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A phenomenological description of single transverse spin effects inhadron-hadron inclusive processes is proposed, assuming a generalizedfactorization scheme and pQCD hard interactions. The transverse momentum, k_T,of the quarks inside the hadrons and of the hadrons relatively to thefragmenting quark, is taken into account in distribution and fragmentationfunctions, and leads to possible non zero single spin asymmetries. The role ofk_T and spin dependent quark fragmentations -- the so-called Collins effect --is investigated in details in p(transv. polarized)-p -> pion + X processes: itis shown how the experimental data could be described, obtaining an explicitexpression for the spin asymmetry of a polarized fragmenting quark, on whichsome comments are made. Predictions for other processes, possible furtherapplications and experimental tests are discussed.Comment: 20+1 pages, LaTeX, 6 eps figures, uses epsfig.sty. Version v2: Some  sentences rephrased and comments added throughout the paper; one reference  added; no changes in results and figures. Final version to be published in  Phys. Rev.

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

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Phenomenology of single spin asymmetries inp↑p→πX