Scalar mesons in ππ and K¯K scattering

Existence of theσmeson below 1 GeV and chiral symmetry

“…The way of realization is a consistent allowance for the nearest singularities on all sheets of the Riemann surface of the S-matrix. Earlier, we have proposed this method for 2-and 3-channel resonances and developed the concept of standard clusters (poles on the Riemann surface) as a qualitative characteristic of a state and a sufficient condition of its existence [1,12]. The cluster kind is related to the state nature.…”

“…For the simultaneous analysis of experimental data on the coupled processes it is convenient to use the Le Couteur-Newton relations [14,15] expressing the S-matrix elements of all coupled processes in terms of the Jost matrix determinant d(k 1 , k 2 ), the real analytic function with the only square-root branch-points at k i = 0. Earlier, this was done by us in the 2-channel consideration [12] with the uniformizing variable z…”

“…which maps the 4-sheeted Riemann surface, having (in addition to two above-indicated unitary cuts) also the left-hand cut starting at s = 0, onto the v-plane. In On v-plane the Le Couteur-Newton relations are [12,16]…”