Semi-inclusive production of spin-$3/2$ hadrons in deep inelastic scattering

We investigate the production of spin-$3/2$ hadrons in semi-inclusive deep inelastic lepton-nucleon scatterings. The complete differential cross section is derived through the kinematic analysis and expressed in terms of 288 structure functions, corresponding to all polarization configurations and azimuthal modulations. For an unpolarized lepton beam, half of the 192 structure functions have nonzero leading order contributions in the parton model, among which 42 are from rank-3 tensor polarized fragmentation functions of the hadron. For a polarized lepton beam, one third of the 96 structure functions contribute at the leading order and 14 of them are from rank-3 tensor polarized fragmentation functions. In addition to the formalism, we perform a model estimation of the spin transfer to a $S_{hLLL}$ polarized hadron and sizable asymmetry is expected. Therefore, these newly defined observables for the production of a spin-$3/2$ hadron in a deep inelastic scattering process can be explored in future experiments to understand nucleon spin structures and spin-dependent fragmentation functions.

Figure 1

The process $e^{-}N\to e^{-}\mathrm{\Omega }X$ with one-photon-exchange approximation.

Figure 2

The unpolarized fragmentation function $z{D}_1(z)$ (left) and the $S_{hLLL}$-dependent fragmentation function $z{G}_{1LLL}(z)$ (right) calculated from the spectator model.

Figure 3

The $S_{hLLL}$-dependent spin transfer in the spectator model.