Hard exclusive electroproduction of two pions and their resonances

We study the hard exclusive production of two pions in the virtual photon f ragmentation region with various invariant masses including the resonance r egion. The amplitude is expressed in terms of two-pion light cone distribut ion amplitudes (2 pi DA's). We derive dispersion relations for these amplit udes, which enable us to fix them completely in terms of pi pi scattering p hases and a few low-energy subtraction constants determined by the effectiv e chiral Lagrangian. Quantitative estimates of the resonance as well as pi pi background DA's at low normalization point are made. We also prove a cer tain new soft pion theorem relating two-pion DA's to the one-pion DA. Cross ing relations between 2 pi DA's and parton distributions in the pion are di scussed. We demonstrate that by studying the shape of the pi pi mass spectra (not th e absolute cross section!) in diffractive electroproduction one can extract the deviation of the meson (pi, rho, etc.) wave functions from their asymp totic form 6z(1 - z) and hence get important information about the structur e of mesons. Also we discuss how the moments of the quark distributions in the pion can be measured in the hard diffraction, We suggest (as an alterna tive to Soding's) a parametrization of ir ir spectra which is suitable for large photon virtuality, (C) 1999 Elsevier Science B.V. All rights reserved .