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Meson Structure in Deep Inelastic Scattering

We study the deep inelastic structure functions of mesons within the Nambu and Jona-Lasinio model. We calculate the valence quark distributions in $π$, $K $, and $ρ$ mesons at the low energy model scale, which are evoluted to the experimental momentum scale in terms of the Altarelli-Parisi equation. The resulting distribution functions show reasonable agreements with experiment. We also discuss the semi-inclusive lepton nucleon scattering process with a slow nucleon in coincidence in the final state, which reveals the off-shell structure of the pion.