Space-time Geometry of Small and Large Collision Systems

TL;DR

The paper questions conventional jet-quenching interpretations by examining the space-time geometry of small and large collision systems with a two-component $p_t$ spectrum framework (TCM) informed by ensemble-mean $\bar p_t$. It shows that exclusivity and relativistic time dilation shape the effective number of nucleon-nucleon interactions per participant, leading to a $p_t$-dependent $\nu(p_t)$ and a non-factorizing hard component, which can mimic jet suppression in traditional $R_{AA}$ analyses. By deriving Pb-Pb and p-Pb geometries from $\bar p_t$ data and applying unfactorized hard-component ratios, the work finds that high-$p_t$ jet production effectively originates from single N-N collisions, while low-$p_t$ jets reflect multiple interactions constrained by quantum timing. The results imply a reinterpretation of jet-quenching signals as consequences of space-time geometry and parton kinematics rather than unambiguous evidence for a dense QCD medium, and they reveal a nuclear-transparency-like behavior across collision systems.

Abstract

Identified-hadron 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 object of study is evidence for jet suppression in small and large collision systems. Conventional methods include Pb-Pb centrality determination via classical Glauber model and evidence for high-$ p_t$ suppression sought via spectrum ratio $R_\text{AA}$. Previous $p$-Pb studies questioned the validity of the classical Glauber model. In the present study A-A geometry is determined instead via ensemble-mean $\bar p_t$ data. 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. These new results indicate that exclusivity (a nucleon may only interact with one nucleon ``at a time'') 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: multiple collisions if associated with low-$x$ (slow) partons, a single collision if associated with high-$x$ (fast) partons experiencing strong time dilation. The effect on parton fragment (jet) distributions on $p_t$ may be misinterpreted as jet suppression, but 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. Actual jet suppression related to QGP formation is not evident.

Figures (7)

• Figure 1: $p_t$ spectra and $R_{AA}$ for (a,b) pions and (c,d) protons in conventional format.
• Figure 2: (a) Glauber $N_{part}/2$ vs $\bar{\rho}_0$, (b) Glauber $(2/N_{part}) \bar{\rho}_0$ vs $\nu$, (c) TCM product $x\nu$ inferred from $\bar{p}_t$ data, (d) Extrapolation of TCM $x\nu$ trend to large Pb-Pb $n_{ch}$.
• Figure 3: TCM (a) $\bar{\rho}_s$ vs $\bar{\rho}_0$ (b) $N_{part} / 2$ vs $\bar{\rho}_0$ (c) $(2/N_{part}) \bar{\rho}_0$ vs $\bar{\rho}_0$ (d) $\nu$ vs $\bar{\rho}_0$
• Figure 4: TCM analysis for pions with (a) $p_t$ spectrum $\bar{\rho}_{0i}(y_t)$, (b) soft-rescaled spectrum $X_i(y_t)$, (c) hard-rescaled hard component $Y_i(y_t)$, (d) ratio $r_{AAi} = Y_i(y_t) / \hat{H}_{0i}(y_t)$
• Figure 5: soft-rescaled spectrum $X_i(y_t)$ for (a) pions and (b) charged kaons, (c) hard-rescaled hard component $Y_i(y_t)$ and (d) ratio $r_{AA} = Y_i(y_t) / \hat{H}_0(y_t)$ for kaons.