Are there approximate relations among transverse momentum dependent distribution functions?

TL;DR

This paper investigates approximate relations among transverse momentum dependent distribution functions in QCD, testing a Wandzura-Wilczek-type approximation using HERMES data and discussing future experimental tests.

Contribution

It evaluates the practical validity of a specific Wandzura-Wilczek-type approximation relating TMD functions using existing data and proposes further experimental tests.

Findings

The approximation holds reasonably well with current data.

Neglecting pure twist-3 terms simplifies the relations.

Future experiments can further validate the approximation.

Abstract

Certain exact relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting h_{1L}^{\perp(1)a}(x) to h_L^a(x), and discuss how it can be further tested by future CLAS and COMPASS data.