Analyticity properties of scattering amplitude in theories with compactified space dimensions

Abstract

We consider a massive scalar, neutral, field theory in a five dimensional flat spacetime. Subsequently, one spatial dimension is compactified on a circle, S1, of radius R. The resulting theory is defined in the manifold, R3,1⊗S1, consists of a states of lowest mass, m0, and a tower of massive Kaluza-Klein states. The analyticity property of the elastic scattering amplitude is investigated in the frame works of Lehmann-Symanzik-Zimmermann formulation of this field theory. In the context of nonrelativistic potential scattering, for R3⊗S1 spatial geometry, it was shown that the forward scattering amplitude does not satisfy analyticity for a class of potentials which might have important consequences if same attribute holds in relativistic quantum field theories. We address this issue with R3,1⊗S1 geometry. We show that the forward scattering amplitude of the theory satisfying LSZ axioms does not suffer from lack of analyticity. The importance of the unitarity constraint is exhibited in displaying the properties of the absorptive part of the forward amplitude.