Responses of multiparticle observables to multidimensional nuclear deformation in relativistic heavy-ion collisions

Abstract

Relativistic heavy-ion collisions provide a unique opportunity to probe ground-state nuclear structure through its imprint on the initial collision geometry. We investigate how multiparticle observables respond to combined variations of quadrupole deformation, triaxiality, and hexadecapole deformation, using ${}^{129}$Xe+${}^{129}$Xe collisions as a representative testing ground. We perform a joint analysis in the three-dimensional $({\hat{I}}_2^2,{\hat{I}}^3,{\hat{I}}_4^2)$ parameter space and construct initial-state estimators for several flow and mean transverse momentum correlation observables. At the initial-state level, $\ddot{I}{}_2$ is primarily sensitive to ${\hat{I}}_2^2$ and ${\hat{I}}^3$, with its sensitivity to ${\hat{I}}^3$ enhanced at nonzero ${\hat{I}}_2^2$. The nonlinear response coefficient $\ddot{I}{‡}_{4,22}$ is predominantly sensitive to ${\hat{I}}_4^2$, while its dependence on ${\hat{I}}_2^2$ and ${\hat{I}}^3$ remains comparatively weak. Higher-order correlators exhibit more complex multidimensional response patterns; in particular, $\ddot{I}{}_{224}$ shows a dependence on ${\hat{I}}^3$ and ${\hat{I}}_4^2$ that becomes more pronounced at finite ${\hat{I}}_2^2$. We further employ the iEBE-VISHNU hybrid model to examine whether these deformation sensitivities survive the subsequent dynamical evolution. The final-state calculations indicate that the sensitivity of $\ddot{I}{}_2$ to ${\hat{I}}_2^2$ and ${\hat{I}}^3$ is largely preserved, whereas the ${\hat{I}}_4^2$ sensitivity of $\ddot{I}{‡}_{4,22}$ is substantially reduced. For the other higher-order observables, the initial-state sensitivities are modified by the evolution or cannot be resolved with the present statistics.

11 pages, 10 figures

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