Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-09-22
Nucl.Phys.B555:231,1999
Physics
High Energy Physics
High Energy Physics - Phenomenology
30 pages, one figure. Discussion of crossing relations between meson distribution amplitudes and quark densities is added
Scientific paper
10.1016/S0550-3213(99)00314-4
We study the hard exclusive production of two pions in the virtual photon fragmentation region with various invariant masses including the resonance region. The amplitude is expressed in terms of two-pion light cone distribution amplitudes ($2\pi$DA's). We derive dispersion relations for these amplitudes, which enables us to fix them completely in terms of $\pi\pi$ scattering phases and a few low-energy subtraction constants determind by the effective chiral lagrangian. Quantitative estimates of the resonance as well $\pi\pi$ background DA's at low normalization point are made. We also prove certain new soft pion theorem relating two-pion DA's to the one-pion DA. Crossing relations between $2\pi$DA's and parton distributions in a pion are discussed. We demontrate that by studying the shape of the $\pi\pi$ mass spectra (not absolute cross section!) in a diffractive electroproduction one can extract the deviation of the meson ($\pi,\rho,$ etc.) wave functions from their asymptotic form $6 z(1-z)$ and hence to get important information about the structure of mesons. Also we discuss how the moments of quark distributions in a pion can be measured in the hard diffraction. We suggest (alternative to S\"oding's) parametrization of $\pi\pi$ spectra which is suitable for large photon virtuality.
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