Physical factorisation scheme for PDFs for non-inclusive applications

Abstract

We introduce the physical factorisation scheme, which is necessary to describe observables which are `not completely inclusive'. We derive the formulae for NLO DGLAP evolution in this scheme, and also for the `rotation' of the conventional MSbar PDFs into the physical representation. Unlike, the MSbar prescription, where, for example, the gluon PDF at NLO obtains an admixture of the quark-singlet PDF, and vice-versa, the physical approach does not mix parton PDFs of different types. That is, the physical approach retains the precise quantum numbers of each PDF. The NLO corrections to DGLAP evolution in the physical scheme are less than those in the MSbar case, indicating a better convergence of the perturbative series

Exclusive $J/\psi $ production at the LHC in thekTfactorisation approach

“…(and HERA electroproduction) data be included in a global PDF fit? One possibility would be to use the above k T factorisation approach and then to transform the result to the MS scheme following [19]. Another possibility is to work in the MS scheme from the beginning, using the optimal factorisation scale obtained from resumming the a x Q ln 1 ln s n 2 ( ( ) ( )) terms, and accounting for the Q 0 power corrections as described in [24].…”

Evolution Kernels for Parton Shower Monte Carlo

“…We can solve it by using a dedicated Monte Carlo factorization scheme [9,12] which redefines projection operators, however, this is beyond the scope of this work and we will not investigate it here. Let us just mention that similar idea has been investigated by Oliveira et al [18,19] in the context of physical factorization scheme allowing for better convergence of perturbative series.…”

Snowmass 2021 Whitepaper: Proton Structure at the Precision Frontier

“…Recently there has been renewed interest in developing alternative factorization schemes [320,[363][364][365][366][367][368], including to investigate the positivity of MS PDFs [320] and to simplify Monte Carlo calculations [365][366][367][368]368]. PDFs in different factorization schemes are related to each other, and to those in the MS scheme, by a transition operator that mixes PDFs of different flavors, f FS = K MS→FS ⊗ f MS , so that for each flavor a we have…”