Do present data on the two-spin asymmetryALLπ0({(−)}{p}p)exclude a large gluon polarization in the proton?

We study carefully the two-spin asymmetry $A_{\mathrm{LL}}^{{\pi }^0}\left(\left\{\mathrm{}\right(-\left)\mathrm{}\right\}\left\{p\right\}p\right)$ for inclusive ${\pi }^0$ production in collisions of longitudinally polarized (anti)protons with longitudinally polarized protons. It is shown that the recent Fermilab data for $A_{\mathrm{LL}}^{{\pi }^0}\left(\left\{\mathrm{}\right(-\left)\mathrm{}\right\}\left\{p\right\}p\right)$ 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 $A_{\mathrm{LL}}^{{\pi }^0}\left(\left\{\mathrm{}\right(-\left)\mathrm{}\right\}\left\{p\right\}p\right)$ we investigate the influence of intrinsic $k_T$ smearing on the asymmetry.