The elliptic and triangular flow coefficients v2 and v3 of prompt D0, D+, and D⁎+ mesons were measured at midrapidity (|y|<0.8) in Pb–Pb collisions at the centre-of-mass energy per nucleon pair of sNN=5.02TeV with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decays in the transverse momentum interval 1<36GeV/c in central (0–10%) and semi-central (30–50%) collisions. Compared to pions, protons, and J/ψ mesons, the average D-meson vn harmonics are compatible within uncertainties with a mass hierarchy for pT≲3GeV/c, and are similar to those of charged pions for higher pT. The coupling of the charm quark to the light quarks in the underlying medium is further investigated with the application of the event-shape engineering (ESE) technique to the D-meson v2 and pT-differential yields. The D-meson v2 is correlated with average bulk elliptic flow in both central and semi-central collisions. Within the current precision, the ratios of per-event D-meson yields in the ESE-selected and unbiased samples are found to be compatible with unity. All the measurements are found to be reasonably well described by theoretical calculations including the effects of charm-quark transport and the recombination of charm quarks with light quarks in a hydrodynamically expanding medium.
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