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 $\Omega$, 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.

arXiv comment42 pages, 4 figures, matching the published version in Physical Review D

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Cited by in corpus (4)

• Several Topics on Transverse Momentum-Dependent Fragmentation Functions
• Spin Density Matrix for ${\Omega }^{-}$ and its Polarization Alignment in $\psi (3686)\to {\Omega }^{-}{\bar{\Omega }}^{+}$
• Generalizing the Soffer Bound: Positivity Constraints on Parton Distributions of Spin-3/2 Particles
• Observation of $\Xi (1530{)}^0$ Polarization and Determination of Its Electric and Magnetic Moments in $\psi (3686)\to \Xi (1530{)}^0\bar{\Xi }(1530{)}^0$