Duality in semi-exclusive processes

Semi-exclusive processes like γp→π+Y are closely analogous to DIS, ep→eX, in the limit where the momentum transfer vertical bar t vertical bar 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 γp→π+ n cross section given by semi-local duality agrees with data for moderate values of vertical bar t vertical bar, 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 γu→π+d. In the case of Compton scattering γp→γp 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. (author)