Multiple Interactions and the Structure of Beam Remnants

TL;DR

The paper tackles the challenge of modeling multiple parton interactions in high-energy hadron collisions by developing a next-generation framework that couples correlated flavour, colour, and momentum distributions for both the initiating partons and beam remnants. It advances the state of the art by introducing impact-parameter dependent overlap functions, refined multi-parton densities, and a detailed treatment of colour topologies including junctions, enabling realistic hadronization within the Lund string model. Through extensive model studies and comparisons to Tevatron and LHC scenarios, it demonstrates how baryon-number flow, junction dynamics, and pedestal effects emerge from the integrated MI framework, while highlighting remaining uncertainties in colour correlations and intertwined showers. The work provides a structured path toward more trustworthy extrapolations to new energies and observables in the underlying event, emphasizing the need for ongoing experimental input to constrain the rich colour-structure of beam remnants.

Abstract

Recent experimental data have established some of the basic features of multiple interactions in hadron-hadron collisions. The emphasis is therefore now shifting, to one of exploring more detailed aspects. Starting from a brief review of the current situation, a next-generation model is developed, wherein a detailed account is given of correlated flavour, colour, longitudinal and transverse momentum distributions, encompassing both the partons initiating perturbative interactions and the partons left in the beam remnants. Some of the main features are illustrated for the Tevatron and the LHC.

Figures (32)

• Figure 1: Schematic illustration of an event with two $2 \to 2$ perturbative interactions.
• Figure 2: The integrated interaction cross section $\sigma_{\mathrm{int}}$ above $p_{\perp\mathrm{min}}$ for the Tevatron, with 1.8 TeV $\mathrm{p}\overline{\mathrm{p}}$ collisions, and the LHC, with 14 TeV $\mathrm{p}\mathrm{p}$ ones. For comparison, the flat lines represent the respective total cross section.
• Figure 3: Overlap profile $\mathcal{O}(b)$ for a few different choices. Somewhat arbitrarily the different parametrizations have been normalized to the same area and average $b$, i.e. same $\int \mathcal{O}(b) \, \mathrm{d}^2 b$ and $\int b \mathcal{O}(b) \, \mathrm{d}^2 b$. (Recall that we have not specified $b$ in terms of any absolute units, so both a vertical and a horizontal scale factor have to be fixed for each distribution separately.) Insert shows the region $b <2$ on a linear scale.
• Figure 4: Distribution of the number of interactions for different overlap profiles $\mathcal{O}(b)$, for $\mathrm{p}\overline{\mathrm{p}}$ at 1.8 TeV, top without momentum conservation constraints, middle with such constraints included but without (initial-state) showers, and bottom also with shower effects included.
• Figure 5: Average number of interactions as a function of the $p_{\perp}$ of the hardest interaction, for $\mathrm{p}\overline{\mathrm{p}}$ at 1.8 TeV, top without momentum conservation constraints, middle with such constraints included but without (initial-state) showers, and bottom also with shower effects included.