Longitudinal and transverse polarizations of $\Lambda$ hyperon in unpolarized SIDIS and $e^+e^-$ annihilation

TL;DR

This paper systematically studies $ ext{Lambda}$ hyperon polarizations in unpolarized lepton-induced reactions, deriving structure functions and polarization expressions in QCD, and suggests ways to measure these polarizations in future experiments.

Contribution

It provides a comprehensive theoretical framework for hyperon polarization in unpolarized SIDIS and $e^+e^-$ annihilation, including new expressions for structure functions and polarization observables.

Findings

Hyperons can be polarized in three orthogonal directions.

Expressions for polarization in terms of parton and fragmentation functions.

Numerical estimates and experimental measurement strategies.

Abstract

We make a systematic study of $\Lambda$ hyperon polarizations in unpolarized lepton induced semi-inclusive reactions such as $e^-N\to e^-\Lambda X$ and $e^+e^-\to\Lambda h X$. We present the general form of cross sections in terms of structure functions obtained from a general kinematic analysis. This already shows that the produced hyperons can be polarized in three orthogonal directions, i.e., the longitudinal direction along the hyperon momentum, the normal direction of the production plane, and the transverse direction in the production plane. We present the parton model results at the leading twist and leading order in perturbative QCD and provide the expressions for these structure functions and polarizations in terms of parton distribution functions and fragmentation functions. We emphasize in particular that by studying the longitudinal polarization and the transverse polarization in the production plane, we can extract the corresponding chiral-odd fragmentation functions $H_{1Lq}^{\perp\Lambda}$, $H_{1Tq}^{\Lambda}$ and $H_{1Tq}^{\perp\Lambda}$. We also present numerical results of rough estimates utilizing available parameterizations of fragmentation functions and approximations. We discuss how to measure these polarizations and point out in particular that they can be carried out in future EIC and/or $e^+e^-$ annihilation experiments such as Belle.