ηππ model of X⁰ and a possible η-π resonance

Abstract

An ηππ model of the X⁰ meson at 960 MeV is proposed through factorable π-π and η-π s-wave forces. The over-all dynamics is described by a three-body Schrödinger equation under a nonrelativistic approximation which is justified by the relatively low Q value (∼120 MeV) of the particle with respect to decay into an ηππ system. The π-π interaction, which is used as input information, is taken to be of two types: (i) a smooth attractive force which falls short of the requirements of a π-π bound state (called ABC-type), and (ii) a force characterized by a long-range barrier surrounding an inner well, which is capable of producing a π-π resonance at several hundred MeV (called σ-type interaction). Using three-body techniques proposed earlier by one of us (A.N.M.), the nature and strength of the η-π interaction is deduced from a knowledge of the energy of the ηππ system at the experimental position of the X⁰-mass. It is found that a σ-type π-π interaction, designed to produce a π-π resonance at 400-600 MeV, requires the existence of a bound η-π system. On the other hand, an ABC-type π-π interaction demands an η-π resonance in the BeV region (via a σ-type η-π interaction). The physical implications of these results are discussed.