Analysis of theJP=1+three-pion system using a generalized Watson theorem for production of multiquark states

We analyze the $J^P=1^{+}$ three-pion production amplitudes obtained from the most recent diffractive, charge-exchange, and backward-production experiments. We have found effects in the amplitudes that we interpret in terms of $q\overline{q}$, $q^2{\overline{q}}^2$, and $q^3{\overline{q}}^3$ interactions. tions. The $q\overline{q}$ piece gives rise to the $A_1$ resonance whose parameters are $M_{A_1}=1230\mathrm{}\pm 30$ MeV and ${\Gamma }_{A_1}=330\mathrm{}\pm 60$ MeV, whereas the backward-production reaction shows a strong $q\overline{q}$ and $q^2{\overline{q}}^2$ interference effect. The $\epsilon \pi$ scattering couples only to the $q^2{\overline{q}}^2$ and $q^3{\overline{q}}^3$, and thus argues in favor of Jaffe's four-quark model of the $\epsilon$.