Scalar mesons and low-mass sigma: Does the σ reveal the confinement singularity?
Abstract
I present a short review of the current understanding of the scalar meson sector, with special attention to the problem of the low-mass
σ
. The dispersion relation
N/D
-method used for the restoration of the low-energy
ππ
(I
J
PC
=
00
++
)
-wave amplitude is discussed. The low-energy
ππ
amplitude was determined from the data in the energy region 280--500 MeV and it was sewn with the previously found
K
-matrix solution for the region 450--1950 MeV. The
N/D
-amplitude has a pole on the second sheet of the complex-
s
plane, near the
ππ
threshold at
s
√
≃430−i325
MeV, that corresponds to the low-mass
σ
-meson. I discuss the hypothesis that this pole may be related to the confinement forces, thus being the eyewitness of confinement.