Skewed and double distributions in the pion and the nucleon

We study the non-forward matrix elements of twist-2 QCD light-ray operators and their representations in terms of skewed and double distributions, considering the pion as well as the nucleon. We point out the importance of explicitly including all twist-2 structures in the double distribution representation, which naturally leads to a “two-component” structure of the skewed distribution, with different contributions in the regions $|X|>\xi /2\mathrm{}$ and $|X|<\xi /2.\mathrm{}$ We compute the skewed and double quark distributions in the pion at a low normalization point in the effective chiral theory based on the instanton vacuum. Also, we derive the crossing relations expressing the skewed quark distribution in the pion through the distribution amplitude for two-pion production. Measurement of the latter in two-pion production in ${\gamma }^{*}\gamma$ and ${\gamma }^{*}N$ reactions could provide direct information about the skewed as well as the usual quark-antiquark distribution in the pion.