Superconvergence Relations and Possible New Resonances in Pion-Baryon Scattering

Superconvergence relations for the $B^{\mathrm{}(+)\mathrm{}}$ amplitudes at $t=0\mathrm{}$ for pion-baryon scattering are well saturated by low-lying resonances, except for the one for the $\pi -\Sigma$ scattering. This remarkable disparity suggests that some new $\pi -\Sigma$ resonances may exist. From the unitarity condition on the $p$-wave $\pi -\Sigma$ scattering, it is shown that the resonances, if any, are in $(I, J^P)=(0, {\frac{3}{2}}^{+}) \mathrm{and} (2, {\frac{3}{2}}^{+})$ states.