Meson-Baryon Interactions with BrokenSU(3)and the Baryon Spectrum in Relativistic Quantum Mechanics

Abstract

The multichannel relativistic Schr\"odinger equation is solved for the ${\frac{1}{2}}^{+}$ and ${\frac{3}{2}}^{+}$ partial-wave amplitudes and their Regge recurrences with an energy-dependent potential obtained by computing the baryon-exchange contribution to the pseudoscalar-meson-baryon interaction. As discussed previously, the model yields the usual ${\frac{3}{2}}^{+}$ decuplet and predicts in addition a 27-dimensional representation and a radially excited decuplet in this partial wave. It is shown that in the range of parameters which fit the usual decuplet, there are also decuplet orbital excitations in the ${\frac{7}{2}}^{+}$ and ${\frac{11}{2}}^{+}$ partial-wave amplitudes which correspond to the known experimental resonances. The ${\frac{1}{2}}^{+}$ octet is obtained as deeply bound states, and a second ${\frac{1}{2}}^{+}$ octet or a $\overline{1}\overline{0}$ representation is predicted, depending on whether the $\frac{F}{D}$ ratio is less than or greater than 0.34. In addition, an orbital excitation of the octet occurs in the ${\frac{5}{2}}^{+}$ partial-wave amplitude at very high energies. The $P$-wave phase shifts are in qualitative agreement with experiments, but there are deviations for the ${P}_{33}$ effective range near threshold and for the ${P}_{13}$ phase shifts at higher energies.