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

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 $(\beta_2,\gamma,\beta_4)$ parameter space and construct initial-state estimators for several flow and mean transverse momentum correlation observables. At the initial-state level, $\rho_2$ is primarily sensitive to $\beta_2$ and $\gamma$, with its sensitivity to $\gamma$ enhanced at nonzero $\beta_2$. The nonlinear response coefficient $\chi_{4,22}$ is predominantly sensitive to $\beta_4$, while its dependence on $\beta_2$ and $\gamma$ remains comparatively weak. Higher-order correlators exhibit more complex multidimensional response patterns; in particular, $\rho_{224}$ shows a dependence on $\gamma$ and $\beta_4$ that becomes more pronounced at finite $\beta_2$. 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 $\rho_2$ to $\beta_2$ and $\gamma$ is largely preserved, whereas the $\beta_4$ sensitivity of $\chi_{4,22}$ 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.