Consistency of pipi phase shift analyses with rho^0(770)-f_0(980) spin mixing in pi(-)p->pi(-)pi(+)n

TL;DR

This paper performs phase shift analyses of pion-pion scattering data using two methods, revealing consistent results and evidence for rho^0(770)-f_0(980) spin mixing, advancing understanding of meson interactions.

Contribution

It introduces a Spin Mixing Mechanism analysis that confirms previous phase shift solutions and provides new evidence for meson spin mixing phenomena.

Findings

Agreement with previous Cracow solutions validates the analyses.

Evidence for rho^0(770)-f_0(980) spin mixing in transversity amplitudes.

Model-independent amplitude analyses support the spin mixing hypothesis.

Abstract

We have performed two analytical pipi phase shift analyses using a Standard amplitude analysis of the CERN data on pi(-)p->pi(-)pi(+)n on polarized target at 17.2 GeV/c and a more recent analysis of the same data using Spin Mixing Mechanism (SMM). There are two solutions for helicity amplitudes labeled (1,1) and (2,2) in the Standard analysis and SpinMixing and S-Matrix in the SMM analysis which are related to the pipi scattering amplitudes. Our first phase shift analysis is an elastic scattering analysis below KKbar threshold. Our second analysis is a joint pipi phase shift analysis of pi(-)pi(+) and pi(0)pi(0) data below 1080 MeV. Our elastic Solution (2,2)1 and elastic Solution SpinMixing 1 for delta^0_S are in a remarkable agreement with the 1997 Cracow Solution Down-flat using the same CERN data on polarized target. Our joint Solution (2,2) and joint Solution SpinMixing are also in a remarkable agreement with the 2002 joint Cracow Solution Down-flat. Solutions elastic (1,1) and joint (1,1) agree with the Cracow Solutions Up-flat and are rejected. Model independent amplitude analyses of measurements of pi(-)p->pi(-)pi(+)n at 17.2 and 1.78 GeV/c and pi(+)n->pi(+)pi(-)p at 5.98 and 11.85 GeV/c reveal evidence for rho^0(770)-f_0(980) spin mixing in the S-wave transversity amplitudes. These transversity amplitudes define single-flip helicity amplitudes which have been related to pipi scattering amplitudes. Our key observation is that the presented and the Cracow solutions are consistent with the evidence for rho^0(770)-f_0(980) spin mixing in the measured transversity amplitudes from which all these phase shifts ultimately arise.