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Within the LO QCD parton model of Semi Inclusive Deep Inelastic Scattering,$\ell N \to \ell h X$, with unintegrated quark distribution and fragmentationfunctions, we study the $\bfP_{hT}$ dependence of the double longitudinal-spinasymmetry $A_{LL}$. We include 1/Q kinematic corrections, which induce anazimuthal modulation of the asymmetry, analogous to the Cahn effect inunpolarized SIDIS. We show that a study of $A_{LL}$ and of the weighted DSA$A_{LL}^{\cos\phi_h}$ allows to extract the transverse momentum dependence ofthe unintegrated helicity distribution function $g_{1L}^q(x,k_\perp)$ [or$\Delta q(x, k_\perp)]$. Predictions, based on some models for the unknownfunctions, are given for ongoing COMPASS, HERMES and JLab experiments.Comment: Replaced with published in PHYSICAL REVIEW D 74, 074015 (2006)  versio

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Transverse momentum dependence of the quark helicity distributions and the Cahn effect in double-spin asymmetry<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub></mml:math>in semiinclusive DIS

Transverse momentum dependence of the quark helicity distributions and the Cahn effect in double-spin asymmetryALLin semiinclusive DIS