Pion-pion scattering and the diffractive production of nucleon resonances

Abstract

The physics related to two aspects of the π N → π π N reaction is studied. We first consider the imposition of the constraints of analyticity, unitarity and, in particular, crossing, on the pion-pion scattering amplitudes, as extracted from studies of the low dipion mass kinematic region of the π N → π π N reaction. The application of the Roy equations to pion-pion scattering is discussed, then physical region crossing sum rules are systematically derived and applied, in conjunction with finite energy sum rules, to obtain information on the asymptotic pion-pion scattering amplitudes. The amplitudes are found to be well described in terms of Regge and pomeron exchange, with rho-f strong exchange degeneracy broken and an asymptotic total cross section for pion-pion scattering rather smaller than that expected from naive factorization arguments. Other evidence for a small meson-meson scattering asymptotic total cross section is collected, and possible explanations for the apparent failure of the pomeron to factorize are discussed. The second part of this thesis deals with diffraction dissociation processes. We discuss how the Deck-Drell-Hiida mechanism, in conjunction with the diffractive production, and subsequent decay, of resonances provides a good qualitative explanation of many of the features of inelastic diffractive scattering. Detailed data on the angular distributions of the diffractively produced pion-nucleon system in the 16 GeV. π N → π π N reaction are then interpreted quantitatively in terms of a simple model based on the above ideas, with full account taken of spin and interference effects. Information is obtained on the pomeron couplings, and the high energy t channel isospin zero pion-pion scattering amplitude, directly determined, is found to be consistent with the sum rule calculation results and a small asymptotic pion-pion scattering total cross section.