  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.
