Abstract
Within the LO QCD parton model of Semi-Inclusive Deep Inelastic Scattering, $\ensuremath{\ell}N\ensuremath{\rightarrow}\ensuremath{\ell}hX$, with unintegrated quark distribution and fragmentation functions, we study the ${\mathbit{P}}_{hT}$ dependence of the double longitudinal-spin asymmetry ${A}_{LL}$. We include $1/Q$ kinematic corrections, which induce an azimuthal modulation of the asymmetry, analogous to the Cahn effect in unpolarized SIDIS. We show that a study of ${A}_{LL}$ and of the weighted DSA ${A}_{LL}^{\mathrm{cos}{\ensuremath{\phi}}_{h}}$ allows to extract the transverse momentum dependence of the unintegrated helicity distribution function ${g}_{1L}^{q}(x,{k}_{\ensuremath{\perp}})$ [or $\ensuremath{\Delta}q(x,{k}_{\ensuremath{\perp}})]$. Predictions, based on some models for the unknown functions, are given for ongoing COMPASS, HERMES and JLab experiments.
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