Transverse-Momentum-Ordered Showers and Interleaved Multiple Interactions

TL;DR

This paper tackles the challenge of modeling high-energy hadronic collisions by interleaving multiple interactions with initial-state radiation in a common, downward sequence of transverse momentum values, and by introducing a new framework of $p_{ imetperp}$-ordered showers for both ISR and FSR. The authors develop a dipole-inspired, $p_{ imetperp}$-ordered shower formalism, with mass corrections and matrix-element matching, and integrate this with a model of correlated multi-parton densities and color connections to study underlying-event activity. First results show improved descriptions of Z$^0$ production and underlying-event observables compared to older mass-ordered approaches, while highlighting remaining challenges such as primordial $k_{ imetperp}$ and potential joined-interaction effects. The work lays a foundation for more realistic collider event generation and sets the stage for future inclusion of joined interactions and full FSR interleaving, with significant implications for jet physics, minimum-bias studies, and tuning to hadron-collider data.

Abstract

We propose a sophisticated framework for high-energy hadronic collisions, wherein different QCD physics processes are interleaved in a common sequence of falling transverse-momentum values. Thereby phase-space competition is introduced between multiple parton-parton interactions and initial-state radiation. As a first step we develop new transverse-momentum-ordered showers for initial- and final-state radiation, which should be of use also beyond the scope of the current article. These showers are then applied in the context of multiple interactions, and a few tests of the new model are presented. The article concludes with an outlook on further aspects, such as the possibility of a shower branching giving partons participating in two different interactions.

Figures (26)

• Figure 1: Schematic figure illustrating one incoming hadron in an event with a hard interaction occurring at $p_{\perp 1}$ and three further interactions at successively lower $p_{\perp}$ scales, each associated with (the potentiality of) initial-state radiation, and further with the possibility of two interacting partons (2 and 3 here) having a common ancestor in the parton showers. Full lines represent quarks and spirals gluons. The vertical $p_{\perp}$ scale is chosen for clarity rather than realism; most of the activity is concentrated to small $p_{\perp}$ values.
• Figure 2: Schematic figure with our standard terminology for (a) a final-state and (b) an initial-state branching $a \to b c$, with a cross marking the central hard process and a recoiling parton $r$ moving out to or coming in from the other side.
• Figure 3: (a) Schematic figure of the clustering of two particles. (b) A topology with a large $\theta_{12}$ but a small $p_{\perp 1,2}$.
• Figure 4: Parton $p_{\perp}$ spectra when 2-parton events of a fixed $p_{\perp} = 50$ GeV, for an 1800 GeV $\mathrm{p}\overline{\mathrm{p}}$ collider, are modified by a single ISR branching with $p_{\perp\mathrm{evol}} = 50$ GeV, using CTEQ5L parton distributions and the standard DGLAP splitting kernels. Owing to $p_{\perp\mathrm{evol}} \neq p_{\perp}$, the parton emitted at the ISR branching has a tail to $p_{\perp}$ values well below 50 GeV. However, this spectrum is comparable with the lower-$p_{\perp}$ of the two hard-scattering partons, after the recoil from the ISR has been taken into account, so there is a certain symmetry if it all is viewed as a $2 \to 3$ process.
• Figure 5: Charged multiplicity distributions, for 1.96 TeV $\mathrm{p}\overline{\mathrm{p}}$ minimum-bias events.