Parton-Based Gribov-Regge Theory

TL;DR

Parton-based Gribov-Regge Theory provides a self-consistent, quantum-mechanical framework for hadron-hadron and initial nucleus-nucleus collisions, unifying cross sections and particle production with energy-conserving multiple scattering. It combines soft and hard scattering without arbitrary cutoffs, introduces profile functions and AGK-consistent decompositions, and develops unitarization and Markov-chain Monte Carlo methods to address high-energy unitarity and complex multi-Pomeron dynamics. Enhanced Pomeron diagrams are discussed as a necessary extension to curb unitarity violations and to modify inclusive spectra via screening effects. The paper also implements a detailed hadronization scheme based on a string model for cut Pomerons and outlines a complete pipeline from parton ladders and cascades to final-state hadrons, enabling practical simulations for RHIC/LHC energies and beyond.

Abstract

We present a new parton model approach for hadron-hadron interactions and, in particular, for the initial stage of nuclear collisions at very high energies (RHIC, LHC and beyond). The most important aspect of our approach is a self-consistent treatment, using the same formalism for calculating cross sections and particle production, based on an effective, QCD-inspired field theory, where many of the inconsistencies of presently used models will be avoided. In addition, we provide a unified treatment of soft and hard scattering, such that there is no fundamental cutoff parameter any more defining an artificial border between soft and hard scattering. Our approach cures some of the main deficiencies of two of the standard procedures currently used: the Gribov-Regge theory and the eikonalized parton model. There, cross section calculations and particle production cannot be treated in a consistent way using a common formalism. In particular, energy conservation is taken care of in case of particle production, but not concerning cross section calculations. In addition, hard contributions depend crucially on some cutoff, being divergent for the cutoff being zero. Finally, in case of several elementary scatterings, they are not treated on the same level: the first collision is always treated differently than the subsequent ones. All these problems are solved in our new approach.

Figures (157)

• Figure 1: Hadron-hadron scattering in GRT. The thick lines between the hadrons (incoming lines) represent a Pomeron each. The different Pomeron exchanges occur in parallel.
• Figure 2: Graphical representation of a contribution to the elastic amplitude of proton-proton scattering. Here, energy conservation is taken into account: the energy of the incoming protons is shared among several "constituents" (shown by splitting the nucleon lines into several constituent lines), and so each Pomeron disposed only a fraction of the total energy, such that the total energy is conserved.
• Figure 3: Graphical representation of a contribution to the elastic amplitude of proton-nucleus scattering, or more precisely a proton interacting with (for simplicity) two target nucleons, taking into account energy conservation. Here, the energy of the incoming proton is shared between all the constituents, which now provide the energy for interacting with two target nucleons.
• Figure 4: A contribution to the elastic amplitude of a nucleus-nucleus collision, or more precisely two nucleons from projectile $A$ interacting with two nucleons from target $B$, taking into account energy conservation. The energy of the incoming nucleons is shared between all the constituents.
• Figure 5: The general elastic scattering amplitude $T$.