Double Collins effect in $e^+ e^-\to\Lambda \bar\Lambda X$ process in a diquark spectator model

TL;DR

This paper models the Collins function for Lambda hyperons using a diquark spectator approach, estimates the resulting asymmetry in electron-positron collisions, and highlights the importance of QCD evolution effects for experimental measurements.

Contribution

It introduces a diquark spectator model calculation of the Lambda Collins function, including evolution effects, to predict measurable asymmetries in $e^+e^-$ processes.

Findings

The asymmetry is sizable and measurable at Belle and BaBar.

QCD evolution effects significantly impact the Collins function analysis.

The model includes both scalar and vector diquark contributions.

Abstract

We study the Collins function $H^\perp_{1}$ of the $\Lambda$ hyperon, which describes the fragmentation of a transversely polarized quark into an unpolarized $\Lambda$ hyperon. We calculate $H^\perp_{1}$ for light quarks of the $\Lambda$ hyperon, in the diquark spectator model with a Gaussian form factor for the hyperon-quark-diquark vertex. The model calculation includes contributions from both the scalar diquark and vector diquark spectators. Using the model result, we estimate the weighted $\cos2\phi_0$ asymmetry in the process $e^+e^- \to \Lambda\bar{\Lambda}X$ contributed by the coupling of two Collins functions. The QCD evolution effects for the first $k_T$-moment of the Collins function and the unpolarized fragmentation function $D_1(z)$ are also included. The results show that asymmetry is sizable and measurable at the kinematical configurations of Belle and BaBar experiments. We also find that the evolution effects play an important role in the phenomenological analysis.