We show that elastic scattering pp→pp differential cross sections as function of the four-momentum transfer square |t| have a universal property, such that the ratio of bump-to-dip positions is constant from the energies of the ISR to the LHC, from tens of GeV and up to the TeV scale. We explore this property to compare the geometrical scaling observed at the ISR with the recently proposed scaling law at the LHC. We argue that, at the LHC, within present experimental uncertainties, there is in fact a family of scaling laws. We discuss the constraints that the scaling laws impose on the parametrization of the elastic pp→pp scattering amplitude.

中文翻译：

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弹性质子-质子散射微分截面的标度定律


我们证明弹性散射 pp→pp 微分截面是四动量传递平方 |t| 的函数具有通用属性，使得从 ISR 到 LHC 的能量，从数十 GeV 到 TeV 尺度，凹凸位置的比率是恒定的。我们探索这一特性，将 ISR 观察到的几何尺度与最近提出的 LHC 尺度定律进行比较。我们认为，在大型强子对撞机上，在目前实验的不确定性范围内，实际上存在一系列标度定律。我们讨论了缩放定律对弹性 pp→pp 散射幅度参数化的约束。