Two-Channel Calculation for theϱMeson by the Effective-Potential Method

Abstract

The width and the mass of the $\rho$ meson are calculated in the coupled $\pi \pi -K\overline{K}$ problem, using an effective potential in a Schrödinger equation to unitarize the input. It is found that the coupling to the closed $K\overline{K}$ channel has a considerable narrowing effect on the $\rho$ resonance. The calculation is free of any arbitrary parameter such as cutoffs or the subtraction points. With about 10% self-consistency we obtain $m_{\rho }\approx 5.5$ pion masses and the reduced width $\approx 0.36$. We also include the effect of $f^0$ to obtain the reduced width $\approx 0.215$ and mass $\approx 4.6$. The width of the $\rho$ comes out considerably smaller than in the usual claculations.