Transverse momentum dependent transversely polarized distributions at next-to-next-to-leading-order

TL;DR

This paper computes the NNLO matching of transversity and pretzelosity TMDs to collinear distributions, revealing that pretzelosity's matching coefficient is zero, indicating it may correspond to a twist-4 distribution.

Contribution

It provides the first NNLO matching calculations for transversity and pretzelosity TMDs, highlighting the unique behavior of pretzelosity.

Findings

Matching coefficient for pretzelosity is zero.

Pretzelosity likely corresponds to a twist-4 distribution.

Matching formulas are provided for both PDFs and fragmentation functions.

Abstract

We calculate the matching of the transversity and pretzelosity transverse momentum dependent distributions (TMD) on transversity collinear distribution at the next-to-next-to-leading order (NNLO). We find that the matching coefficient for pretzelosity distribution is zero, despite the matrix element for it is nontrivial. This result suggests that the pretzelosity matches a twist-4 distribution. The matching for transversity TMD distributions is provided for both parton distribution functions and fragmentation functions cases.