$D^0$-$D_s^+$ Elliptic-Flow Splitting under Event-Shape Engineering: A Probe of Sequential Charm Hadronization

Abstract: Recent work has proposed sequential hadronization of open-charm hadrons in the quark-gluon plasma, wherein more tightly bound species such as $D_s^+$ form earlier near $1.2 T_c$ and $D^0$ forms later at $T_c$. That work showed that this mechanism naturally reverses the sign of the $D^0-D_s^+$ elliptic-flow splitting relative to the conventional simultaneous baseline. In this work, we demonstrate that event-shape engineering (ESE) provides a sharper discrimination between the two pictures than inclusive measurements alone. By selecting large-$q_2$ and small-$q_2$ events in 0--10\% and 30--50\% centrality classes in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, we show that the geometry-driven enhancement of charm-meson $v_2$ can be separated from the hadronization-time response: the positive $Δv_2(D^0-D_s^+)$ in the sequential scenario grows systematically with $q_2$, while the corresponding response slope $χ$ reveals a species-dependent hierarchy $χ(D^0) > χ(D_s^+)$ that is robust against the overall flow normalization and absent in the simultaneous baseline. In the simultaneous case, the splitting is near zero or negative and does not follow the same geometry scaling. Notably, the semi-central 30--50\% class emerges as the optimal window, because the non-monotonic interplay between QGP lifetime and initial eccentricity maximizes the late-stage flow conversion. The $q_2$ ratios of the $D_s^+/D^0$ yield ratio remain close to unity, confirming that the splitting is a dynamical flow effect rather than a chemical yield modification. These results establish $Δv_2(D^0-D_s^+)$ and the response slope $χ$ under ESE as complementary differential probes of the space-time structure of charm hadronization near the QCD transition temperature.