Forward Physics at the LHC; Elastic Scattering

TL;DR

This paper discusses the expected features of elastic proton-proton scattering at the LHC, including the structure of the scattering cone, the diffraction minimum, and the transition from soft to hard physics, emphasizing model-independent measurements and potential saturation effects.

Contribution

It provides detailed predictions for the near-forward elastic scattering effects at the LHC, including the structure of the cone, diffraction minima, and the transition from soft to hard regimes, with emphasis on model-independent analysis.

Findings

Predicted a break in the cone near |t|≈0.1 GeV^2 due to the two-pion threshold.

Expected the diffraction minimum to occur between 0.4 and 1 GeV^2, with specific depth characteristics.

Discussed the potential saturation of the black disc limit and its implications.

Abstract

The following effects in the nearly forward ("soft") region of the LHC are proposed to be investigated: 1) At small |t| the fine structure of the cone (Pomeron) shouldbe scrutinized: a) a break of the cone near $t\approx - 0.1 ~ GeV$^2, due to the two-pion threshold, and required by t-channel unitarity, is expected, and b) possible small-period oscillations between $t=0$ and the dip region. 2) In measuring the elastic $pp$ scattering and total $pp$ cross section at the LHC, the experimentalists are urged to treat the total cross section $\sigma_t,$ the ratio $\rho$, the forward slope $B$ and the luminosity ${\cal L}$ as free arameters, and to publish model-independent results on ${dN/{dt}}.$ 3) Of extreme interest are the details of the expected diffraction minimum in the differential cross section. Its position, expected in the interval $0.4<-t<1$ GeV$^2$ at the level of about $10^{-2} {\rm mb} \cdot$ GeV$^{-2}\div 10^{-1} {\rm mb}\cdot$ GeV$^{-2}$, cannot be predicted unambiguously, and its depth, i.e. the ratio of $d\sigma/dt$ at the minimum to that at the subsequent maximum (about $-t=5 $GeV$^2$, which is about 5 is of great importance. 4) The expected slow-down with increasing $|t|$ of the shrinkage of the second cone (beyond the dip-bump), together with the transition from an exponential to a power decrease in $-t$, will be indicative of the transition from "soft" to "hard" physics. Explicit models are proposed to help in quantifying this transition. 5) In a number of papers a limiting behavior, or saturation of the black disc limit (BDL) was predicted. This controversial phenomenon shows that the BDL may not be the ultimate limit.