We consider within a generalized QCD factorization approach, the high energyinclusive polarized process p p --> pion + X, including all intrinsic partonicmotions. Several new spin and k_T-dependent soft functions appear andcontribute to cross sections and spin asymmetries. We present here formalexpressions for transverse single spin asymmetries and double longitudinalones. The transverse single spin asymmetry, A_N, is considered in detail, andall contributions are evaluated numerically. It is shown that the azimuthalphase integrations strongly suppress most contributions, leaving at work mainlythe Sivers effect.
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