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

Abstract

We investigate the inclusive and semi-inclusive productions of spin-3/2 hadrons, such as Ω, 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 by integrating over quark transverse momentum, and only two TMD FFs with rank-3 tensor polarization have nonvanishing collinear counter parts. 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.

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“…It is worth noting that our decomposition of the physical interpretation for S xy LT T differs from the one presented in Refs. [17,31], allowing for a refined analysis of parity or CP symmetries.…”

“…While our definitions generally align with those in Refs. [17,31], we introduce a notable variation in the definition of S xy LT T for a refined analysis of polarization symmetries. The domains of these components are not normalized to 1, as outlined in Appendix B.…”

“…In this paper, we analyze the polarization states of particles using spin density matrices in their rest frames, focusing on particles with spins of 1/2 and 3/2. Various methods are available for decomposing polarization components, including the helicity formalism [47] and the general spin density matrix formalism [17,29,31]. Although these methods are fundamentally similar, their varying conventions often cause confusion.…”

“…Compared to spin-1/2 particles, which possess the spin vector and two form factors, spin-3/2 particles present a broader range of information. They include the spin vector, the rank-2 (quadrupole) spin tensor, and the rank-3 (octupole) spin tensor, totaling fifteen polarization components [29][30][31], along with four form factors [9]. There have been some measurements on the form factors [21,22,24] and polarization of the Omega particle [32,33].…”