Single-Channel Calculation of theρResonance with Inelastic Unitarity

The width and shape of the $\rho$ resonance are computed from a single-channel $\frac{N}{D}$ formalism with inelastic unitarity. The input force is assumed to be furnished primarily by the exchange of the $\rho$ in the crossed channels. The input mass (760 MeV) and width (∼100 MeV) are taken from experiment. The inelastic factor $\eta$ is assumed to be determined by the $\pi \pi \to \pi \omega$ reaction at low energy and fitted to various arbitrary forms at higher energies. A cutoff is adjusted to produce the $\rho$ resonance at the observed energy. The smallest output width obtained is 250 MeV, as compared with 600 MeV for the pure-elastic-scattering ($\eta \equiv 1$) calculation. A more nearly symmetric shape for the resonance is obtained when inelastic effects are considered.