Elliptic flow of ${\pi }^0$ mesons in Cu$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV and U$+$U at $\sqrt{s_{{}_{NN}}}=193$ GeV

The second-order azimuthal anisotropy coefficients ($v_2$) of neutral $\pi$ mesons (${\pi }^0$) have been measured as a function of the transverse momentum ($p_T$) and centrality of Cu$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$~GeV and U$+$U at $\sqrt{s_{{}_{NN}}}=193$ GeV at the Relativistic Heavy Ion Collider. The analysis used experimental data collected by the PHENIX experiment at midrapidity $\mathrm{\mid }\eta \mathrm{\mid }<0.35$ over a broad $p_T$ range up to $\approx 10$~GeV/$c$, and the obtained results are compared with previous PHENIX measurements in Au$+$Au collisions at $\sqrt{s_{{}_{NN}}}=200$~GeV. In all three collision systems, the ${\pi }^0$~$v_2$ values follow the scaling with the second-order participant eccentricity and the cube root of the number of participating nucleons (${\epsilon }_2{N}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}^{1\mathrm{/}3}$) up to $\approx 4$~GeV/$c$. Furthermore, the behavior of the azimuthal-dependent ${\pi }^0$ nuclear-modification factors and associated fractional parton-energy losses are evaluated from measured nonzero $v_2$ values of ${\pi }^0$ at $p_T>5$ GeV/$c$ and found to be approximately the same for similar values of $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}^{1\mathrm{/}3}$ in these collision systems. These findings demonstrate that the mechanism of ${\pi }^0$ $v_2$ generation exhibits a high degree of universality across different initial geometries of heavy-ion collisions.