Self-Consistent ρ Trajectory in the New Form of the Strip Approximation

The new form of the strip approximation, devised by Chew, is applied to the problem of "bootstrapping" a ρ trajectory in the π-π system. Even in the absence of other trajectories it is possible to obtain a self-consistent ρ trajectory and residue functions α(t) and γ(t) for $t<0$, with strip widths in the range 150 to 300 m_π^_². A particular example is given in detail. The absence of the force from other trajectories, and the rapid variation of α(t) and γ(t) for $t>~0$, mean that our results can not represent the real ρ trajectory, but at least they confirm the viability of the methods used.