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The analyticity properties of the scattering amplitude for a massive scalarfield is reviewed in this article where the spacetime geometry is$R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigatedthe analyticity of scattering amplitude in a nonrelativitstic potential modelin three dimensions with an additional compact dimension. He showed that, undercertain circumstances, the forward amplitude is nonanalytic. He argued that inhigh energy scattering if such a behaviour persists it would be in conflictswith the established results of quantum field theory and LHC might observe suchbehaviors. We envisage a real scalar massive field in flat Minkowski spacetimein five dimensions. The Kaluza-Klein (KK) compactification is implemented on acircle. The resulting four dimensional manifold is $R^{3,1}\otimes S^1$. TheLSZ formalism is adopted to study the analyticity of the scattering amplitude.The nonforward dispersion relation is proved. In addition the Jin-Martin boundand an analog of the Froissart-Martin bound are proved. A novel proposal ispresented to look for evidence of the large-radius-compactification scenario. Aseemingly violation of Froissart-Martin bound at LHC energy might hint that anextra dimension might be decompactified. However, we find no evidence forviolation of the bound in our analysis.

Analyticity Properties of Scattering Amplitude in Theories with Compactified Space Dimensions: The Proof of Dispersion Relations