Reviewing model calculations of the Collins fragmentation function

TL;DR

The paper reevaluates four model calculations of the Collins fragmentation function for quark-to-pion fragmentation, correcting sign errors and clarifying the role of loop corrections. By computing D1 and H1^⊥ across pseudoscalar and pseudovector couplings with pion and gluon loops, it reveals systematic diagram-by-diagram cancellations and cases where a single diagram dominates depending on parameters. The authors provide corrected expressions, quantify H1^⊥/D1 over parameter ranges, and compare predicted SIDIS asymmetries to HERMES data, finding that pionic degrees of freedom alone are insufficient and that some parameter regions (notably high-μ pseudovector coupling) are disfavored. The study highlights the sensitivity to coupling type, cutoffs, and the possible need for form factors to reconcile models with data.

Abstract

The Collins fragmentation function describes a left/right asymmetry in the fragmentation of a transversely polarized quark into a hadron in a jet. Four different model calculations of the Collins function have been presented in the literature. While based on the same concepts, they lead to different results and in particular to different signs for the Collins function. The purpose of the present work is to review the features of these models and correct some errors made in previous calculations. A full study of the parameter dependence and the possible modifications to these models is beyond the scope of the paper. However, some general conclusions are drawn.

Figures (13)

• Figure 1: Tree-level cut diagram describing the fragmentation of a quark into a pion. This diagram is common to all models, but the specific form of the pion-quark vertex can change.
• Figure 2: Unpolarized fragmentation function $D_1^{u\to \pi^+}$ in a fragmentation model with pseudoscalar pion-quark coupling. Left panel: dependence on the parameter $\mu$ (for $m=0.3$ GeV). Right panel: dependence on the parameter $m$ (for $\mu=1$ GeV).
• Figure 3: Single pion-loop corrections to the fragmentation of a quark into a pion.
• Figure 4: Contributions to $H_1^{\perp (1/2)}/D_1$ from the diagrams of Fig. \ref{['f:pspion']} and their sum.
• Figure 5: Single gluon-loop corrections to the fragmentation of a quark into a pion.