Ioffe-time distributions instead of parton momentum distributions in the description of deep inelastic scattering

We argue that parton distributions in coordinate space provide a more natural object for nonperturbative methods compared to the usual momentum distributions in which the physics of different longitudinal distances is being mixed. To illustrate the advantages of the coordinate space formulation, we calculate the coordinate space distributions for valence quarks in the proton using the QCD sum rule approach. A remarkable agreement is found between the calculated and the experimentally measured u-quark distribution up to light-cone distances ${\mathrm{\Delta }}^{\mathrm{-}}$=${\mathrm{\Delta }}^0$-${\mathrm{\Delta }}^3$ of order ∼1 fm in the proton rest frame. The calculation for valence d quarks gives much worse results; the reasons for this discrepancy are discussed.