Improvement of multichannel amplitudes for the pion-pion scattering using the dispersion relations

TL;DR

This paper refines multichannel pion-pion scattering amplitudes by applying dispersion relations and crossing symmetry, achieving better consistency with experimental data and revealing shifts in key resonance poles.

Contribution

It introduces modifications to existing amplitudes using dispersion relations and crossing symmetry, enhancing their accuracy in the low-energy region.

Findings

Amplitudes agree with experimental data up to 1.8 GeV

Dispersion relations are satisfied up to 1.1 GeV

S-wave pole positions are significantly altered

Abstract

The multichannel S- and P-wave amplitudes for the pion-pion scattering, constructed requiring analyticity and unitarity of the S-matrix and using the uniformization procedure, are elaborated using the dispersion relations with imposed crossing symmetry condition. The amplitudes are modified in the low-energy region to improve their consistency with experimental data and the dispersion relations. Agreement with data is achieved for both amplitudes from the threshold up to 1.8 GeV and with dispersion relations up to 1.1 GeV. Consequences of the applied modifications, e.g. changes of the S-wave lowest-pole positions, are presented.