On the Validity of the Regge Formula in the Unqeual-Mass Case

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Abstract
The validity of the Regge formula in the relativistic scattering theory is examined on the basis of the Green's function formalism. It is shown that in the unequal-mass case some Regge trajectories on the mass shell become ghosts in a certain real interval of the invariant energy squared. THis result clarifies how the kinematical unphysical singularities appearing in the Khuri formula are canceled by the daughter trajectories proposed by Freedman and Wang. The order of the daughter trajectory is identified with n-l-1, where n and l are the principal and the azimuthal (angular momentum) quantum number, respectively. The Khuri asymptotic formula in the unequal-mass case is discussed in a ladder model of massless-scalar-particle exchange, and is explicitly demonstrated to be free from the kinematical unphysical singularities.

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