Parameter space stability of multiple soft interactions

TL;DR

This paper analyzes the stability of multiple soft interactions in cosmic ray event generators, examining fluctuation behaviors, stability regions, and the impact of higher-order corrections across various energy scales.

Contribution

It introduces a comprehensive fluctuation stability analysis of soft interactions, incorporating higher-order corrections and energy-dependent effects, enhancing the understanding of hadron collision models.

Findings

Identifies stable and unstable fluctuation regions for Pomeron-Reggeon densities.

Shows optimal stability at GRV model-predicted densities.

Highlights the indeterminate nature of the impact parameter profile at certain scales.

Abstract

We study the fluctuation theory analysis of multiple soft interactions that are used to design SIBYLL 2.1 and related cosmic ray event generators. We examine fluctuation stabilities of Lund string fragmentation involving quark-antiquark and diquark-antidiquark pairs. Using the primordial transverse momentum hadron-hadron pairs, we find that the resulting Gaussian distribution yields an ill-defined ensemble under fluctuation of the model parameters of parent quark and diquarks. Further, we investigate the nature of multiple soft interactions through Pomeron-Reggeon fluctuations at various energy scales. We show that there are both stable and unstable regions under fluctuations of the Reggeon and Pomeron densities and all initial energy scales. The optimal stability zone is achieved at the Reggeon and Pomeron densities as predicted by GRV model. For hadron-hadron collisions, the limiting Gaussian profile as a function of the impact parameters of soft interactions for proton-proton collisions corresponds to an indeterminate statistical basis. Subsequently, we add higher order corrections in the Regge trajectory of constituent hadrons that play an important role in determining the shape of a proton or meson profile function in the realm of minijet model. We also discuss the accelerated nucleons with jerks and soft profile functions at off-shell-conditions. In addition, we illustrate the wall of stability/instability for multiple soft interactions by considering energy dependent soft contributions to scattering cross section as the model embedding. Qualitative discussions are provided at physical energy scales ranging from 1 GeV to 1800 GeV. This includes the analysis of CDF, P238, UA5 and ZEUS experiments.