Semi-Exclusive Processes: New Probes of Hadron Structure

We define and study hard ``semi-exclusive'' processes of the form $A+B \to C + Y$ which are characterized by a large momentum transfer between the particles $A$ and $C$ and a large rapidity gap between the final state particle $C$ and the inclusive system $Y$. Such reactions are in effect generalizations of deep inelastic lepton scattering, providing novel currents which probe specific quark distributions of the target $B$ at fixed momentum fraction. We give explicit expressions for photo- and leptoproduction cross sections such as $\gamma p \to \pi Y$ in terms of parton distributions in the proton and the pion distribution amplitude. Semi-exclusive processes provide opportunities to study fundamental issues in QCD, including odderon exchange and color transparency, and suggest new ways to measure spin-dependent parton distributions.