Modified Phase Representation and Effects of Inelasticity in N/D Calculation of p-Wave Pion-Pion Scattering

An N/D formalism based on a modified phase representation is used to study the effects of inelasticity on the ρ-wave pion-pion amplitude. The effects of high-energy inelasticity are introduced in terms of the assumed behavior of the high-energy phase (not phase shift) of the partial-wave amplitude. Using a ρ-exchange input force with the experimental ρ mass and a ρ width of about 100 MeV, and the assumption that the average phase is (1/2)π, for total c.m. energies greater than about 8Mπ, we find that there is no appreciable reduction in the width of the calculated ρ-wave resonance. We also investigate the effects of low-energy inelastic channels that may contribute through the inelasticity parameter η for E ≤ Ei, where Ei is the energy above which the phase assumption is made. None of the forms for η that were used resulted in an output width less than about 280 MeV