Scaling approach to rigid and soft nuclear deformation through flow fluctuations in high-energy nuclear collisions

Abstract

The nature of octupole deformation, whether static or vibrational, remains an open question in nuclear physics. Here, we propose a scaling approach to probe this ambiguity by triangular flow fluctuations using multi-particle cumulants, $c_{3,\epsilon }\{4\}$, in relativistic ${}^{238}$U+${}^{238}$U collisions. We demonstrate that both $|c_{3,\epsilon }\{4\}|$ and the ratio $|c_{3,\epsilon }\{4\}/c_{3,\epsilon }^2\{2\}|$ scale linearly with the fourth-order moment of octupole deformation, $⟨{\beta }_{3,\mathrm{U}}^4⟩$. Combined with the known linear relation of $c_{3,\epsilon }\{2\}$ to $⟨{\beta }_{3,\mathrm{U}}^2⟩$, this new relation provides a direct extraction of both the mean and variance of the octupole deformation fluctuations, finally discriminating between static and dynamic origins. This work establishes a new tool to probe the static and dynamic collective modes in high-energy nuclear collisions, advancing a significant step toward refining the initial conditions of quark-gluon plasma.

Comments: 8 Pages, 4 figures