Do present data on the two-spin asymmetry ALL pi 0(p(-)p) exclude a large gluon polarization in the proton?

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We study carefully the two-spin asymmetry ${A}_{\mathrm{LL}}^{{\ensuremath{\pi}}^{0}}({(\ensuremath{-})}{p}p)$ for inclusive ${\ensuremath{\pi}}^{0}$ production in collisions of longitudinally polarized (anti)protons with longitudinally polarized protons. It is shown that the recent Fermilab data for ${A}_{\mathrm{LL}}^{{\ensuremath{\pi}}^{0}}({(\ensuremath{-})}{p}p)$ do not exclude a large polarization of gluons in the proton and are consistent with most proton spin scenarios suggested up to now. In order to study the reliability of perturbative QCD predictions for ${A}_{\mathrm{LL}}^{{\ensuremath{\pi}}^{0}}({(\ensuremath{-})}{p}p)$ we investigate the influence of intrinsic ${k}_{T}$ smearing on the asymmetry.