Introduction to the physics of the total cross section at LHC

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 60 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 γ p, 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.

Analysis and implications of precision near-forward TOTEM data

“…7. Both items 5 and 6 above suggest that cross sections very likely rise less fast than L 2 (s) [8]. Clearly, further data are required to settle this crucial issue.…”

“…Hence, these are predictions for the absolute differential cross section at √ s = 8 and 13 TeV as well as for the total cross section σ tot , the elastic one σ el and ρ parameter, that are discussed later. Figures 1 and 2 show differential cross sections data, model predictions dσ j /dt(s 8,13 ,t) and the corresponding residuals R j (s,t), in the four cases labeled with j = 0, 1, 2, 3 and at √ s = 8 and 13 TeV. The jth differential cross section is obtained as…”

“…Using the nomenclature from the soft-gluon resummation work reviewed in Ref. [8], we may write the forward elastic amplitude-using the rule discussed in Sec. III-as follows.…”

“…In the present paper, we shall analyze the TOTEM results for the CNI region at √ s = 8 and 13 TeV through a recently studied model [7,8], which is a modified version of a model originally proposed by Barger and Phillips (BP) [9]. The BP amplitude was proposed as an "independent" model to highlight the main characteristics of the elastic diffractive cross section, namely the forward peak, the dip-bump structure arising from the zero of the imaginary part of the amplitude in pp, the slower, powerlike decrease at large −t.…”

The Phillips–Barger model for the elastic cross section and the Odderon

“…In particular, the high-precision measurement of the elastic differential cross section data (dσ/dt) in the Coulomb-Nuclear interference region in proton-proton (pp) scattering, performed by the TOTEM Collaboration [7], has allowed the determination of the ρ parameter, which is defined as the ratio between the real and imaginary part of the elastic scattering amplitude in the forward direction. The value obtained experimentally is lower than those predicted by different Regge inspired models that take into account the Reggeon and Pomeron exchange contributions for the scattering amplitude, whose predictions for the total cross section (σ tot ) are compatible with the measurements [12]. Such result has motivated an intense debate about the possible contribution of the Odderon [13][14][15][16][17][18][19][20].…”