Inclusive and semi-inclusive production of spin-3/2 hadrons in $e^+e^-$ annihilation

TL;DR

This paper develops a comprehensive framework for describing the production and polarization of spin-3/2 hadrons in electron-positron annihilation, introducing new fragmentation functions and analyzing their contributions to observable cross sections.

Contribution

The paper defines the first complete set of quark transverse momentum dependent fragmentation functions for spin-3/2 hadrons, including 14 newly introduced functions, and analyzes their role in $e^+ e^-$ annihilation processes.

Findings

Only two structure functions are nonzero in single-hadron production.

Half of the structure functions are nonzero in back-to-back two-hadron production.

Ten rank-3 tensor polarized TMD FFs contribute in two-hadron production.

Abstract

We investigate the inclusive and semi-inclusive productions of spin-3/2 hadrons, such as $\Omega$, in unpolarized $e^+ e^-$ annihilation. The general differential cross sections are expressed in terms of structure functions in accordance to the polarization of the hadron and the azimuthal modulations. We derive a complete definition of quark transverse momentum dependent (TMD) fragmentation functions (FFs) to spin-3/2 hadrons for the first time from the decomposition of the quark-quark correlation matrix at leading twist, 14 of which are newly defined corresponding to rank-3 tensor polarized hadron. The collinear FFs are obtained from the $k_T$-integrated correlation matrix, and only two TMD FFs with rank-3 tensor polarization have nonvanishing collinear counterparts. Then we perform a leading order calculation of the unpolarized differential cross sections. In the single-hadron inclusive production, only two structure functions are found nonzero and none of the rank-3 tensor polarized FFs contributes. For the nearly back-to-back two-hadron production, half of the 48 structure functions are found nonzero even if the spin of the second hadron is not analyzed, and ten of the rank-3 tensor polarized TMD FFs contribute. Therefore, one can study the rank-3 tensor polarized FFs via the production of a spin-3/2 hadron and an unpolarized hadron in unpolarized $e^+ e^-$ collision experiments. These newly defined FFs can be further applied in semi-inclusive deep inelastic scattering processes for the study of nucleon structures.