Parton Interpretation and Twist-4 Parton Distributions

TL;DR

This paper demonstrates that twist-4 parton distributions lack a straightforward parton interpretation, as they can exhibit unphysical momentum fractions greater than 1 or less than -1, and are power-divergent for |x|>1.

Contribution

The study clarifies the limitations of twist-4 parton distributions in the collinear factorization framework, highlighting their non-interpretability as parton momentum fractions.

Findings

Twist-4 distributions are power-divergent for |x|>1.

Transverse momentum dependent distributions are finite and have no parton interpretation.

Parton distributions can carry unphysical momentum fractions exceeding 1 or -1.

Abstract

Through explicit examples we show that twist-4 parton distributions have no parton interpretation in the sense that parton or partons inside a hadron can carry the momentum fraction $x$ of the hadron with $x >1$ or $x<-1$. The studied twist-4 parton distributions of collinear factoization are power-divergent for $\vert x\vert >1$. The corresponding transverse momentum dependent parton distributions have also no parton interpretation. They are finite. The implications of our results are discussed.