Model calculation for the Y₀^∗(1405) resonance state

Abstract

The Y₀^*(1405) resonance state is considered in terms of a multichannel potential arising from vector meson (V) exchange between the baryon octet (B) and the pseudoscalar meson octet (P). The interactions are assumed to follow SU(3) symmetry; the only symmetry breaking included is that arising from the PB threshold separations, due to the P and B mass splittings. The resonance mass corresponds to a reasonable value (f²/4π =1.25) for the VPP coupling; the width then calculated is 27 MeV, comparable with the empirical value. The unitary impurities found in this Y₀^* (1405) state are quite small, the octet admixtures being dominant and only 15% in total intensity. The effective range calculated for the K̅ N scattering length is not large, being of order 1/m_V. The relationship between the various choices possible for the definition of the resonance energy is also discussed explicitly for this case.