# Measurement of prompt D$^0$, D$^+$, D$^{*+}$, and D$^+_s$ production in p$-$Pb collisions at $\mathbf{\sqrt{{\textit s}_{\rm NN}}~=~5.02~TeV}$

The measurement of the production of prompt D$^0$, D$^+$, D$^{*+}$, and D$^+_s$ mesons in proton$-$lead (p$-$Pb) collisions at the centre-of-mass energy per nucleon pair of $\sqrt{s_{\rm NN}}$ = 5.02 TeV, with an integrated luminosity of $292\pm 11$ $\mu$b$^{-1}$, are reported. Differential production cross sections are measured at mid-rapidity ($-0.96<~y_{\rm cms}<~0.04$) as a function of transverse momentum ($p_{\rm T}$) in the intervals $0<~ p_{\rm T} <~ 36$ GeV/$c$ for D$^0$, $1<~ p_{\rm T} <~36$ GeV/$c$ for D$^+$ and D$^{*+}$, and $2<~ p_{\rm T} <~24$ GeV/$c$ for D$^+_s$ mesons. For each species, the nuclear modification factor $R_{\rm pPb}$ is calculated as a function of $p_{\rm T}$ using a proton-proton (pp) reference measured at the same collision energy. The results are compatible with unity in the whole $p_{\rm T}$ range. The average of the non-strange D mesons $R_{\rm pPb}$ is compared with theoretical model predictions that include initial-state effects and parton transport model predictions. The $p_{\rm T}$ dependence of the D$^0$, D$^+$, and D$^{*+}$ nuclear modification factors is also reported in the interval $1<~ p_{\rm T} <~ 36$ GeV/$c$ as a function of the collision centrality, and the central-to-peripheral ratios are computed from the D-meson yields measured in different centrality classes. The results are further compared with charged-particle measurements and a similar trend is observed in all the centrality classes. The ratios of the $p_{\rm T}$-differential cross sections of D$^0$, D$^+$, D$^{*+}$, and D$^+_s$ mesons are also reported. The D$^+_s$ and D$^+$ yields are compared as a function of the charged-particle multiplicity for several $p_{\rm T}$ intervals. No modification in the relative abundances of the four species is observed with respect to pp collisions within the statistical and systematic uncertainties.

Figures

## Figure 1

 Examplary invariant-mass distributions for $\Dzero$, $\Dplus$, and $\Ds$ candidates (plus charge conjugates) and the mass difference $\Delta M = M_{{\rm K} \pi\pi} -M_{{\rm K} \pi}$ for $\Dstar$ candidates (and charge conjugates) in p--Pb collisions at $\sqrtsNN=5.02~\tev$ The dashed curves represent the fit applied to the background, while the solid lines represent the total fit function In the case of the $\Dzero$ meson, the contribution of signal reflections in the invariant-mass distribution is shown using a gray dot-dashed line. In the case of the $\Ds$ invariant-mass distribution, an additional Gaussian is used in the fit function in order to describe the $\Dplus$ signal peak on the left side of the $\Ds$ signal.

## Figure 2

 The product of acceptance and efficiency for $\Dzero$, $\Dplus$, $\Dstar$, and $\Ds$ mesons as a function of transverse momentum in p--Pb collisions at $\sqrtsNN=5.02~\tev$ The values for prompt (solid line) and feed-down (dashed line) D mesons are shown

## Figure 3

 Invariant-mass distributions of $\DtoKpi$ candidates (andcharge conjugates) for $0< \pt< 1~\gev/c$. The left panel displaysthe invariant-mass distribution of all ULS K$\pi$ pairs together with thebackground distribution estimated with the track-rotation technique. The right panel shows the invariant-mass distribution after subtracting the background estimated with the track-rotation technique. The fit function is superimposed.

## Figure 4

 Product of acceptance and efficiency of $\DtoKpi$ (and charge conjugates) in \pPb~collisions for the analyses with and without reconstruction of decay vertex.

## Figure 5

 Left: Exemplary fits to the impact-parameter distributions of $\Dzero$, $\Dplus$, and $\Dstar$ candidates. The curves show the fit functions describing the prompt, feed-down, and background contributions as well as their sum, as described in the text Right: fraction of prompt $\Dzero$, $\Dplus$, and $\Dstar$ raw yield as a function of transverse momentum $\pt$ compared with the values obtained with the FONLL-based approach. The results from the data-driven method are shown as square markers with the error bars (boxes) representing the statistical (systematic) uncertainty. The central values of $\fprompt$ from the FONLL-based approach are shown as the dashed lines and the uncertainty as red boxes

## Figure 6

 Left: inclusive $\Dzero$-meson production cross sections from the analysis without decay-vertex reconstruction in p--Pb collisions and pp collisions, both at $\sqrtsNN =5.02~\tev$. The cross section measured in pp collision ~ is scaled by the Pb mass number ($A=208$) and corrected for the rapidity shift in p--Pb collisions using FONLL calculations. Right: $\pt$-differential production cross section of prompt $\Dzero$ mesons with $-0.96< y_{\rm cms}< 0.04$ in p--Pb collisions at $\sqrtsNN =5.02~\tev$, measured with and without decay-vertex reconstruction. The vertical bars and the empty boxes represent the statistical and systematic uncertainties. The inset shows the ratio of the measurements in their common $\pt$ range

## Figure 7

 $\pt$-differential production cross sections of prompt $\Dzero$, $\Dplus$, $\Dstar$, and $\Ds$ mesons with $-0.96< y_{\rm cms}< 0.04$ in p--Pb collisions at $\sqrtsNN=5.02~\tev$ compared with the respective pp reference cross sections~ scaled by the Pb mass number ($A=208$) and corrected for the rapidity shift. For the $\Dzero$ meson, the results in the range $0< \pt< 1~\gev/c$ are obtained from the analysis that was performed without decay-vertex reconstruction, while those in the range \mbox{$1< \pt< 36~\gev/c$} are taken from the analysis with decay-vertex reconstruction The vertical bars and the empty boxes represent the statistical and systematic uncertainties

## Figure 8

 Nuclear modification factors $\RpPb$ of prompt D mesons in p--Pb collisions at $\sqrtsNN=5.02~\tev$ Left: $\RpPb$ of $\Dzero$, $\Dplus$, and $\Dstar$ mesons. Right: average $\RpPb$ of non-strange D-meson species in the interval $1< \pt< 36~\gev/c$~, shown together with the $\Dzero$ $R_{\rm pPb}$ in $0< \pt< 1~\GeV/c$ and the $\RpPb$ of $\Ds$ mesons in the interval $2< \pt< 24~\gev/c$ The vertical bars and the empty boxes represent the statistical and systematic uncertainties The black-filled box at $\RpPb=1$ represents the normalisation uncertainty.

## Figure 9

 Nuclear modification factor $\RpPb$ of prompt non-strange D mesons in p--Pb collisions at $\sqrtsNN=5.02~\tev$. In the left panel, the data are compared with calculations of theoretical models that include only CNM effects: CGC~, FONLL~ with EPPS16 nPDFs~, a LO pQCD calculation (Vitev et al.)~, and a calculation based on incoherent multiple scatterings (Kang et al.)~. In the right panel, the predictions of the Duke~ and POWLANG~ transport models are compared with the measured D-meson $\RpPb$ The vertical bars and the empty boxes represent the statistical and systematic uncertainties The black-filled box at $\RpPb=1$ represents the normalisation uncertainty.

## Figure 10

 Nuclear modification factors of prompt D mesons as a function of $\pt$ in 0--10\The vertical bars represent the statistical uncertainties while the empty boxes and the shaded boxes represent the systematic uncertainties for the prompt D mesons and for the charged particles. The colour-filled boxes at $\QpPb$ $=1$ represent the normalisation uncertainties on the $\langle \TpPb \rangle$~.

## Figure 12

 Average D-meson and charged-particles~ $\Qcp$ using the yields measured in 0--10\

## Figure 13

 Ratios of prompt D-meson production cross sections as a function of $\pt$ in p--Pb collisions at \mbox{$\sqrtsNN=5.02~\tev$} The results are compared with those of pp collisions at the same centre-of-mass energy~. The vertical bars and the empty boxes represent the statistical and systematic uncertainties.

## Figure 14

 $\Ds/\Dplus$-meson yield ratios, as a function of primary charged particles per unity of pseudorapidity in pp~, p--Pb, and Pb--Pb~ collisions at $\sqrtsNN=5.02 ~\tev$ in five different $\pt$ intervals from 2 to 16 $\gev/c$.