Complementary Approach to Anisotropic Flows in Heavy-Ion Collisions

We introduce a no-reaction-plane (no-RP) method for extracting directed ($v_1$) and elliptic ($v_2$) flows in heavy-ion collisions, which eliminates the need for event-plane reconstruction. %by scanning over fixed test angles and using simple count asymmetries. The method is validated with PHSD model simulations of Au+Au collisions at $\sqrt{s_{NN}} = 9.2$ GeV at freeze-out (impact parameter $b = 4$ fm). We demonstrate that the two asymmetries for each harmonic contribute equally, i.e., $\langle A_{\mathrm{ud}}^2\rangle \approx \langle A_{\mathrm{lr}}^2\rangle$ and $\langle A_1^2\rangle \approx \langle A_2^2\rangle$, so that a single asymmetry measurement suffices for a good flow estimate. Event-by-event comparisons with direct calculations using the true reaction plane yield Pearson correlation coefficients of 0.985 for $v_2$ and 0.883 for $v_1$, confirming that the no-RP method captures flow fluctuations well enough.