Transverse $\Lambda$ polarization in $e^+e^-$ processes within a TMD factorization approach and the polarizing fragmentation function

TL;DR

This paper re-analyzes Belle and OPAL data on transverse Lambda polarization in e+e- annihilation using a TMD factorization approach, leading to a refined extraction of the polarizing fragmentation function and insights into QCD scale dependence and nonperturbative effects.

Contribution

It introduces a comprehensive TMD factorization analysis of Lambda polarization data, incorporating QCD scale dependence and nonperturbative effects, extending previous simplified models.

Findings

Confirmed features of previous analyses

Extracted the polarizing fragmentation function with QCD scale dependence

Tested consistency across different energy datasets

Abstract

We perform a re-analysis of Belle data for the transverse $\Lambda$ and $\bar\Lambda$ polarization in $e^+ e^-$ annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of $\Lambda$'s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive $\Lambda$ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenomenological study carried out in a more simplified TMD approach, leading to a new extraction of the polarizing fragmentation function (FF). While confirming several features of the previous analysis, here we include the proper QCD scale dependence of this TMD FF and carefully exploit the role of its nonperturbative component. The compatibility, within a unique TMD factorization scheme, of double and single-inclusive hadron production is discussed in detail. Moreover, we consider another data set for inclusive $\Lambda$ production, at much larger energies, from the OPAL Collaboration, in order to test the consistency of the entire approach. Finally, we elaborate on some fundamental issues like the role of $SU(2)$ isospin symmetry and the heavy quark contributions.