Duality in Meson Electroproduction

We propose to study quark-hadron duality in meson electroproduction. While duality between inclusive electron-hadron scattering in the resonance and deep inelastic regimes (Bloom-Gilman or quark-baryon duality) is well established, the existence of a similar duality in meson electroproduction has not yet been tested. In the inclusive case, duality implies that single-quark scattering governs the scale of the reaction: the nucleon resonances act at low Q as one would expect from a scaling behavior. In the semi-inclusive case, the nucleon resonances may similarly a ect a scaling behavior in the nal meson channel. On the other hand, it could be that (for example) the resonance does not fall anomalously fast in semi-inclusive scattering, which would provide us with important clues about that phenomenon. New evidence for factorization of the cross section at low energy loss into two pieces quark scattering and quark fragmentation guides our approach to this measurement. We discuss an appropriate framework in which to investigate semi-inclusive duality, and propose a measurement designed to look for the existence of pionand, with lower statistics, kaon-tagged duality, which could be at the root of the unexpected low energy cross section factorization. This proposal addresses two issues, which are possibly related. Firstly, does the cross section still factorize at low energy loss, and can one reproduce the fragmentation functions determined from high energy scattering? Secondly, do the nucleon resonances average around these high energy fragmentation functions?