A Local Duality Scheme and a Uniquely Determined - Born Amplitude

We apply a local duality scheme to a construction of a new Born amplitude for 7[-'7[+ scattering. We start with the most general Veneziano-type amplitude, which contains an infinite number of parameters, and restrict it by the two conditions: 1) A local duality scheme, which includes the SU(6)(8)O(3h hadron spectrum of the quark model. 2) An asymptotic convergence condition. The infinite number of paramete~s reduces to only four by condition 1) and further to three by 2). Apart from the overall multiplying factor the amplitude has only two parameters: the Regge slope times the square of the pion mass and the zero-intercept of the trajectory. In this parameter space we determine the region which is ghost-free for all resonant states and find that the physical values are included in this region. The overall multiplying factor is adjusted by p~27[ width. The predicted partial widths of low-lying resonances are in good agreement with available experiments. It also turns out that the amplitude satisfies Adler's PCAC condition in the limit of zero pion-mass. The amplitude takes two simple forms for certain values of the parameters; one is the same as the Neveu-Schwarz-Ramond amplitude and the other is quite a new one.