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 $\rho(v_{n}^{2}, \delta p_{\rm T})$, $[p_{\rm T}]$ 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.