Experimental disagreements with Extended Unitarity

TL;DR

The paper tests Extended Unitarity in production processes involving overlapping resonances and finds experimental disagreements, proposing a new approach based on observed magnitudes that better fits the data.

Contribution

It challenges the validity of Extended Unitarity in certain production processes and introduces a revised unitarity relation based on observed magnitudes.

Findings

Four data sets disagree with EU predictions.

Different relative magnitudes of sigma and fo(980) are required.

A new unitarity hypothesis fits the data better.

Abstract

In production processes, e.g. J/Psi -> omega-pi-pi or pbar-p -> 3pi, the sigma and fo(980) overlap in the same partial wave. The conjecture of Extended Unitarity (EU) states that the pi-pi pair should have the same phase variation as pi-pi 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 pi-pi 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 sigma and fo(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.