Connection between quark-model eigenstates and low-energy scattering

We propose a new method of analyzing low-energy hadron-hadron scattering designed to reveal internal quark-gluon eigenstates. Our method is a modification of the Wigner-Eisenbud formalism suited to the case of confining boundary conditions. We have identified a matrix function of the energy (which we call $P$) whose poles and residues correspond to the masses and channel projections of quark-gluon eigenstates calculated with spherical bag boundary conditions. To illustrate the formalism we apply it to the low-energy $S$-wave scattering of pseudoscalar mesons. We find from the data clear evidence of internal states corresponding to quark-model predictions of $Q^2{\overline{Q}}^2$ states at 0.69 and 1.04 GeV in the $I=0\mathrm{}$ channel, at 0.96 GeV in the $I=\frac{1}{2}$ channel, at 1.19 GeV in the $I=\frac{3}{2}$ channel, and at 1.04 GeV in the $I=2\mathrm{}$ channel. We believe the $I=\frac{3}{2} \mathrm{and} 2$ internal states to be the low-energy exotics long predicted by quark models.