Probing Nuclear Geometry through Multi-Particle Azimuthal Correlations and Rapidity-Even Dipolar Flow in ${}^{16}$O+${}^{16}$O Collisions

We study symmetric and asymmetric cumulants as well as rapidity-even dipolar flow in ${}^{16}$O+${}^{16}$O collisions at $\sqrt{s_{NN}} = 200$~GeV to explore $\alpha$-clustering phenomena in light nuclei within the viscous relativistic hydrodynamics framework. Signatures of $\alpha$-clustering manifest in the anisotropic flow coefficients and their correlations -- particularly in observables involving elliptic-triangular flow correlations. We show that final-state symmetric and asymmetric cumulants -- especially $\mathrm{NSC}(2,3)$ and $\mathrm{NAC}_{2,1}(2,3)$ -- are sensitive to the initial nuclear geometry. Additionally, we observe a significant difference in rapidity-even dipolar flow, $v_1^{\text{even}}$, between $\alpha$-clustered and Woods--Saxon configurations in high-multiplicity events. These findings underscore the pivotal role of nuclear structure in heavy-ion collision dynamics and provide observables for distinguishing nuclear geometries, particularly in ultra-central collisions.