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-质子散射差分截面的缩放定律


我们表明，弹性散射 pp→pp 差分截面是四动量传递平方 |t|具有通用特性，因此从 ISR 到 LHC 的能量，从几十 GeV 到 TeV 标度，凸点与浸入位置的比率是恒定的。我们探索了这一特性，以比较在 ISR 上观察到的几何缩放与 LHC 最近提出的缩放定律。我们认为，在 LHC，在目前的实验不确定性中，实际上存在一系列缩放定律。我们讨论了缩放定律对弹性 pp→pp 散射振幅参数化的约束。