Modified S-wave $\pi\pi$ scattering amplitude for multiparticle PWA

TL;DR

This paper proposes a modified S-wave $ o \, ext{pi} ext{pi}$ scattering amplitude, mAMP, to better describe broad $S$-wave interactions in multiparticle PWA, addressing limitations of the AMP model at higher energies.

Contribution

The paper introduces a phenomenological modification to the AMP amplitude, improving its applicability for multiparticle PWA by better modeling threshold behavior and broad structures.

Findings

mAMP describes threshold behavior of $ o \, ext{pi} ext{pi}$ scattering.

It captures the broad structure around 1400 MeV/c^2.

The amplitude excludes $ o KK$ scattering, focusing on $ o \, ext{pi} ext{pi}$.

Abstract

Suggested by Au, Morgan, Pennington (AMP) S-wave isospin I=0 $\pi\pi$, $KK$ scattering amplitude is good enough to describe experimental data for the moment. Still it has two disadvantages for use in multiparticle partial wave analysis (PWA), namely sharp drop at the $KK$ threshold and unreasonable behavior at $M(\pi\pi) > 1.6\,GeV/c^2$. The drop is not seen in multiparticle systems. We suggest the modified AMP amplitude, mAMP, for the only aim, namely to describe the broad part of $S$-wave $\pi\pi\,\to\,\pi\pi$ scattering in the wide $M(\pi\pi)$ range in multiparticle PWA. The mAMP amplitude describes threshold behavior of the $\pi\pi\,\to\,\pi\pi$ scattering and the wide structure at $M\sim 1400\,MeV/c^2$ reasonably well. It is assumed that narrow objects $f_0(980)$, $f_0(1500)$ are included in PWA separately. The amplitude does not describe $\pi\pi\to KK$ scattering. The mAMP amplitude is purely phenomenological.