  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.

High Energy Physics - Phenomenology