Geometric scaling of elastic $pp$ cross section at the LHC

Abstract

We show that geometric scaling conjectured and observed at the ISR more than 50 years ago, still holds at the LHC. We discuss regularities of the dip-bump structures of the differential elastic cross sections, emphasizing the fact that the ratio of bump to dip positions is constant from the ISR to the LHC. Applying crossing and analyticity we identify imaginary and real parts of the scattering amplitude and compute the $\rho$ parameter and the ratio of bump to dip values of the differential $pp$ cross sections. We also discuss the energy dependence of the total elastic cross section and the violation of geometrical scaling outside the dip-bump region at the LHC.

10 pages, 4 figures. v2 accepted in Physics Letters B

References in corpus (6)

• Measurement of the total cross section from elastic scattering in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector
• Measurement of the total cross section from elastic scattering in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Hadronic forward scattering: Predictions for the Large Hadron Collider and cosmic rays
• Comparison of $pp$ and $p\bar{p}$ differential elastic cross sections and observation of the exchange of a colorless $C$-odd gluonic compound
• Measurement of the total cross section and $\rho$-parameter from elastic scattering in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector
• Scaling properties of elastic proton-proton scattering at LHC energies