Amati-Bertocchi-Fubini-Stanghellini-Tonin Equation and Complex Regge Poles

The $J$-plane singularity structure of the solution of an Amati-Bertocchi-Fubini-Stanghellini-Tonin (ABFST) equation is explored numerically. One real pole and two complex conjugate pairs of poles are found in the region $\mathrm{Re}J>-2\mathrm{}$. The values of the imaginary parts of the complex-pole positions depend only on the multiparticle amplitude in the region of extremely small momentum transfer between links ($-t\lesssim {m_{\pi }}^2$). This result arises from the fact that the dependence of the diagonalized ABFST equation on the small-momentum-transfer region is strongly enhanced for $\mathrm{Re}J<\mathrm{}0\mathrm{}$. The residues of first pair of complex poles and the real pole are determined. The dependence of the pole positions and residues on the coupling constant is discussed.