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The production cross sections of the prompt charmed mesons D$^0$, D$^+$,D$^{*+}$ and D$_s$ were measured at mid-rapidity in p-Pb collisions at acentre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=5.02$ TeV with theALICE detector at the LHC. D mesons were reconstructed from their decaysD$^0\rightarrow{\rm K}^-\pi^+$, D$^+\rightarrow{\rm K}^-\pi^+\pi^+$,D$^{*+}\rightarrow D^0\pi^+$, D$_s^+\rightarrow\phi\pi^+\rightarrow{\rmK}^-{\rm K}^+\pi^+$, and their charge conjugates. The $p_{\rm T}$-differentialproduction cross sections were measured at mid-rapidity in the interval$1<p_{\rm T}<24$ GeV/$c$ for D$^0$, D$^+$ and D$^{*+}$ mesons and in $2<p_{\rmT}<12$ GeV/$c$ for D$_s$ mesons, using an analysis method based on theselection of decay topologies displaced from the interaction vertex. Theproduction cross sections of the D$^0$, D$^+$ and D$^{*+}$ mesons were alsomeasured in three $p_{\rm T}$ intervals as a function of the rapidity $y_{\rmcms}$ in the centre-of-mass system in $-1.26<y_{\rm cms}<0.34$. In addition,the prompt D$^0$ cross section was measured in pp collisions at $\sqrt{s}=7$TeV and p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV down to $p_{\rm T}=0$using an analysis technique that is based on the estimation and subtraction ofthe combinatorial background, without reconstruction of the D$^0$ decay vertex.The nuclear modification factor $R_{\rm pPb}(p_{\rm T})$, defined as the ratioof the $p_{\rm T}$-differential D-meson cross section in p-Pb collisions andthat in pp collisions scaled by the mass number of the Pb nucleus, wascalculated for the four D-meson species and found to be compatible with unitywithin experimental uncertainties. The results are compared to theoreticalcalculations that include cold-nuclear-matter effects and to transport modelcalculations incorporating the interactions of charm quarks with an expandingdeconfined medium.

D-meson production in p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and in pp collisions at $\sqrt{s}=7$ TeV