On the Shape of Hadron Structure Functions

The hypothesis that, in the leading twist approximation and to all orders of perturbative QCD, there exists a momentum scale Q$ at which hadrons are pure valence quark (or antiquark) bound states gives good results for nucleon, pion and kaon structure functions. Perturbative QCD tells us how hadron structure functions, e.g., F;N(x,Q2), evolve with Q2 for high enough Q2. But what about their shapes as functions of x? Our aim here is to investigate the possibility of predicting those shapes. To do so we consider the experimental structure functions in a Q2 region where hi her than twist two effects (l/Q* terms) are negligible (Q2 B 2 l-10 GeV ) and extrapolate them at low Q2 using perturbative QCD. We assume that this procedure leads to a momentum scale Qs at which the extrapolated hadron pictures correspond to pure valence quark or antiquark bound states with no glue and no sealm4 (qqq sta te for the nucleon and q{ states for pion and kaon). Of course those perturbative QCD extrapolations of hadron structure functions have nothing to do with what is actually measured at the scale Qz because of the presence of very large higher twist effects at this scale. Our model consists in using perturbative QCD in the leading twist approximation with the following boundary conditions xG(x,Q$=xq,(x,Q@=O (G and qs stand respectively for gluon and light quark sea distributions). The valence boundary distributions xq,(x,Qi) are the bound state distributions computed in the leading twist approximation (l/Q; terms neglected) as given, e.g., in the meson case, by the diagram of Fig. 1. Note that we never have to precise the exact value of Qg. We are able to predict the kaon structure functions in terms of the pion ones by using data on pion structure functions5 together with the following formula3