LOW-ENERGY PION-PION SCATTERING AND PION ELECTROMAGNETIC VERTEX FUNCTIONS (TIME REVERSAL, ELECTRON-POSITRON)

In this thesis we investigate low energy pion-pion scattering and pion electromagnetic vertex functions.; A two-channel N/D method is used to analyze the (pi)(pi) scattering p-wave phase shift and inelasticity data up to 2 GeV c.m. energy. We show that if the inelastic scattering of the pions is represented by the second quasi-two-body channel, a two-channel parameteriza- tion with two subtractions provides an excellent representation of the data. In addition, the correct p-wave scattering length is obtained in agreement with dispersive sum rules.; The same two-channel model is used to construct 2(pi) and 4(pi) electromagnetic form factors. We find that a good representation of the pion form factor can be achieved but only at the expense of the F(,4(pi)) form factor. It seems to be difficult to reconcile all of the data in the (rho)(1600) region within a two resonance framework indicating additional rho-like resonant structure in this energy region. As a byproduct of our analysis, new values of the electromagnetic pion radius are obtained.; A minimal multichannel N/D model which can describe the pion-pion scattering processes ((pi)(pi) (--->) (pi)(pi), (pi)('0)(omega), 4(pi)) has three channels one of which is nonresonant. N and D are parameterized in the channel space as 3 x 3 matrices. The matrix elements N(,ij) and D(,ij) are represented by a dispersion relation. The pion form factors and pion-pion elastic scattering amplitude are obtained from the model and compared to the existing data to reveal the resonance structure in the p-wave amplitude up to SQRT.(s) = 2 GeV c.m. energy. We find that a three-channel model represents the elastic (e('+)e('-) (--->) (pi)(pi)) as well as inelastic (e('+)e('-) (--->) 4(pi)) data very well and that the p-wave amplitude has only two resonances (rho)(770) and (rho)(1600). We also investigate the possibility of a (rho)(1250) resonance state and find that the p-wave amplitude is not consistent with the data if such a resonance is assumed to exist.