Diffraction and correlations at the LHC: definitions and observables

TL;DR

This paper analyzes the ambiguity in defining diffractive events at the LHC, contrasting unitarity-based and LRG/Pomeron-exchange definitions and highlighting that LRGs can stem from Reggeon exchange or fluctuations. It combines analytic estimates and Monte Carlo studies to show that fluctuations can mimic sizable diffractive signals, complicating the extraction of Pomeron contributions, especially for DPE processes. The authors propose measuring long-range rapidity correlations (R2) and multi-gap events in early LHC runs as probes of soft, multi-Pomeron dynamics, and discuss detector coverage requirements to disentangle backgrounds. Overall, the work argues for a cautious, model-aware interpretation of diffraction signals and outlines experimental strategies to constrain soft QCD physics at the LHC.

Abstract

We note that the definition of diffractive events is a matter of convention. We discuss two possible `definitions': one based on unitarity and the other on Large Rapidity Gaps (LRG) or Pomeron exchange. LRG can also arise from fluctuations and we quantify this effect and some of the related uncertainties. We find care must be taken in extracting the Pomeron contribution from LRG events. We show that long-range correlations in multiplicities can arise from the same multi-Pomeron diagrams that are responsible for LRG events, and explain how early LHC data can illuminate our understanding of `soft' interactions.

Figures (8)

• Figure 1: (a) The single-channel eikonal description of elastic scattering; (b) the multichannel eikonal formula which allows for low-mass proton dissociations in terms of diffractive eigenstates $|\phi_i\rangle,~|\phi_k\rangle$; and (c) the inclusion of the multi-Pomeron-Pomeron diagrams which allow for high-mass dissociation. In all these diagrams the exchanged lines represent Pomeron exchange.
• Figure 2: (a) A 'soft' high energy interaction in which the sea partons which originate from the dissociation of the colliding protons overlap in rapidity. The overlap illustrates the impossibility of achieving a unique definition of diffraction in terms of Good-Walker diffractive eigenstates; (b) is a corresponding Pomeron loop diagram. Plot (c) is a Reggeon loop diagram. There are four different cuts of the Pomerons in the loop of diagram (b): we may cut either the left or the right or neither or both of the Pomerons corresponding to processes of diagram (a) where the coherence of the partons in the central ('overlapping') rapidity region is destroyed or saved in the right or left parton shower. A cut of a Pomeron means that the coherence of the corresponding parton shower is destroyed. A rapidity gap occurs when neither Pomeron in the loop is cut.
• Figure 3: Probability for finding a rapidity gap larger than $\Delta\eta$ in an inclusive QCD event (cluster hadronisation) for different gap definitions. 'All gaps' refers to a scenario where the gap can be anywhere in the acceptance, while in 'central gaps' the gap is required to be central (i.e. $\eta=0$ has to lie in the gap). The $p_\perp$ threshold is [500]MeV and no trigger condition was required, $\sqrt{s}=\unit[7]{TeV}$.
• Figure 4: Probability for finding a rapidity gap (definition 'all') larger than $\Delta\eta$ in an inclusive QCD event for different threshold $p_\perp$. From top to bottom the thresholds are $p_{\perp,\,\text{cut}}=\unit[1.0\, ,\, 0.5\, ,\, 0.1]{GeV}$. Note that the lines for cluster and string hadronisation lie on top of each other for $p_{\perp,\,\text{cut}}=\unit[1.0]{GeV}$. No trigger condition was required, $\sqrt{s}=\unit[7]{TeV}$.
• Figure 5: Beam energy dependence of the probability for finding a rapidity gap (definition 'all') larger than $\Delta\eta$ in an inclusive QCD event ($p_{\perp,\,\text{cut}}=\unit[0.5]{GeV}$, no trigger condition, cluster hadronisation).