Nonlinear collective flow reveals the breakdown of quadrupole--hexadecapole scaling in heavy ion collisions

Abstract

Determining the role of intrinsic hexadecapole deformation ($\beta_4$) in nuclear structure remains a long-standing challenge. Relativistic heavy-ion collisions provide a unique opportunity to address this problem by converting the initial nuclear geometry into the collective motion of the quark--gluon plasma (QGP). Using event-by-event viscous hydrodynamic simulations of ultra-central $^{238}$U+$^{238}$U collisions at $\sqrt{s_{NN}}=193$ GeV, we investigate whether higher-order collective flow can isolate the contribution of $\beta_4$ and test the $\beta_2-\beta_4$ correlation. We demonstrate that information carried by the sign of $\beta_4$ survives the QGP evolution and is enhanced through nonlinear hydrodynamic response: the fourth-order flow harmonic acquires its topology dependence predominantly from the linear response, whereas the sensitivity of the sixth-order harmonic originates almost entirely from nonlinear mode coupling. As a consequence, the nonlinear response coefficient $\xi_{6,222}$ cleanly separates the $(\beta_2,\beta_4)$ intrinsic nuclear topologies. These results establish the sign of $\beta_4$ as an experimentally accessible signature of deviations from the quadrupole--hexadecapole correlation, demonstrating that higher-order collective flow provides a direct probe of nuclear multipole structure while revealing how nonlinear QGP dynamics encode subtle higher-order geometric information into final-state observables.