Reinterpreting several narrow ‘resonances’ as threshold cusps

Abstract

The threshold p¯p peak in BES data for J/Ψ→γp¯p may be fitted as a cusp. It arises from the well-known threshold peak in p¯p elastic scattering due to annihilation. Several similar examples are discussed. The PS185 data for p¯p→Λ¯Λ require an almost identical cusp at the Λ¯Λ threshold. There is likewise a cusp at the ΣN threshold in K−d→π−(Λp). Similar cusps are likely to arise at thresholds for all 2-body de-excitation processes, providing the interaction is attractive; likely examples are Λp¯, Σp¯, and K¯Λ. The narrow peak observed by Belle at 3872 MeV in π+π−J/Ψ may be a JPC=1++ cusp due to the DD¯* threshold. The narrow Ξ*(1862) observed by NA49 may be due to a threshold cusp in Σ(1385)K¯ coupled to Ξπ and ΣK¯. The relation of cusps to known resonances such as f0(980) is discussed.