On the positivity of MSbar distributions

TL;DR

This paper investigates the positivity of parton distribution functions within the ar scheme, demonstrating that ar PDFs are positive above 5 GeV^2 and aligning with physical and polarized PDFs.

Contribution

It provides a detailed analysis of the positivity of ar PDFs and their relation to physical observables, clarifying their behavior in the perturbative regime.

Findings

ar PDFs inherit positivity from physical PDFs in the perturbative regime.

ar PDFs are positive for Q^2 > 5 GeV^2.

Longitudinally polarized PDFs align with unpolarized PDFs in positivity.

Abstract

We discuss the positivity of parton distribution functions using the common $\overline{MS}$ factorization scheme. We find that in the perturbative regime $\overline{MS}$ PDFs inherit the strict positivity of physical PDFs. We explicitly discuss the scheme transformation by using suitable physical observables and find that $\overline{MS}$ PDFs are positive above the scale $Q^2$ > 5 GeV^2. Finally, we comment on the direct counterpart of longitudinally polarized PDFs, finding agreement with the unpolarized counterpart.