AI 中文总结
研究弹性质子-质子碰撞中的几何标度，通过交叉对称性等确定散射振幅实虚部，计算相关参数，探讨总弹性截面能量依赖性及峰谷外几何标度违反情况，论证其在LHC仍成立。
AI 中文摘要
五十多年前在ISR就推测并观测到了几何标度。我们认为它在LHC仍然成立。我们表明，微分弹性截面的峰谷结构呈现出显著的规律性，即从23 GeV到13 TeV，峰谷位置之比恒定。利用交叉对称性、解析性和光学定理，我们确定了散射振幅的实部和虚部。这使我们能够计算ρ参数和微分质子-质子截面的峰谷值之比。最后，我们讨论了总弹性截面与总截面相比的能量依赖性，以及LHC峰谷区域外几何标度的违反情况。
英文摘要
Geometric scaling was conjectured and observed at the ISR more than 50 years ago. We argue that it still holds at the LHC. We show that the dip-bump structures of the differential elastic cross-sections exhibit a remarkable regularity, namely that the ratio of the bump to dip positions is constant from 23 GeV to 13 TeV. Using crossing symmetry, analicity and the optical theorem, we identify the imaginary and real parts of the scattering amplitude. This allows us to compute the $ρ$ parameter and the ratio of the bump to dip values of the differential $pp$ cross-section. Finally, we discuss the energy dependence of the total elastic cross-section as compared to the total cross-section, and the violation of geometrical scaling outside the dip-bump region at the LHC.
Comments9 pages, 6 figures, presented at 53rd International Symposium on Multiparticle Dynamics (ISMD 2025), Corfu, Greece, Sep 21 - 26, 2025
Journal refPoS(CORFU2025)426
