Measurement of D0, D+, D*+ and D s + production in Pb-Pb collisions at <math> <msqrt> <msub> <mi>s</mi> <mrow> <mi>N</mi> <mi>N</mi> </mrow> </msub> </msqrt> <mo>=</mo> <mn>5.02</mn> </math> $$ \sqrt{{\mathrm{s}}_{\mathrm{NN}}}=5.02 $$ TeV

We report measurements of the production of prompt D0, D+, D*+ and D s + mesons in Pb–Pb collisions at the centre-of-mass energy per nucleon-nucleon pair s N N = 5.02 $$ \sqrt{s_{\mathrm{NN}}}=5.02 $$ TeV, in the centrality classes 0–10%, 30–50% and 60–80%. The D-meson production yields are measured at mid-rapidity (|y| < 0.5) as a function of transverse momentum (p T). The p T intervals covered in central collisions are: 1 < p T < 50 GeV/c for D0, 2 < p T < 50GeV/c for D+, 3 < p T < 50GeV/c for D*+, and 4 < p T < 16GeV/c for D s + mesons. The nuclear modification factors (R AA) for non-strange D mesons (D0, D+, D*+) show minimum values of about 0.2 for p T = 6–10 GeV/c in the most central collisions and are compatible within uncertainties with those measured at s N N = 2.76 $$ {\sqrt{s}}_{\mathrm{NN}}=2.76 $$ TeV. For D s + mesons, the values of R AA are larger than those of non-strange D mesons, but compatible within uncertainties. In central collisions the average R AA of non-strange D mesons is compatible with that of charged particles for p T > 8 GeV/c, while it is larger at lower p T. The nuclear modification factors for strange and non-strange D mesons are also compared to theoretical models with different implementations of in-medium energy loss.