Experimental disagreements with Extended Unitarity

In production processes, e.g. J/Ψ → ωππ or p̄p → 3π, the σ and f0(980) overlap in the same partial wave. The conjecture of Extended Unitarity (EU) states that the ππ pair should have the same phase variation as ππ elastic scattering. This is an extension of Watson’s theorem beyond its original derivation, which stated only that the s-dependence of a single resonance should be universal. The prediction of EU is that the deep dip observed in ππ elastic scattering close to 1 GeV should also appear in production data. Four sets of data disagree with this prediction. All require different relative magnitudes of σ and f0(980). That being so, a fresh conjecture is to rewrite the 2-body unitarity relation for production in terms of observed magnitudes. This leads to a prediction different to EU. Central production data from the AFS experiment fit naturally to this hypothesis. PACS numbers: 13.25.-k, 13.25.Gv, 13.75.Lb