A Note on Pretzelosity TMD Parton Distribution

TL;DR

This paper demonstrates that the Pretzelosity TMD parton distribution function is zero at all orders for a massless quark state, indicating it is not factorized with collinear transversity at twist-2, but is related to twist-4 distributions.

Contribution

It reveals that Pretzelosity is zero at all orders for a single massless quark, clarifying its non-factorization with collinear transversity and its relation to higher-twist distributions.

Findings

Pretzelosity function is zero at all orders for a massless quark.

Explicit calculation shows nonzero Pretzelosity for a quark-gluon state.

Pretzelosity relates to twist-4 operators, not twist-2.

Abstract

We show that the transverse-momentum-dependent parton distribution, called as Pretzelosity function, is zero at any order in perturbation theory of QCD for a single massless quark state. This implies that Pretzelosity function is not factorized with the collinear transversity parton distribution at twist-2, when the struck quark has a large transverse momentum. Pretzelosity function is in fact related to collinear parton distributions defined with twist-4 operators. In reality, Pretzelosity function of a hadron as a bound state of quarks and gluons is not zero. Through an explicit calculation of Pretzelosity function of a quark combined with a gluon nonzero result is found.