Construction of Crossing-Symmetric Amplitudes Satisfying Duality

Abstract

The general problem of constructing crossing-symmetric amplitudes satisfying duality for spinless two-body scattering processes is studied. An integral representation is first given for a sum of direct-channel resonance contributions. When one demands that this sum be dual and crossing-symmetric, the integrand is found to satisfy equations and asymptotic conditions, the general solutions to which are obtained. An infinity of solutions is found, implying that an infinity of amplitudes may then be constructed. The Veneziano amplitude is shown to be among the simplest. The Regge-pole content of these amplitudes is then given, and factorization is shown to be satisfied only at the expense of a degeneracy in the angular momentum spectrum.