[Paper Review] A Soft Interaction Model at Ultra High Energies: Amplitudes, Cross Sections and Survival Probabilities

E. Gotsman, E. Levin+1 more|ArXiv.org|Aug 10, 2007

High-Energy Particle Collisions Research3 references6 citations

TL;DR

This paper presents a two-channel eikonal model that describes soft hadronic scattering at ultra-high energies, replacing the traditional soft Pomeron with a partonic amplitude saturated at long distances. It predicts a slow approach to the black disc unitarity bound and a low survival probability of 0.7% for exclusive Higgs boson production at the LHC, significantly lower than previous estimates, due to non-perturbative soft rescattering effects.

ABSTRACT

In this paper we present a two channel model with the goal of reproducing the soft scattering data available in the ISR-Tevatron energy range, and extend the model results to LHC and Cosmic Rays energies. A characteristic feature of the model is that we represent the sum of all diffractive final states at a vertex, by a single diffractive state. Our two main results are: (i) The approach of the elastic scattering amplitude to the black disc bound is very slow, reaching it at energies far higher than the GZK ankle cutoff. (ii) Our predicted survival probability for Higgs exclusive central diffractive production at the LHC is 0.7%, which is considerably smaller than our previous estimate. The above features are compatible with a parton-like model in which the traditional soft Pomeron is replaced by an amplitude describing the partonic system, which issaturated in the soft (long distance) limit.

Motivation & Objective

• To develop a two-channel eikonal model that reproduces soft hadronic scattering data from ISR to Tevatron energies.
• To extend the model’s predictions to LHC and cosmic ray energies, including unitarity constraints up to the Planck scale.
• To calculate the survival probability for exclusive Higgs boson production via central diffractive processes at the LHC.
• To analyze the rate at which the elastic amplitude approaches the black disc unitarity bound in impact parameter space.
• To assess the reliability of the model by comparing its predictions with experimental data on total, elastic, single and double diffractive cross sections.

Proposed method

• The model uses a two-channel eikonal approach to solve the s-channel unitarity equation, with opacity functions Ωi,k(s,b) representing interaction strength in impact parameter space.
• The scattering amplitude is expressed as Aij,kl(s,b) = i δij δkl (1 − exp(−Ωik(s,b)/2)), with the imaginary part dominant at high energies.
• The model relaxes factorization of coupling constants, moving beyond the single-channel soft Pomeron assumption to include partonic saturation effects in the soft limit.
• It incorporates experimental data on σtot, σel, σsd, σdd, and Bel from p-p and p̄-p collisions in the ISR-Tevatron range to constrain parameters.
• The survival probability SH² is calculated by accounting for soft rescattering effects on the spectator partons, using the b-distribution of the elastic amplitude.
• The model is validated by extending calculations to the Planck scale to ensure unitarity compliance.

Experimental results

Research questions

• RQ1 How rapidly does the elastic scattering amplitude approach the black disc unitarity bound in impact parameter space at ultra-high energies?
• RQ2 What is the survival probability for exclusive Higgs boson production via central diffractive processes at the LHC, and how does it compare to previous estimates?
• RQ3 How well can a two-channel eikonal model with non-factorized opacities reproduce soft scattering data across the ISR-Tevatron energy range?
• RQ4 To what extent do non-perturbative soft rescatterings suppress the signal for exclusive Higgs production at the LHC?
• RQ5 How does the model’s parametrization of the b-dependence of the amplitude affect predictions for diffractive slopes and survival probabilities?

Key findings

• The elastic scattering amplitude approaches the black disc unitarity bound at energies far beyond the GZK ankle, indicating a slow saturation of unitarity.
• The predicted survival probability for exclusive Higgs boson production at the LHC is 0.7%, significantly lower than the previous estimate of 2.7% from a two-amplitude model.
• The model's prediction of SH² = 0.7% is robust under variations of the hard slope parameters B_el^H and B_in^H, provided the ratio V²_p→d / B_in^H is kept constant.
• The model reproduces the forward cone of elastic scattering (containing >95% of the data) but cannot describe the diffractive dip structure due to its Gaussian b-dependence.
• The model's results are consistent with unitarity up to the Planck scale, supporting its reliability in the high-energy regime.
• The model suggests that Pomeron-enhanced diagrams for high-mass diffraction are not fully captured, indicating a need to include semi-hard processes in future extensions.