[Paper Review] Ensemble-mean $\bf p_t$ and hadron production in high-energy nuclear collisions

T. A. Trainor|arXiv (Cornell University)|Aug 30, 2017

High-Energy Particle Collisions Research3 citations

TL;DR

This paper proposes a two-component model (TCM) of hadron production in high-energy nuclear collisions, linking ensemble-mean transverse momentum ($\bar{p}_t$) to minimum-bias dijet contributions. It shows that $\bar{p}_{th}$ (hard component) scales quadratically with multiplicity in $p$-$p$ collisions, transitions to eikonal behavior in Pb-Pb, and explains $p$-Pb as an intermediate case, challenging hydrodynamic interpretations of $\bar{p}_t$ trends.

ABSTRACT

A two-component (soft + hard) model (TCM) of hadron production in high-energy nuclear collisions is applied to ensemble-mean $p_t$ (denoted by $\bar p_t$) data for $p$-$p$, $p$-Pb and Pb-Pb collisions from the relativistic heavy ion collider (RHIC) and large hadron collider (LHC). This $\bar p_t$ TCM is directly related to a recently-published TCM for the charge-multiplicity $n_{ch}$ and collision-energy dependence of $p_t$ spectrum data from $p$-$p$ collisions. Multiplicity dependence of the $p$-$p$ spectrum hard component observed in the previous study is consistent with similar behavior for $\bar p_t$ hard component $\bar p_{th}$. $p$-$p$ $\bar p_t$ $n_{ch}$ dependence is observed to follow a noneikonal trend for the TCM hard component (dijet production $\propto n_{ch}^2$), whereas the trend for Pb-Pb collisions is consistent with the eikonal approximation assumed for the Glauber A-A centrality model. The $p$-Pb trend is intermediate, transitioning from the noneikonal $p$-$p$ trend for more-peripheral collisions to an eikonal trend for more-central collisions. The multiplicity dependence of participant number $N_{part}$ and binary-collision number $N_{bin}$ inferred from $p$-Pb $\bar p_t$ data differs strongly from a Glauber Monte Carlo model of that system. The rapid increase with $n_{ch}$ and large magnitude of $\bar p_t$ for the $p$-$p$ and $p$-Pb systems suggests that minimum-bias jets (TCM hard component) dominate $\bar p_t$ variation. The trend for $\bar p_{th}$ in Pb-Pb collisions is consistent with quantitative modification of jet formation in more-central A-A collisions.

Motivation & Objective

• To interpret $\bar{p}_t$ trends across $p$-$p$, $p$-Pb, and Pb-Pb collisions using a two-component model (TCM) of soft and hard hadron production.
• To determine whether $\bar{p}_t$ variations are driven by jet production or hydrodynamic flow mechanisms.
• To test the consistency of $\bar{p}_{th}$ multiplicity dependence with dijet production and jet fragmentation in $p$-$p$ and $p$-Pb systems.
• To assess whether the $\bar{p}_t$ behavior in A-A collisions aligns with Glauber centrality models or requires modified jet dynamics.
• To establish a direct quantitative link between $\bar{p}_t$ TCM parameters and independently measured jet spectra and fragmentation functions.

Proposed method

• The TCM models the $p_t$ spectrum as a sum of soft (thermal-like) and hard (dijet) components, with the hard component parameterized by Gaussian widths $\sigma_{y_t+}$, $\sigma_{y_t-}$, and exponential tail parameter $q$, all dependent on soft component density $\bar{\rho}_s = n_s / \Delta\eta$.
• The $\bar{p}_t$ hard component $\bar{p}_{th}(n_s, \sqrt{s})$ is derived from the TCM spectrum model and fitted to $\bar{p}_t$ data from $p$-$p$, $p$-Pb, and Pb-Pb collisions at RHIC and LHC energies.
• The $n_{ch}$ dependence of $\bar{p}_{th}$ is analyzed to test whether it follows a noneikonal $n_{ch}^2$ trend (as in $p$-$p$) or an eikonal trend (as in central A-A).
• The model uses parametrized $\sigma_{y_t+}$, $\sigma_{y_t-}$, and $q$ as functions of $\bar{\rho}_s$, with forms derived from prior $p_t$ spectrum analysis of $p$-$p$ collisions at 200 GeV and 13 TeV.
• The $p$-Pb system is modeled as a transition between $p$-$p$ (noneikonal) and Pb-Pb (eikonal) behavior, based on effective participant pairs.
• The TCM is validated by comparing $\bar{p}_{th}$ predictions to measured jet spectra and fragmentation functions, confirming quantitative consistency with dijet production.

Experimental results

Research questions

• RQ1 Does the $\bar{p}_t$ trend in $p$-$p$ collisions arise from minimum-bias dijet production, as suggested by the TCM?
• RQ2 How does the multiplicity dependence of $\bar{p}_{th}$ in $p$-Pb collisions transition between $p$-$p$ and Pb-Pb behaviors?
• RQ3 Is the $\bar{p}_t$ hard component in Pb-Pb consistent with eikonal scaling or modified jet dynamics in central collisions?
• RQ4 Can the $\bar{p}_t$ data across $p$-$p$, $p$-Pb, and Pb-Pb be quantitatively described by a single TCM framework without invoking hydrodynamic flow?
• RQ5 To what extent do the TCM parameters for $\bar{p}_{th}$ reflect measured jet properties such as fragmentation and transverse momentum distribution?

Key findings

• The $\bar{p}_{th}$ component in $p$-$p$ collisions scales quadratically with multiplicity ($n_{ch}^2$), consistent with noneikonal dijet production.
• The $p$-Pb $\bar{p}_t$ trend transitions from $p$-$p$-like noneikonal behavior in peripheral collisions to eikonal-like behavior in central collisions.
• The $\bar{p}_{th}$ multiplicity dependence in Pb-Pb is consistent with the eikonal approximation assumed in the Glauber A-A centrality model.
• The inferred $N_{part}$ and $N_{bin}$ from $p$-Pb $\bar{p}_t$ data differ significantly from predictions of a Glauber Monte Carlo model, suggesting non-trivial geometry effects.
• The $\bar{p}_{th}$ component in Pb-Pb shows quantitative agreement with measured jet spectra and fragmentation, confirming its dijet origin.
• The $\bar{p}_t$ TCM provides a precise, simple description of $\bar{p}_t$ data across all systems using only a few parameters, with no need to invoke hydrodynamic flow.