-gluon Monte Carlo shower

Abstract

Methodology of including QCD NLO corrections in the quark-gluon Monte Carlo shower is outlined. The work concentrates on two issues: (i) constructing leading order (LO) parton shower Monte Carlo from scratch, such that it rigorously extends collinear factorization into the exclusive (fully unintegrated) one which we call the Monte Carlo factorization scheme; (ii) introducing next-to-leading-order (NLO) corrections to the hard process in this new environment. The presented solution is designed to be extended to the full NLO level Monte Carlo, including NLO corrections not only in the hard process but in the whole shower. The issue of the difference between the factorization scheme implemented in the Monte Carlo (MC) solution and the standard MS scheme is addressed. The principal MC implementation is designed for the electroweak boson production process at the LHC, but in order to discuss universality -process independence, the deep inelastic lepton-hadron scaterring is also brought into the MC framework.

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.…”

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

“…A more complete discussion of the KrkNLO scheme with the introduction of PDFs in the Monte Carlo (MC) factorisation scheme was provided in Ref. [1], but the MC implementation was still on top of the not-so-realistic Double-CMC PS. Finally, in recent Ref.…”

“…[1] and tested numerically in Ref. [2] using a not very realistic parton shower Monte Carlo (PS MC).…”

Parton distribution functions in Monte Carlo factorisation scheme

“…[1,2], the essence of the KrkNLO method is that certain NLO correction terms in an unintegrated/exclusive form present in the MS scheme, which are proportional to unphysical Dirac-delta terms in transverse momentum of emitted real partons, are removed in the KrkNLO methodology by means of redefinition of PDFs from the MS to MC scheme. These 'pathological' terms are preventing the use of a simple multiplicative MC weight for implementing NLO corrections in the MS scheme in real-emission phase space, and they complicate implementation of the MC@NLO and POWHEG methods.…”

“…[1] it was defined for gluonstrahlung only (albeit for two different processes, DY and DIS). In Ref.…”