Space-time geometry of small and large collision systems at LHC energies

TL;DR

This paper reexamines 2.76 TeV Pb-Pb and $p$-$p$ PID $p_t$ spectra using a two-component (soft + hard) decomposition, challenging conventional Glauber geometry and the factorization of hard components. By inferring collision geometry from ensemble-mean $\bar p_t$ and applying an AB-TCM, it finds that central Pb-Pb collisions have far fewer participant nucleons than Glauber estimates and that jet fragments show limited suppression, with high-$y_t$ spectra aligning with $p$-$p$ references after soft rescaling. The work introduces a factorization-free view of jet components and highlights exclusivity and time-dilation effects on parton interactions, suggesting nuclear transparency-like behavior rather than a dense flowing medium. Overall, the results call into question jet-quenching as a universal signature of QGP in these systems and emphasize the need to reinterpret jet production through parton-level dynamics and geometry rather than conventional centrality measures.

Abstract

Identified-hadron (PID) spectra from 2.76 TeV Pb-Pb and $p$-$p$ collisions are analyzed via a two-component (soft + hard) model (TCM) of hadron production in high-energy nuclear collisions. The Pb-Pb TCM is adopted with minor changes from a recent analysis of PID hadron spectra from 5 TeV $p$-Pb collisions. The object of study is evidence for jet suppression in small and large collision systems as indicating quark-gluon plasma (QGP) formation there. Conventional methods have included Pb-Pb centrality determination via classical Glauber model and evidence for high-$p_t$ suppression sought via spectrum ratio $R_\text{AA}$. In the present study alternative geometry determination via ensemble-mean $\bar p_t$ data reveals that the number of participant nucleons in central Pb-Pb collisions is about 1/3 of the Glauber estimate. Based on certain features of Pb-Pb spectra the validity of the factorization assumption is also questioned. The entire jet contribution is therefore treated without factorization in ratio to a $p$-$p$ spectrum model as reference. The new results indicate that exclusivity and time dilation (experienced by participant partons) play an essential role in jet production not incorporated in Glauber model or hard-component factorization. The combination determines an effective number of N-N collisions per participant nucleon given specific Pb-Pb centrality. The effect on parton fragment (jet) distributions on $p_t$ is similar to projectile-proton fragment distributions on pseudorapidity from fixed-target $p$-A experiments where low-$η$ densities scale with A while high-$η$ densities are consistent with $p$-$p$ collisions. $p$-Pb and Pb-Pb spectra similarly analyzed reflect the same physics given different geometries. Jet suppression related to QGP formation is not evident.

Figures (14)

• Figure 1: Left: $p_t$ spectra for three species of identified hadrons from six centrality classes of 2.76 TeV Pb-Pb collisions (solid) and from $p$-$p$ collisions (open) alicepbpbpidspec. Right: Spectrum ratios (nuclear modification factors) $R_\text{AA}(p_t)$ derived from data in the left panels (bold curves of various line styles). The thin solid reference curves are described below Eq. (\ref{['raann']}).
• Figure 2: Left: Glauber Monte Carlo values of $N_{part}/2$ and $N_{bin}$ from Table \ref{['ppbparams1']} illustrating power-law relationships. Right: Empirical power-law relation between $N_{part}/2$ and charge density $\bar{\rho}_0$. See Fig. \ref{['story']} (b). The dashed line is a reference.
• Figure 3: Left: Ratios $\tilde{z}_{i}(n_s) = z_{hi}/z_{si}$ inferred from $z_{si}$ and $z_{hi}$ measurements reported in Ref. pidpart1 for charged (solid dots) and neutral (open circles) hadrons. The lines are linear parametrizations $\tilde{z}_i = \tilde{z}_i^* + \delta \tilde{z}_i^* x(n_s) \nu(n_s)$ that describe the ratio data: solid, dashed and dotted for pions, kaons and baryons respectively. Right: Coefficients $\tilde{z}_i^*$ and $\delta \tilde{z}_i^*$ for linear descriptions of ratio data in the left panel plotted vs hadron mass. The lines represent proportionality to hadron mass. The solid dots are values inferred in Ref. pidpart1. Open circles provide linear extrapolations on hadron mass for $\Xi$ and $\Omega$.
• Figure 4: Left: Unidentified-hadron charge density $\bar{\rho}_0$ per participant-nucleon pair from Ref. alicepbpbyields (points) vs number of binary N-N collisions per participant pair $\nu$. The dashed curve corresponds to N-N linear superposition (fixed $p$-$p$ value $x = 0.045$). The TCM vertical arrow and bold dotted curve are described in the text. Right: $x(\nu)$ vs $\nu$ transformed from the left panel (solid points, bold dotted) via inverting Eq. (\ref{['npartrho']}) and (solid curve) as defined by Eq. (\ref{['16']}). The dash-dotted curve is described in the text. Open boxes represent Glauber $x(\nu)$ on $\bar{\rho}_0$ values for the present study.
• Figure 5: Left: Product $x\nu$ (open points) extracted from $\bar{p}_t$ data via Eq. (\ref{['proddd']}). Dash-dotted and upper dashed curve are TCM predictions. The lower dashed curve is a TCM description of Pb-Pb data derived from Eqs. (\ref{['xmodel']}) and (\ref{['nueq']}). The solid points and curve are derived from Glauber solid points and curves in Fig. \ref{['900a']}. Right: Extrapolation of the TCM trend from the left panel over the full Pb-Pb multiplicity range. The Glauber points and curve are from Fig. \ref{['900a']} solid points and solid curves.