Pomeron Weights in QCD Processes at High Energy and the $S$-Matrix Unitarity Constraint

TL;DR

This paper compares eikonal and U-matrix unitarization schemes in high-energy QCD, revealing that the U-matrix better incorporates diffraction, fluctuations, and correlations of pomerons, making it more suitable for modeling energy-growing cross-sections.

Contribution

It introduces a generalized expansion of the unitarized elastic amplitude to analyze pomeron weights and their effects on multiplicity, fluctuation, and correlation in high-energy QCD processes.

Findings

U-matrix incorporates more diffraction into multi-pomeron vertices

Fluctuations become significant only beyond a high-energy threshold

Higher-order pomeron correlations increase with energy and impact parameter

Abstract

The pomeron topological cross-section is derived for the eikonal and the $U$-matrix unitarization schemes using a generalized expansion of the unitarized elastic amplitude in an effort to examine pomeron characteristics, namely the multiplicity distribution, fluctuation, and correlation, and to reveal the impact of pomeron weights on the $pp$ multiplicity distribution. The results demonstrate that the U-matrix inherently incorporates a larger amount of diffraction production into the multi-pomeron vertices, yielding a larger pomerons' variability regardless of the energy range, while such fluctuations become significant only beyond a specific high-energy threshold in the eikonal and quasi-eikonal schemes. Most importantly, our findings indicate that within the $U$-matrix scheme, an increase in exchanged pomerons results in more pronounced higher-order pomeron correlations, which are affected by the energy and the impact parameter. Interestingly, our outcomes also highlight that the correlated pomeron exchanges within the U-matrix summation play a key role in enhancing multi-parton collisions. In light of these results, we can argue that the U-matrix is fundamentally more valid for theories with growing cross-sections with energy, such as QCD at high energies.