Dynamical equations for a Regge theory with crossing symmetry and unitarity. II. The case of strong coupling, and elimination of ghost poles

Abstract

Equations for the construction of a crossing-symmetric unitary Regge theory of meson-meson scattering are described. In the case of strong coupling, Regge trajectories are to be generated dynamically as zeros of the $D$ function in a nonlinear $\frac{N}{D}$ system. This paper is concerned mainly with writing the inputs to the $\frac{N}{D}$ system in such a way that a convergent theory with exact crossing symmetry is defined. The scheme demands elimination of ghosts, i.e., bound-state poles at energies below threshold where trajectories pass through zero. A method for ghost elimination is proposed which entails an $s$-wave subtraction constant, and allows the physical $s$ wave to be different from the $l$-analytic amplitude evaluated at $l = 0$. A dynamical model is suggested in which the subtraction constant alone generates the meson-meson interaction. An alternative ghost-elimination scheme proposed by Gell-Mann, in which only $l$-analytic amplitudes are involved, can be discussed in a formalism including channels with spin.