Isospin Symmetry of Fragmentation Functions

TL;DR

This paper systematically examines the isospin symmetry of fragmentation functions, considering decay contributions, and finds that isospin symmetry holds approximately, with tiny violations in certain cases, supported by experimental data.

Contribution

It provides a detailed analysis of isospin symmetry in fragmentation functions, including decay effects, and offers estimates of symmetry violations consistent with experimental observations.

Findings

Isospin symmetry holds for unpolarized $\\Lambda$ fragmentation functions.

Tiny violations are allowed for nucleons and pions due to weak decays.

Recent Belle data on $\\Lambda$ polarization can be explained assuming isospin symmetry.

Abstract

We make a systematic study of the isospin symmetry of fragmentation functions by taking decay contributions into account. We assume the isospin symmetry in strong interactions and show that in the unpolarized case the isospin symmetry is held for fragmentation functions of $\Lambda$ and only tiny violations are allowed for other hadrons such as nucleon and pions due to the contributions from weak decays. We present a rough estimate of the magnitudes of such violations. In the polarized case, we show that the isospin symmetry violation for $\Lambda$ production should be tiny and the recent Belle data on the transverse polarization of $\Lambda$ can be reproduced if the isospin symmetry is kept in the corresponding polarized fragmentation functions.