\pi\pi, K\pi and \pi N potential scattering and a prediction of a narrow \sigma meson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.Comment: 42 pages, 17 PS figures, REFTeX, epsfig.sty needed, submitted to Phys. Re

Mesonic cloud contribution to the nucleon and delta masses

Pion-nucleon elastic scattering in the dominant $P_{33}$ channel is examined in the model in which the interaction is of the form $\pi + N\leftrightarrow N, \Delta(1232)$. New expressions are found for the elastic pion-nucleon scattering amplitude which differ from existing formula both in the kinematics and in the treatment of the renormalization of the nucleon mass and coupling constant. Fitting the model to the phase shifts in the $P_{33}$ channel does not uniquely fix the parameters of the model. The cutoff for the pion-nucleon form factor is found to lie in the range $\beta = 750\pm350$ MeV/c. The masses of the nucleon and the $\Delta$ which would arise if there were no coupling to mesons are found to be $m_{_N}^{(0)}= 1200\pm 200$ MeV and $m_\Delta^{(0)} = 1500\pm 200$ MeV. The difference in these bare masses, a quantity which would be accounted for by a residual gluon interaction, is found to be $\delta m^{(0)}=350\pm 100$ MeV.Comment: 26 pages, 9 figures, significant rewrit