Positivity of NLO Spin-Dependent Parton Distributions

TL;DR

This paper proves that the positivity of the hadron density matrix in QCD is maintained during NLO evolution if certain kernel conditions are met, impacting the choice of factorization schemes for spin-dependent distributions.

Contribution

It demonstrates the preservation of positivity in NLO spin-dependent parton distributions and discusses the implications for factorization scheme choices.

Findings

Positivity is preserved in QCD evolution under specific kernel conditions.

The relation |P_{ij}(z)|  P_{ij} is crucial for positivity.

Positivity restrictions influence the selection of NLO factorization schemes.

Abstract

We discuss the positivity of the hadron density matrix in QCD. This basic property is shown to be preserved by QCD evolution, provided the relation $|\Delta P_{ij}(z)| \leq P_{ij}$ is valid for all kernels for $z < 1$, and the usual "+" prescription is used. We comment on the positivity restrictions for the choice of the NLO factorization scheme for the evolution of the spin-dependent parton distributions.