Soft diffraction and the elastic slope at Tevatron and LHC energies: a multi-Pomeron approach

TL;DR

The paper develops a multi-Pomeron framework that combines the non-linear pion-loop corrections to the Pomeron trajectory, a two-channel eikonal treatment of $s$-channel unitarity including low-mass diffractive excitations, and high-mass diffractive dissociation via triple-Pomeron graphs. This unified model accurately describes $\sigma_{tot}$, $d\sigma_{el}/dt$, and the $t$-dependent elastic slope $B(t)$ from ISR to Tevatron, and provides robust LHC predictions for soft diffractive observables and gap-survival probabilities $S^2$, with two extreme diffractive scenarios (minimal and maximal) bracketing the uncertainties. Key results include $\sigma_{tot}(14\,\text{TeV}) \approx 99$–$105$ mb, $d\sigma_{el}/dt|_{t=0} \approx 506$–$564$ mb/GeV$^2$, $B(0) \approx 20$–$22$ GeV$^{-2}$, $\sigma_{SD} \approx 9$–$15$ mb, $\sigma_{DD} \approx 9.5$ mb, and $S^2$ values that depend on gap topology (e.g., $S^2 \sim 0.04$–$0.08$ for central diffractive Higgs production at LHC). This framework offers practical guidance for diffractive measurements, luminosity calibration, and Higgs-diffractive studies in high-energy hadron colliders.

Abstract

We present a formalism for high energy soft processes, mediated by Pomerons, which embodies pion-loop insertions in the Pomeron trajectory, rescattering effects via a two-channel eikonal and high-mass diffractive dissociation. It describes all the main features of the data throughout the ISR to Tevatron energy interval. We give predictions for soft diffractive phenomena at the LHC energy, and we calculate the different survival probabilities of rapidity gaps which occur in various diffractive processes.

Figures (12)

• Figure 1: The Pomeron exchange contribution, graph (a), together with unitarity corrections, graphs (b--e), to the $pp$ elastic amplitude. Note that graphs $(d, e)$ are the ' square' of the single- and double-diffractive dissociation amplitudes respectively.
• Figure 2: A two pion-loop insertion in the Pomeron trajectory, generated from the single loop by $t$-channel unitarity.
• Figure 3: Typical $t$ dependence of the elastic slope $B (t)$ of (\ref{['eq:a2']}) found in the model of the Pomeron introduced in Section 3. The diffractive dip, arising from the destructive interference between the Pomeron pole and cut contributions, is located at smaller $-t$ for higher collider energies $\sqrt{s}$. The effect on $B(t)$ is seen from the dashed curves in Fig. 9. The inclusion of high-mass diffraction in Sections 5 and 6 modifies the behaviour of $B(t)$ in the dip region, again see Fig. 9.
• Figure 4: The model descriptions of high energy $pp$ (or $p\bar{p}$) total cross section data TOT. The continuous, dotted and dashed curves correspond, respectively, to the minimal, maximal diffractive models and to the model of the Pomeron in which high-mass diffraction is neglected. The discrepancy between the curves and the data at the lower ISR energies is entirely due to our neglect of the (secondary) meson Regge trajectories.
• Figure 5: The data for $d\sigma_{\rm el}/dt$ versus $| t |$ obtained at the ISR ISR and at the Tevatron E710CDFEL, compared with the Pomeron model descriptions. The model predictions for $d\sigma_{\rm el}/dt$ at the LHC energy are also shown. The curves are as described in Fig. 4. (Note the inclusion of factors of 100 and 10 at the ISR and Tevatron energies respectively.)