The analyticity properties of the scattering amplitude for a massive scalar field are reviewed in this paper where the space–time geometry is [Formula: see text], i.e. one spatial dimension is compact. Khuri investigated the analyticity of scattering amplitude in a nonrelativistic 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 behavior 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 space–time in five dimensions. The Kaluza–Klein (KK) compactification is implemented on a circle. The resulting four-dimensional manifold is [Formula: see text]. 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.

中文翻译：

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紧缩空间维数理论中散射幅度的解析性质：色散关系的证明

本文回顾了大质量标量场散射幅度的解析特性，其中时空几何为[公式：见正文]，即一个空间维度是紧致的。Khuri 研究了非相对论势模型中散射幅度的解析性，该模型在三个维度上具有额外的紧致维度。他表明，在某些情况下，正向幅度是非解析的。他认为，在高能散射中，如果这种行为持续存在，它将与量子场论的既定结果相冲突，LHC 可能会观察到这种行为。我们设想在五个维度的平坦 Minkowski 时空中存在一个真正的标量大质量场。Kaluza-Klein (KK) 紧化是在一个圆上实现的。得到的四维流形是[公式：见正文]。采用LSZ形式来研究散射幅度的解析性。证明了非前向色散关系。此外，还证明了 Jin-Martin 界和 Froissart-Martin 界的类似物。提出了一个新的提议来寻找大半径压缩场景的证据。在 LHC 能量上看似违反 Froissart-Martin 束缚可能暗示一个额外的维度可能会被解压缩。但是，我们在分析中没有发现违反界限的证据。在 LHC 能量上看似违反 Froissart-Martin 束缚可能暗示一个额外的维度可能会被解压缩。但是，我们在分析中没有发现违反界限的证据。在 LHC 能量上看似违反 Froissart-Martin 束缚可能暗示一个额外的维度可能会被解压缩。但是，我们在分析中没有发现违反界限的证据。