Impact of Geometric Inflation on Nucleon Size Sensitivity in Relativistic Heavy-Ion Collisions

Abstract

The intrinsic transverse size of nucleons, parameterized by a Gaussian width $w$, is a critical yet uncertain input in the initial-state modeling of relativistic heavy-ion collisions. Using a finite $w$ in standard initial geometry models introduces an unintentional ``geometric inflation'' that alters the initial nuclear density profile. In this study, we implement a self-consistent density correction to eliminate this artifact and investigate its impact on final-state observables. Through hybrid (viscous hydrodynamics + hadronic transport) simulations of $^{208}$Pb+$^{208}$Pb collisions at the LHC, we demonstrate that removing geometric inflation significantly modifies the sensitivity of observables to the nucleon width $w$. While elliptic flow and mean transverse momentum ($\langle [p_{\rm T}]\rangle$) become less sensitive to variations in $w$, the Pearson correlation coefficient $ρ(v_{n}^{2}, δp_{\rm T})$, $[p_{\rm T}]$ fluctuations, and triangular flow exhibit enhanced sensitivity to fluctuations in nucleon positions. Our results indicate that uncorrected geometric inflation can bias the extraction of nucleon structure and quark-gluon plasma properties. This underscores the necessity of a self-consistent initial-state geometry for reliable Bayesian inference in heavy-ion collisions.

Figures (5)

• Figure 1: (Color online) (Left panels) Centrality dependence of $\rho(v_{2}^{2}, \delta p_{\rm T})$ and $\rho(v_{3}^{2}, \delta p_{\rm T})$ with and without geometric inflation corrections in $^{208}$Pb+$^{208}$Pb collisions at $\sqrt{s_{\rm NN}}=5.02 \ \mathrm{TeV}$ from iEBE-VISHNU simulations. The right panels show the nucleon-size dependence of the corresponding initial predictors ($\rho_{2;\varepsilon}$ and $\rho_{3;\varepsilon}$) from TRENTo simulations, which capture the relative differences between the two scenarios. Experimental data are from Ref. ALICE:2021gxt.
• Figure 2: (Color online) (Left panels) Centrality dependence of $v_{2}^{2}$, $v_{3}^{2}$ and $\langle(\delta p_{\rm T})^{2}\rangle$ with and without geometric inflation corrections in $^{208}$Pb+$^{208}$Pb collisions at $\sqrt{s_{\rm NN}}=5.02 \ \mathrm{TeV}$ from iEBE-VISHNU simulations. The corresponding initial predictors from TRENTo are rescaled by a constant to match the magnitude of the final-state observables for shape comparison, as the hydrodynamic response is approximately linear. (Right panels) Nucleon-size dependence of the initial predictors $\varepsilon_{2}^{2}$, $\varepsilon_{3}^{2}$, and $\langle (\delta d_\perp)^2\rangle$ from TRENTo simulations.
• Figure 3: (Color online) (a) Centrality dependence of $\langle [p_{\rm T}]\rangle$ with and without geometric inflation corrections in $^{208}$Pb+$^{208}$Pb collisions at $\sqrt{s_{\rm NN}}=5.02 \ \mathrm{TeV}$ from iEBE-VISHNU simulations. The corresponding initial predictors are rescaled by a constant for shape comparison. (b) Nucleon-size dependence of the initial predictor $\langle d_{\perp}\rangle$ from TRENTo simulations.
• Figure 4: (Color online) Nucleon-size dependence of initial predictors (a) $\rho_{2;\,\varepsilon}$ and (b) $\rho_{3;\,\varepsilon}$ in $^{48}$Ca+$^{48}$Ca collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV from TRENTo simulations.
• Figure 5: (Color online) Nucleon-size dependence of initial predictors for $^{48}$Ca+$^{48}$Ca collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV: (a) elliptic eccentricity $\varepsilon_{2}^{2}$, (b) triangular eccentricity $\varepsilon_{3}^{2}$, (c) relative fluctuations of the initial gradient $\langle (\delta d_\perp)^2\rangle$, and (d) mean initial gradient $\langle d_{\perp}\rangle$.