Precision Tests of the Nonlinear Mode Coupling of Anisotropic Flow via High-Energy Collisions of Isobars

Valuable information on dynamics of expanding fluids can be inferred from the response of such systems to perturbations in their initial geometry. We apply this technique in high-energy ⁹⁶Ru+⁹⁶Ru and ⁹⁶Zr+⁹⁶Zr collisions to scrutinize the expansion dynamics of the quark-gluon plasma, where the initial geometry perturbations are sourced by the differences in deformations and radial profiles between ⁹⁶Ru and ⁹⁶Zr, and the collective response is captured by the change in anisotropic flow V_n between the two collision systems. Using a transport model, we analyze how the nonlinear coupling between lower-order flow harmonics V₂ and V₃ to the higher-order flow harmonics V₄ and V₅, expected to scale as $V_{4\mathrm{NL}}={\chi }_4{V}_2^2$ and V_5NL = χ₅V₂V₃, gets modified as one moves from ⁹⁶Ru+⁹⁶Ru to ⁹⁶Zr+⁹⁶Zr systems. We find that these scaling relations are valid to high precision: variations of order 20% in V_4NL and V_5NL due to differences in quadrupole deformation, octupole deformation, and nuclear skin modify χ₄ and χ₅ by about 1–2%. Percent-level deviations are however larger than the expected experimental uncertainties and could be measured. Therefore, collisions of isobars with different nuclear structures are a unique tool to isolate subtle nonlinear effects in the expansion of the quark-gluon plasma that would be otherwise impossible to access in a single collision system.