Mode-by-mode evolution of Pb-Pb collisions at 5.02 TeV in a hybrid model

TL;DR

This work develops and applies a mode-by-mode decomposition of fluctuating Pb–Pb initial states at $5.02\ \text{TeV}$ to a state-of-the-art hybrid evolution (KøMPøST + MUSIC + iSS + SMASH) across two centrality classes. By decomposing initial profiles into a smooth average $\bar{\Psi}$ and uncorrelated fluctuation modes $\Psi_l$, and evaluating linear and quadratic response coefficients $L_{\alpha,l}$ and $Q_{\alpha,ll'}$, the authors connect specific initial modes to final-state observables such as $dN_{ch}/d\eta$, $\langle p_T\rangle$, and $v_n^{c/s}$. They find that ultracentral events resemble fixed-b scenarios with a small set of dominant modes, while mid-peripheral collisions exhibit modes carrying meaningful energy content that reflect impact-parameter variation, significantly influencing multiplicity and $\langle p_T\rangle$ fluctuations. Implementing a hadronic afterburner with SMASH is feasible but demands large oversampling to overcome statistical noise, indicating both the promise and computational challenges of fully mode-resolved, mode-by-mode evolution in realistic, 3D, nonboost-invariant settings. These results provide a quantitative framework to relate initial geometry fluctuations to final-state observables, aiding model discrimination and extraction of QGP properties from data.

Abstract

We determine the average state and the uncorrelated modes that characterize the event-by-event fluctuations of the initial state in two typical centrality classes of Pb-Pb collisions at 5.02 TeV. We find that modes in a narrow central bin are similar to those in events at fixed vanishing impact parameter, while those in a mid-peripheral centrality class are affected by the impact-parameter variation. We study how each fluctuation mode affects observables both in the initial state and in the final state of the collisions, at the end of a state-of-the-art boost-invariant hybrid evolution with KoMPoST + MUSIC + iSS + SMASH, and show that implementing a hadronic transport cascade in such a mode-by-mode analysis with reasonable statistical noise is costly but feasible.

Figures (18)

• Figure 1: Average initial state $\Bar{\Psi}$ for events in the 0--2.5% (left) and 30--40% (right) centrality bins. In each bin the average is computed over $N_\mathrm{ev} = 2^{21}$ initial states. Both axes are in units of the half-density radius $R=6.62$ fm.
• Figure 2: Relative weights $\{w_l\}$ of the first 256 fluctuation modes and of the average initial state ($\bar{w}$, larger symbols at $l = -1$) for each centrality class.
• Figure 3: Normalized transverse profile of the first $60$ modes for central events. Both axes are in units of the half-density radius $R=6.62$ fm.
• Figure 4: Normalized transverse profile of the first $60$ modes for events in the 30--40% centrality bin. Both axes are in units of the half-density radius $R=6.62$ fm.
• Figure 5: Relative energy content ($|\tilde{\varepsilon}_0|_l$) and spatial anisotropies $|\tilde{\varepsilon}_n|_l$ [see Eqns. \ref{['eq:mode_eccentricities1']}--\ref{['eq:mode_eccentricities2']}] with $1\leq n\leq 5$ of the first 40 fluctuation modes for events in the 0--2.5% (left) and the 30-40% (right) centrality class.