Understanding the role of Cahn and Sivers effects in Deep Inelastic Scattering

The role of intrinsic $k_\perp$ in semi-inclusive Deep Inelastic Scattering (SIDIS) processes ($l p \to l h X$) is studied with exact kinematics within QCD parton model at leading order; the dependence of the unpolarized cross section on the azimuthal angle between the leptonic and the hadron production planes (Cahn effect) is compared with data and used to estimate the average values of $k_\perp$ both in quark distribution and fragmentation functions. The resulting picture is applied to the description of the weighted single spin asymmetry $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ recently measured by the HERMES collaboration at DESY; this allows to extract parameters for the quark Sivers functions. The extracted Sivers functions give predictions for the COMPASS measurement of $A_{UT}^{\sin(\phi_\pi - \phi_S)}$ in agreement with recent data, while their contribution to HERMES $A_{UL}^{\sin\phi_\pi}$ is computed and found to be small. Predictions for $A_{UT}^{\sin(\phi_K - \phi_S)}$ for kaon production at HERMES are also given.