Dispersion Relation Analyses of Pion Form Factor, Chiral Perturbation Theory and Unitarized Calculations

The Vector Pion form factor below 1 GeV is analyzed using experimental data on its modulus, the P-wave pion pion phase shifts and dispersion relation. It is found that causality is satisfied. Using dispersion relation, terms proportional to s squared and s cubed are calculated using the experimental data, where s is the momentum transfer. They are much larger than the one-loop and two-loop Chiral Perturbation Theory calculations. Unitarized model calculations agree very well with dispersion relation results.Comment: 10 pages, 4 PostScript figures some minor changes and added reference

When is it possible to use perturbation technique in field theory ?

The vector pion form factor is used as an example to analyze this question. Given the experimental radius of the pion, the crucial question is whether perturbative methods could be used for the effective chiral lagrangian to calculate the pion form factor. Our analysis shows that the pion rms radius is far too large (or the related rho resonance mass is too low) for the perturbation theory to be valid.Comment: 11 pages, Latex, 4 eps figs. Contribution to the proceedings of the workshop "QCD2000" Villefranche-sur-Mer, France, January 200

Dispersion Relations and Sum Rules for the pi ->gamma gamma* and gamma* ->gamma pi form factor

Sum rules for the off-shell isovector form factor pi -> gamma gamma* are given in terms of the pion form factor and the gamma pi ->pi pi experimental data. Similarly the corresponding sum rules for the isoscalar form factor are given in terms of the experimental photon-3 pi form factor and the gamma pi -> 3 pi amplitude. For some set of parameters, e.g. rho -> pi gamma width = 90 KeV, the pi -> gamma gamma rate and the slope parameter of the decay pi -> gamma e plus e minus are in good agreement with the experimental data.Comment: 13 page

Linear and nonlinear photonic Jackiw-Rebbi states in waveguide arrays

We study analytically and numerically the optical analogue of the Jackiw-Rebbi states in quantum field theory. These solutions exist at the interface of two binary waveguide arrays which are described by two Dirac equations with opposite sign masses. We show that these special states are topologically robust not only in the linear regime, but also in nonlinear regimes (with both focusing and de-focusing nonlinearity). We also reveal that one can generate the Jackiw-Rebbi states starting from Dirac solitons.Comment: 4 pages, 3 figure