Do we understand the single-spin asymmetry for $pi^0$ inclusive production in pp collisions?

The cross section data for $\pi^0$ inclusive production in $pp$ collisions is considered in a rather broad kinematic region in energy $\sqrt{s}$, Feynman variable $x_F$ and transverse momentum $p_T$. The analysis of these data is done in the perturbative QCD framework at the next-to-leading order. We find that they cannot be correctly described in the entire kinematic domain and this leads us to conclude that the single-spin asymmetry, $A_N$ for this process, observed several years ago at FNAL by the experiment E704 and the recent result obtained at BNL-RHIC by STAR, are two different phenomena. This suggests that STAR data probes a genuine leading-twist QCD single-spin asymmetry for the first time and finds a large effect.