Introduction to the physics of the total cross-section at LHC: A Review of Data and Models

Abstract

This review describes the development of the physics of hadronic cross sections up to recent LHC results and cosmic ray experiments. We present here a comprehensive review -written with a historical perspective -about total cross-sections from medium to the highest energies explored experimentally and studied through a variety of methods and theoretical models for over sixty years. We begin by recalling the analytic properties of the elastic amplitude and the theorems about the asymptotic behavior of the total cross-section. A discussion of how proton-proton cross-sections are extracted from cosmic rays at higher than accelerator energies and help the study of these asymptotic limits, is presented. This is followed by a description of the advent of particle colliders, through which high energies and unmatched experimental precisions have been attained. Thus the measured hadronic elastic and total cross-sections have become crucial instruments to probe the so called soft part of QCD physics, where quarks and gluons are confined, and have led to test and refine Regge behavior and a number of diffractive models. As the c.m. energy increases, the total cross-section also probes the transition into hard scattering describable with perturbative QCD, the so-called mini-jet region. Further tests are provided by cross-section measurements of γp, γ * p and γ * γ * for models based on vector meson dominance, scaling limits of virtual photons at high Q 2 and the BFKL formalism. Models interpolating from virtual to real photons are also tested. It seems to us to be a necessary task to explore bit-by-bit the rigorous consequences of analyticity, unitarity and crossing. Who knows if someday one will not be able to reassemble the pieces of the puzzle. -A.

Relative entropy in scattering and the S-matrix bootstrap

“…(1.2) and related expressions, the quantity of interest that appears is ln σ ′ el (x) and its second derivative. Curiously, when experimentalists model the diffraction peak in scattering, they introduce a slope parameter which involves precisely this quantity and its first derivative [46] 18 -the second derivative is presumably related to the curvature of the diffraction peak. As such this formula appears to be quite suited for experimental investigations in the future.…”

Quark-Gluon Backscattering in the Regge Limit at One-Loop

“…When the logarithms are resummed, the amplitude scales like (s/t) γ where γ is called the Regge trajectory [1][2][3][4][5][6][7]. The structure of scattering amplitudes in the Regge limit is of interest in a wide variety of applications, including the total cross sections at colliders [8], unitarity constraints, integrability [9,10], factorization-violation [11][12][13][14], and bootstrapping scattering amplitudes in N = 4 super-Yang Mills theory [15][16][17][18][19][20].…”

Investigation of the leading and subleading high-energy behavior of hadron-hadron total cross sections using a best-fit analysis of hadronic scattering data

“…The study of soft high-energy physics has so far mostly proceeded through phenomenological models (for a recent review see Ref. [2]), on one side, and through general results obtained using basic properties of the theory, like unitarity and analyticity. Such general results are usually incorporated in the phenomenological models, for example exploiting them to set constraints on the functional form of observables concerning their dependence on energy and momentum transfer.…”

“…The recent measurements of σ tot at the Large Hadron Collider (LHC) at CERN have brought back the attention to the energy dependence of this quantity at high energy, with several new phenomenological analyses of the data (see Ref. [2] and references therein). Such measurements, made by the TOTEM Collaboration at √ s = 7 TeV and √ s = 8 TeV [8][9][10][11][12],…”