TTP01-28 Duality in Semi-Exclusive Processes

Semi-exclusive processes like $\gamma p \to \pi^+ Y$ are closely analogous to DIS, $ep \to eX$, in the limit where the momentum transfer $|t|$ to the pion and the mass of the inclusive system $Y$ are large but still much smaller than the total CM energy. We apply Bloom-Gilman duality to this semi-exclusive process. The energy dependence of the $\gamma p \to \pi^+ n$ cross section given by semi-local duality agrees with data for moderate values of $|t|$, but its normalization is underestimated by about two orders of magnitude. This indicates that rather high momentum transfers are required for the validity of PQCD in the hard subprocess $\gamma u \to \pi^+ d$. In the case of Compton scattering $\gamma p \to \gamma p$ the analogous discrepancy is about one order of magnitude. In electroproduction the virtuality of the incoming photon can be used to directly measure the hardness of the subprocess.