Dynamical equations for a Regge theory with crossing symmetry and unitarity. I. Introduction, and the case of weak coupling

A program for construction of a crossing-symmetric unitary Regge theory of meson-meson scattering is proposed. The construction proceeds through solution of a nonlinear functional equation, psi = G (psi), for certain partial-wave scattering functions psi. The functional equation is analogous to a conventional dynamical equation, in that the scattering amplitude is generated from input functions which describe the primary forces between mesons and possible inelastic effects. A solution of the equation provides a scattering amplitude having Mandelstam analyticity, exact crossing symmetry, exact unitarity below the production threshold, and meromorphy of partial waves in the right-half l plane, with the consequent Regge asymptotics. Inelastic unitarity (0 < or = eta (l,s) < or = 1) is not guaranteed, but may perhaps be achieved through constraints on inputs. In any case, the partial waves are bounded throughout the physical region; such a bound was not ensured in earlier schemes based on the Mandelstam iteration. In this first paper of a series, the equations are formulated for the case of weak coupling, in which no Regge poles enter the right-half l plane. Inelastic effects are described by crossed two-particle processes and assigned input functions. Later papers will treat the case of strong coupling,more » in which Regge trajectories are generated dynamically, and the extension of the formalism to include many coupled channels.« less