Kπ scattering, k Meson, and current algebra

Abstract

We discuss Kπ scattering, using a low-energy-dominated sum rule derived from the SU(3)⊗SU(3) algebra of currents, assuming the pionic and the kaonic pole dominance hypotheses. The exact validity of the latter assumptions implies a much larger S-wave Kπ scattering in the I=½ channel than in the I=3/2 channel. The use of the current-algebra scattering lengths for threshold elastic Kπ scattering suggests that this discrimination is due to a scalar I=½ resonance. If this is the κ(725), a width ≥28±2 MeV is predicted. If, however, the error in kaonic pole dominance is greater than 30%, the existence of the κ would not be required.