Analytic Approximation to the LowEnergy Solutions of Inverse Amplitude Dispersion Relations
Abstract
An analytic approximation to the solution of the inverse amplitude dispersion relations exhibiting two resonances with the same quantum numbers is presented. It is shown that, given a solution exhibiting one resonance, a double resonance solution can be produced without violating crossing symmetry if a CDD (Castillejo, Dalitz, and Dyson) pole is inserted near the original resonance position. In the presence of inelastic scattering the CDD pole must be off the real axis and will occur on an unphysical sheet. For various values of the pionpion coupling constant in the range 0.15<=λ<=0.1 the masses and widths of the ζ and ρ resonances are calculated.
 Publication:

Physical Review
 Pub Date:
 January 1963
 DOI:
 10.1103/PhysRev.129.937
 Bibcode:
 1963PhRv..129..937G