Deep-inelastic scattering from the pion and the choice of phenomenological wave functions

Abstract

We review the relation between covariant calculations and light-front calculations of pion properties. We describe the results obtained for the pion structure function in both formalisms. Conventional (phenomenological) light-front wave functions yield poor results for the structure function unless these results are evolved to higher energies. Our covariant calculation of the structure function has its basis in the Bethe-Salpeter approach to the solution of the two-body problem. Our study shows how an alternative specification of the light-front wave function of the pion leads to a good fit to the (valence) structure function, while also providing good fits for the pion-decay constant, ${\mathit{f}}_{\mathrm{\pi }}$, and the pion electromagnetic form factor (for ${\mathit{Q}}^2$${\mathrm{GeV}}^2$). We also review the standard scheme for evolving distributions from a scale ${\mathit{Q}}_0^2$ to a scale ${\mathit{Q}}^2$ and contrast such procedures with our methods.