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