Analyzing the Boer-Mulders function within different quark models

TL;DR

This paper develops a formalism to calculate the Boer-Mulders function, applying it to two quark models of the proton, and compares the results to previous calculations and the Sivers function, confirming the approach's validity.

Contribution

It introduces a unified formalism for evaluating time reversal odd distributions and compares results across different models and functions, highlighting model-dependent differences.

Findings

Results are consistent with the pattern of same sign for u and d flavors.

The formalism successfully reproduces known sum rule behaviors.

Differences are found between models, especially in the MIT bag model evaluations.

Abstract

A general formalism for the evaluation of time reversal odd parton distributions is applied here to calculate the Boer-Mulders function. The same formalism when applied to evaluate the Sivers function led to results which fulfill the Burkardt sum rule quite well. The calculation here has been performed for two different models of proton structure: a constituent quark model and the MIT bag model. In the latter case, important differences are found with respect to a previous evaluation in the same framework, a feature already encountered in the calculation of the Sivers function. The results obtained are consistent with the present wisdom, i.e., the contributions for the $u$ and $d$ flavors turn out to have the same sign, following the pattern suggested analyzing the model independent features of the impact parameter dependent generalized parton distributions. It is therefore confirmed that the present approach is suitable for the analysis of time reversal odd distribution functions. A critical comparison between the outcomes of the two models, as well as between the results of the calculations for the Sivers and Boer-Mulders functions, is also carried out.