The azimuthal single target-spin asymmetries for pi (+) production in semi-inclusive deep inelastic scattering of leptons off longitudinally polarized protons are evaluated using two main approaches available in the literature, It is shown that the approximation where the twist-2 transverse quark spin distribution in the longitudinally polarized nucleon is small enough to be neglected leads to a consistent description of all existing asymmetries observed by the HERMES experiment. (C) 2001 Elsevier Science B,V. All rights reserved.
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