Quark-model relations among TMDs in the parton model

TL;DR

This paper investigates the covariant parton model's ability to support quark-model relations among TMDs, showing that pure-spin states uphold these relations while mixed-spin states do not, offering insights into their possible realization in QCD.

Contribution

It demonstrates that quark-model relations among TMDs hold only in the pure-spin state version of the covariant parton model, providing a new perspective on their applicability in QCD.

Findings

Pure-spin state CPM supports quark-model relations among TMDs.

Mixed-spin state CPM does not support these relations.

Imposing pure-spin conditions can enforce the relations in the CPM.

Abstract

The covariant parton model (CPM) is a consequent application of the parton model concept to the nucleon structure. In this model, there is a choice to put quarks either in a pure-spin state or in a mixed-spin state. We show that the mixed-spin version of the CPM does not support the quark-model relations among transverse momentum dependent parton distributions (TMDs) which were shown to hold in a large class of quark models. One can enforce the quark-model relations to be valid in the CPM by imposing a condition which is equivalent to putting the quarks in a pure-spin state. This gives a complementary perspective on the connection of the pure- and mixed-spin state CPM versions, and provides a fresh view on the question whether the quark-model relations could be realized in QCD as "approximate relations" with some useful numerical accuracy.