# The Polarising Fragmentation Function and the Lambda polarisation in e+ e- processes

## TL;DR

This paper explores how the polarising fragmentation function (PFF) can explain Lambda hyperon polarization in unpolarized e+ e- processes, providing explicit formulas and predictions consistent with recent Belle data.

## Contribution

It introduces a simplified model linking PFFs to Lambda polarization in e+ e- annihilation, offering explicit expressions and testable predictions.

## Key findings

- PFFs can generate non-zero Lambda polarization in e+ e- processes.
- Qualitative agreement between model predictions and Belle data.
- Recommendations for future measurements to extract PFFs.

## Abstract

The surprising polarisation of Lambdas and other hyperons measured in many unpolarised hadronic processes, p N --> Lambda X, has been a long standing challenge for QCD phenomenology. One possible explanation was suggested, related to non perturbative properties of the quark hadronisation process, and encoded in the so-called Polarising Fragmentation Function (PFF). Recent Belle data have shown a non zero Lambda polarisation also in unpolarised e+ e- processes, e+ e- --> Lambda X and e+ e- --> Lambda h X. We consider the single inclusive case and the role of the PFFs. Adopting a simplified kinematics it is shown how they can originate a polarisation P_Lambda different from 0 and give explicit expressions for it in terms of the PFFs. Although the Belle data do not allow yet, in our approach, an extraction of the PFFs, some clear predictions are given, suggesting crucial measurements, and estimates of P_Lambda are computed, in qualitative agreement with the Belle data.