Are all Boer-Mulders functions alike?

TL;DR

This paper compares various models and lattice results for chiral-odd GPDs and the Boer-Mulders function, revealing consistent signs and insights into spin-orbit correlations in nucleons and pions.

Contribution

It provides a comparative analysis of GPD $ar{E}^q_T$ across models and lattice data, highlighting the sign consistency of the Boer-Mulders function.

Findings

$ar{E}^q_T>0$ for nucleons and pions

Boer-Mulders functions are expected to be negative

Sign determined by Dirac component sign

Abstract

Chirally odd generalized parton distributions (GPDs) and the Boer-Mulders function provide valuable information about spin-orbit correlations for quarks in nucleons and other hadrons. We compare results for the relevant GPD $\bar{E}^q_T$ from a variety of phenomenological models as well as recent lattice results. We find that $\bar{E}^q_T>0$ for nucleons as well as the pion and for both $u$ and $d$ quark. As a result, the corresponding Boer Mulders functions are all expected to be negative. The sign of $\bar{E}^q_T$ arises from the relative sign between the upper and lower Dirac components for the quark wave functions.