Further study of the pi-pi S-wave isoscalar amplitude below the K - Kbar threshold

TL;DR

This paper analyzes the S-wave isoscalar pi-pi amplitude below the K-Kbar threshold using CERN--Cracow-Munich data, revealing limitations of narrow resonance models and suggesting more complex phase behavior.

Contribution

It provides a detailed analysis of S-wave amplitudes below the K-Kbar threshold and evaluates the physical plausibility of different solutions, challenging narrow resonance interpretations.

Findings

Narrow f0(750) resonance is incompatible with the data.

Certain solutions exhibit unphysical inelasticity behavior.

Phase shifts increase slowly in the rho(770) region.

Abstract

We continue the analysis of S-wave production amplitudes for the reaction pi- p -> pi+ pi- n involving the data obtained by the CERN--Cracow-Munich collaboration on a transversely polarized target at 17.2 GeV/c pi- momentum. This study deals with the region below the K - Kbar threshold. In particular, we study the "up-steep" solution containing a narrow S-wave resonance under the rho(770). This solution exhibits a considerable inelasticity (eta) which does not have any physical interpretation. Assuming that this inelasticity behaviour represents an unlikely fluctuation we impose eta = 1 for all data points. This leads to non-physical results in one third of the pi+pi- effective mass bins and in the remaining mass bins some parameters behave in a queer way. The situation is even worse for the "down-steep" solution. We conclude that the 17.2 GeV data cannot be described by a relatively narrow f0(750). The "down-flat" and "up-steep" solutions which easily pass the eta = 1 constraint exhibit a slow increase of phase shifts in the rho(770) mass range.