Soft diffraction at the LHC: a partonic interpretation

TL;DR

This paper develops a new generation model for soft proton-proton interactions that merges multichannel eikonal scattering with a rich set of multi-Pomeron vertices, enabling a unified description of $\sigma_{tot}$, $d\sigma_{el}/dt$, and both low- and high-mass diffractive dissociation within a partonic evolution framework. By introducing Good–Walker diffractive eigenstates and resumming enhanced multi-Pomeron diagrams through generalized vertices, the authors show that absorptive effects are stronger than in naive triple-Pomeron treatments but can be mitigated by the complex vertex structure, leading to a prediction of $\sigma_{tot}$ around 90 mb at LHC energies and nontrivial survival factors for rapidity gaps. The model is tuned to ISR–Tevatron data and explores various proton-eigenstate size scenarios (A vs B), finding that size-differentiated models (B) generally fit elastic and diffractive data better and yield more realistic diffractive cross sections. The work provides a theoretically consistent, partonic interpretation of soft diffraction, assesses gap-survival effects, and offers practical predictions for LHC phenomenology, including central exclusive production and diffractive dissociation channels. Overall, it demonstrates that combining multichannel eikonal dynamics with comprehensive multi-Pomeron contributions yields a coherent description of soft hadronic interactions with implications for collider phenomenology and cosmic-ray physics.

Abstract

We present a `new generation' model for high energy proton-proton `soft' interactions. It allows for a full set of multi-Pomeron vertices, as well as including multichannel eikonal scattering. It describes the behaviour of the proton-proton total, sigma(total), and elastic dsigma(el)/dt, cross sections together with those for low and high mass proton dissociation. Although the model contains a comprehensive set of multi-Pomeron diagrams, it has a simple partonic interpretation. Including the more complicated multi-Pomeron vertices reduces the absorptive effects as compared to the predictions in which only the triple-Pomeron vertex is considered. Tuning the model to describe the available `soft' data in the CERN ISR - Tevatron energy range, we predict the total, elastic, single- and double-diffractive dissociation cross sections at the LHC energy. An inescapable consequence of including multichannel eikonal and multi-Pomeron effects is that the total cross section is expected to be lower than before: indeed, we find sigma(total) \simeq 90 mb at the LHC energy. We also present differential forms of the cross sections. In addition we calculate soft diffractive central production.

Figures (24)

• Figure 1: A typical multi-Pomeron fan diagram contributing to the interaction between a small size beam particle and a large size target particle.
• Figure 2: The connection between the full amplitude $F_{ik}$ and the irreducible amplitude $f_{ik}$ for scattering between $i$ and $k$ diffractive eigenstates.
• Figure 3: A 'soft' high energy interaction in which partons originating from the dissociations of the colliding protons overlap in rapidity. The overlap illustrates the impossibility of describing high-mass diffraction in terms of a pure eikonal (Good-Walker) formalism. Note that the master equations which describe the evolution of these 'parton showers' are introduced in Section 4.2.
• Figure 4: The addition of the triple-Pomeron diagram which allows for high-mass, $M$, diffractive dissociation.
• Figure 5: The diagrams on the left-hand-side constitute the Schwimmer model. We also show a more complicated diagram.