A QCD motivated model for soft interactions at high energies

TL;DR

This work presents a QCD-motivated framework for soft high-energy scattering that fuses the Good-Walker mechanism for low-mass diffraction with enhanced multi-Pomeron interactions governed by perturbative QCD inputs. By treating Pomeron exchanges as short-distance processes and employing a generating-function approach alongside the Mueller-Patel-Salam-Iancu scheme, the authors sum triple-Pomeron diagrams while enforcing both $t$-channel and $s$-channel unitarity. The model achieves a good description of ISR-Tevatron data and provides detailed predictions for LHC and cosmic-ray energies, including a notably small Higgs-diffraction survival probability of about $1.5\times10^{-3}$. The contrast with other approaches (e.g., KMR) highlights the impact of including Pomeron enhancements on diffractive observables and unitarity saturation, with important implications for forward physics and ultra-high-energy phenomenology.

Abstract

In this paper we develop an approach to soft scattering processes at high energies,which is based on two mechanisms: Good-Walker mechanism for low mass diffractionand multi-Pomeron interactions for high mass diffraction. The pricipal idea, that allows us to specify the theory for Pomeron interactions, is that the so called soft processes occur at rather short distances ($r^2 \propto 1 /<p_t>^2 \propto α'_\pom \approx 0.01 GeV^{-2}$), where perturbative QCD is valid. The value of the Pomeron slope $α'_\pom $ was obtained from the fit to experimental data. Using this theoretical approach we suggest a model that fits all soft data in the ISR-Tevatron energy range, the total, elastic, single and double diffractive cross sections, including $t$ dependence of the differential elastic cross section, and the mass dependence of single diffraction. In this model we calculate the survival probability of diffractive Higgs production, and obtained a value for this observable, which is smaller than 1% at the LHC energy range.

Figures (5)

• Figure 1: An example of enhanced diagrams, that contribute to the unitarity constraint in the $t$-channel. Wave lines denote the Pomerons. $\gamma$ is the amplitude of the dipole-dipole interaction at low energies (at rapidity $Y_0 \approx 1/\bar{\alpha}_S$ ). The particular set of diagrams shown in this figure, corresponds to the MPSI approach MPSIKOLE.
• Figure 2: Several examples of the Pomeron diagrams that lead to a different source of the diffractive dissociation that cannot be described in the framework of the G-W mechanism. Fig. \ref{['sdex']}-a is the simplest diagram that describes the process of diffraction in the region of large mass $Y - Y_1 = \ln(M^2/s_0)$. Fig. \ref{['sdex']}-b and Fig. \ref{['sdex']}-c give examples of more complicated diagrams in the region ofsph1.eps large mass. The dashed line shows the cut Pomeron, which describes the production of hadrons (see Fig. \ref{['sdex']} -a which illustrates this point).
• Figure 3: The MPSI approximation for the cross section of single diffractive production of mass ($M^2$,$Y - Y_M = \ln (M^2/s_0)$). The dashed lines shows the cut Pomerons. All other notations, are as in Fig. \ref{['gefunenh']}.
• Figure 4: Several examples of the Pomeron diagrams that lead to the double diffractive production. Fig. \ref{['ddex']}-a is the simplest diagram that describes the process of double diffraction in the regions of large mass $Y - Y_1 = \ln(M^2_1/s_0)$ and $Y_2 = \ln(M^2_2/s_0)$. Fig. \ref{['sdex']}-b contains examples of more complicated diagrams in the region of large masses. The dashed line indicates the cut Pomeron which describes the production of hadrons (see Fig. \ref{['ddex']}-a).
• Figure 5: Dependence of single inclusive cross section on $1 - x_L = M^2/s$, where $M$ is the mass of the diffractively produced system. Data are taken from Refs. GOMOCDFDD.