Vector-axial vector lattice cross section and valence parton distribution in the pion from a chiral quark model

Abstract

Within a chiral quark model, we evaluate the good cross section in the Euclidean space in the vector - axial vector channel, proposed recently by Ma and Qiu as means to extract the so far elusive parton distribution functions of the pion from lattice QCD. Our results are remarkably simple at the quark model scale and agree well, after the necessary QCD evolution, with with the most recent lattice calculations at the scale $\mu \sim 2$ GeV for various values of the lattice pion mass. Comparisons are made as functions of the Ioffe time variable. We also comment on the information on the lowest moments in the momentum fraction $x$, generically extractable from such analyses, as well as on the inaccessibility of the $x \to 1$ limit from the present data.