Recent preliminary PHENIX data are consistent with a negative and sizable longitudinal double-spin asymmetry A_LL^pi for pi^0 production at moderate transverse momentum p_perp simeq 1 - 4 GeV and central rapidity. By means of a systematic investigation of the relevant degrees of freedom we show that the perturbative QCD framework at leading power in p_perp produces at best a very small negative asymmetry in this kinematic range.
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