EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2022-082 LHCb-PAPER-2022-007 7 May 2022

Measurement of the prompt ${D}^{0}$ nuclear modification factor in $p$Pb
collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16\text{\,Te\kern-2.07413ptV}$

LHCb collaboration

The production of prompt ${D}^{0}$ mesons in proton-lead collisions in the
forward and backward configurations at a center-of-mass energy per nucleon
pair of
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16\text{\,Te\kern-1.00006ptV}$ is
measured by the LHCb experiment. The nuclear modification factor of prompt
${D}^{0}$ mesons is determined as a function of the transverse momentum
$p_{\mathrm{T}}$, and rapidity in the nucleon-nucleon center-of-mass frame
$y^{*}$. In the forward rapidity region, significantly suppressed production
is measured, which provides a stringent test of the nuclear parton
distribution down to the very low Bjorken-$x$ region of $\sim 10^{-6}$. In the
backward rapidity region, a suppression with a significance of $2-4$ standard
deviations compared to theoretical predictions is observed in the kinematic
region of $p_{\mathrm{T}}>6\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$-3.25<y^{*}<-2.5$.

Submitted to Phys. Rev. Lett.

© 2024 CERN for the benefit of the LHCb collaboration. CC BY 4.0 licence.

Charm and beauty quarks are produced in the early stage of ultra-relativistic
heavy-ion collisions and are strongly affected by the presence of hot and
dense nuclear matter, known as quark-gluon plasma (QGP) [1, 2, 3, 4, 5, 6], as
well as by cold nuclear matter (CNM) effects. The latter can be studied in the
proton-nucleus collisions where QGP effects are not expected to be dominant.
Heavy-flavor hadrons, i.e. hadrons containing one or more heavy quark, are
affected by CNM effects at all stages of their production. In the initial
state, the parton distribution functions in a nuclear environment (nPDF) [7,
8, 9] differ from those in isolated nucleons. At LHC energies, the most
relevant effect is nuclear shadowing [10], which leads to a decrease of parton
density at small Bjorken momentum fraction $x$. The parton distributions at
small $x$ can also be described by the color-glass condensate effective theory
(CGC) as a saturated gluonic system [11]. Moreover, multiple scattering and
energy loss may occur when the incoming partons and the charm quarks traverse
the nuclear medium [12, 13, 14]. Other initial-state or even final-state
effects [15, 16] may also modify the kinematic distributions of produced
heavy-flavor hadrons, as suggested by their surprisingly large elliptic flow
values in high-multiplicity $p$Pb collisions [17, 18].

The LHCb collaboration has recently measured the production cross-section of
various heavy-flavor hadrons in $p$Pb collisions, including the production of
prompt ${D}^{0}$ and ${\mathchar 28931\relax}^{+}_{c}$ hadrons at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02$ TeV [19, 20], and the production
of ${J\mskip-3.0mu/\mskip-2.0mu\psi}$, ${B}^{0}$, ${{B}^{+}}$, ${\mathchar
28931\relax}^{0}_{b}$ and ${\mathchar 28935\relax}(nS)$ states at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16$ TeV [21, 22, 23]. The ALICE
collaboration has also measured the production cross-section of $D$ mesons at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-1.00006ptV}$ [24,
25, 26, 27]. CNM effects have also been investigated with heavy-quark
production at the RHIC collider in $d$Au collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}$ = 200 GeV [28, 29]. This has led to
significantly reduced uncertainties in the small-$x$ region [30, 31],
especially with the constraints from the LHCb ${{D}^{0}}$ measurements at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-1.00006ptV}$ [19].

This Letter reports the measurement of the production cross-section, the
nuclear modification factor $R_{p\mathrm{Pb}}$, and the forward-backward
production ratio $R_{\mathrm{FB}}$ of prompt ${D}^{0}$ mesons in $p$Pb
collisions at $\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16$ TeV performed with
the LHCb detector [32]. The quantity $R_{p\mathrm{Pb}}$ is defined as the
ratio of the cross-section in $p$Pb collisions to the corresponding cross-
section in $pp$ collisions scaled by the mass number of Pb, and the prompt
mesons are those directly produced in proton-lead collisions rather than in
decays of $b$-hadrons. This measurement uses a data sample 20 times larger
than that used for the LHCb ${D}^{0}$ measurements at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-1.00006ptV}$[19].

The LHCb detector [32, 33] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing heavy-flavor quarks. The high-precision tracking system consists of
a silicon-strip vertex detector surrounding the interaction region [34], a
large-area silicon-strip detector located upstream of a dipole magnet with a
bending power of about $4{\mathrm{\,Tm}}$, and three stations of silicon-strip
detectors and straw drift tubes [35] placed downstream of the magnet. The
tracking system provides measurements of the track momentum and impact
parameter and is used to reconstruct primary vertices (PVs). Different types
of charged hadrons are distinguished using information from two ring-imaging
Cherenkov detectors [36]. Events are selected for storage by a trigger system
consisting of a hardware stage followed by a two-stage software trigger[37].

The data sample for this analysis consists of $p\mathrm{Pb}$ collisions
collected with the LHCb detector at the end of 2016, including two different
configurations: forward collisions ($p$ beam coming from upstream of the
vertex detector) and backward collisions ($p$ beam coming from downstream of
the vertex detector), corresponding to an integrated luminosity of $12.2\pm
0.3$$\text{\,nb}^{-1}$ ($18.6\pm 0.5$$\text{\,nb}^{-1}$) for forward
(backward) collisions [22, 38].

Simulation samples are required to model the effects of the detector
acceptance and the selection requirements. The ${D}^{0}$ mesons are generated
using Pythia 8 [39, *Sjostrand:2007gs] and embedded into minimum-bias $p$Pb
events from the EPOS generator[41], calibrated with LHC data [42]. Decays of
unstable particles are described by EvtGen [43], in which final-state
radiation is generated using Photos [44]. The interaction of the generated
particles with the detector, and its response, are implemented using the
Geant4 toolkit [45, *Agostinelli:2002hh] as described in Ref. [47].

The double differential cross-section for prompt ${D}^{0}$ production is
measured as a function of $y^{*}$, the rapidity in the nucleon-nucleon center-
of-mass frame and $p_{\mathrm{T}}$, the transverse momentum with respect to
the beam direction. The $y^{*}$ is related to the rapidity in the laboratory
frame $y_{\mathrm{lab}}$ by $y^{*}=y_{\mathrm{lab}}-0.465$ for $p$Pb
collisions and the positive $z$-axis is defined as the direction of the proton
beam. The differential cross-section in a given ($p_{\mathrm{T}}$, $y^{*}$)
interval is defined as

$\frac{\mathrm{d}^{2}\sigma}{\mathrm{d}p_{\mathrm{T}}\mathrm{d}y^{*}}\equiv\frac{N({{D}^{0}}\\!\rightarrow{{K}^{\mp}}{{\pi}^{\pm}})+N({{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}\\!\rightarrow{{K}^{\pm}}{{\pi}^{\mp}})}{\mathcal{L}\times\varepsilon_{\text{tot}}\times\mathcal{B}({{D}^{0}}\\!\rightarrow{{K}^{\mp}}{{\pi}^{\pm}})\times\Delta
p_{\mathrm{T}}\times\Delta y^{*}}~{},$ (1)

where $N({{D}^{0}}\\!\rightarrow{{K}^{\mp}}{{\pi}^{\pm}})$ and $N({{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}\\!\rightarrow{{K}^{\pm}}{{\pi}^{\mp}})$
are the ${D}^{0}$ and ${\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$
signal yields, $\mathcal{L}$ is the integrated luminosity,
$\varepsilon_{\mathrm{tot}}$ is the total efficiency,
$\mathcal{B}({{D}^{0}}\\!\rightarrow{{K}^{\mp}}{{\pi}^{\pm}})=(3.96\pm
0.03)\%$ is the sum of branching fractions for the decays
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}$ [48], and $\Delta
p_{\mathrm{T}}$ and $\Delta y^{*}$ are the $p_{\mathrm{T}}$ and $y^{*}$
interval widths. The ${D}^{0}$ mesons are reconstructed through the
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ and
${{D}^{0}}\\!\rightarrow{{K}^{+}}{{\pi}^{-}}$ decay channels and their charge
conjugates. The measurement is performed within a $p_{\mathrm{T}}$ range of
$0<p_{\mathrm{T}}<30\text{\,Ge\kern-1.00006ptV\\!/}c$, and a rapidity range
for the forward sample of $1.5<y^{*}<4.0$ and for the backward sample of
$-5.0<y^{*}<-2.5$. Throughout the analysis, the measurements are for the
combined sample of ${D}^{0}$ and ${\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}$ mesons. The signal yields and the
total efficiency are determined in each kinematic interval.

The ${D}^{0}$ candidates are built from ${K}^{\mp}$ and ${\pi}^{\pm}$
candidate tracks. The selection criteria are similar to those used in
${D}^{0}$ production measurements in $p\mathrm{Pb}$ collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-1.00006ptV}$ [19].
The reconstructed ${K}^{\mp}$ and ${\pi}^{\pm}$ tracks are required to have
transverse momentum greater than $0.4\text{\,Ge\kern-1.00006ptV\\!/}c$. Both
tracks are also required to be of good quality, come from a common vertex, and
pass particle identification (PID) requirements.

The inclusive ${D}^{0}$ signal yield is the sum of the prompt ${D}^{0}$ mesons
and those produced in the decays of $b$ hadrons, denoted “from-$b$”. This
inclusive yield is determined using an extended unbinned maximum-likelihood
fit to the distribution of the $K$ $\pi$ invariant mass, $M({K}{\pi})$. The
$M({K}{\pi})$ distribution of the signal is described by a sum of a Crystal
Ball function [49] and a Gaussian function, where both functions share a
common mean value, while the background shape is described by a linear
function, following the measurement of Ref. [19]. The prompt signal yield is
determined by fitting the distribution of
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ of the ${D}^{0}$ candidates,
where $\chi^{2}_{\mathrm{IP}}$ is defined as the difference in the vertex-fit
$\chi^{2}$ of a given PV reconstructed with and without the ${D}^{0}$
candidate under consideration. The background component in the
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ distribution is subtracted using
the sPlot technique [50] with $M({K}{\pi})$ as the discriminating variable.
The shapes of the $\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ distribution
corresponding to the prompt and from-$b$ components are described
independently by Bukin functions [51], which are asymmetric functions with
tails described by Gaussian functions. The parameters of the functions
describing the prompt and from-$b$ components are fixed to those from
simulation. The invariant-mass and
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ distributions of the forward and
backward samples are given in the Supplemental Material [52].

The total efficiency $\varepsilon_{\mathrm{tot}}$ is the product of the
geometrical acceptance of the detector, the selection and reconstruction
efficiency, the PID efficiency and the trigger efficiency, with each component
determined separately. The geometrical acceptance, and the selection,
reconstruction and trigger efficiencies are evaluated with the $p\mathrm{Pb}$
simulation samples. The simulation sample is weighted in order to match the
occupancy of the tracking system observed in the data. The track
reconstruction efficiency is calibrated with minimum-bias
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow{\mu^{+}}{\mu^{-}}$ and
${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ samples, using
the tag-and-probe approach employed in Ref. [53]. The PID efficiency is
estimated with a tag-and-probe method [54, 55], using the ${D}^{*}$-tagged
decay chain ${{D}^{*+}}\\!\rightarrow{{D}^{0}}{{\pi}^{+}}$ with
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$ decays.

Several sources of systematic uncertainty are considered and are evaluated
separately for the forward and backward samples, unless stated otherwise. A
summary of the systematic uncertainties is provided in the Supplemental
Material [52]. The uncertainty of the invariant-mass fit is determined by
describing signal and background shapes with alternative fitting models. For
the estimation of the uncertainty due to the
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ fit, the data are refitted with
different models and varying fixed parameter values to evaluate the variation
of the signal yield. The uncertainties of the tracking and PID calibration are
dominated by those arising from the limited calibration sample size. The
uncertainty arising from matching the simulated detector occupancy
distribution to the data is estimated by weighting with different variables.
For the trigger efficiency, the difference between the efficiencies derived
from the simulation and from collision data [56] are considered as the
uncertainty. The uncertainties arising from the luminosity, the
$\mathcal{B}({{D}^{0}}\\!\rightarrow{{K}^{\mp}}{{\pi}^{\pm}})$ branching
fractions and the limited simulation sample size are also included.

The measured double-differential cross-section of prompt ${D}^{0}$ mesons is
shown in Fig. 1, with an integrated cross-section of $297.6\pm 0.6\pm
14.0\text{\,mb}$ in the kinematic range of
$0<p_{\mathrm{T}}<30\text{\,Ge\kern-1.00006ptV\\!/}c$ and $1.5<y^{*}<4.0$ for
the forward rapidity region, and $315.2\pm 0.2\pm 17.8\text{\,mb}$ in the
kinematic range of $0<p_{\mathrm{T}}<30\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$-5.0<y^{*}<-2.5$ in the backward rapidity region. The first uncertainties are
statistical and the second systematic. The numerical values for the double-
differential cross-section are given in the Supplemental Material [52].

Figure 1: Double-differential cross-sections of prompt ${D}^{0}$ mesons in
$p$Pb collisions in the (top) forward and (bottom) backward rapidity regions.
To display the differential cross-section values in different rapidity
intervals, multiplicative factors of $10^{-n}$ are used with $n$ increasing
with rapidity value. The uncertainties are too small to be visible in the
figures.

The nuclear modification factor $R_{p\mathrm{Pb}}$ is defined as

$R_{p\mathrm{Pb}}(p_{\mathrm{T}},y^{*})\equiv\frac{1}{A}\frac{\mathrm{d}^{2}\sigma_{p\text{Pb}}(p_{\mathrm{T}},y^{*})/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y^{*})}{\mathrm{d}^{2}\sigma_{pp}(p_{\mathrm{T}},y^{*})/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y^{*})}~{},$
(2)

where $A=208$ is the mass number of the lead nucleus and $\sigma_{pp}$ is the
prompt ${D}^{0}$ production cross-section in $pp$ collisions at
$\sqrt{s}=8.16\text{\,Te\kern-1.00006ptV}$. $\sigma_{pp}$ is obtained from a
power-law interpolation of LHCb measurements at
$\sqrt{s}=5\text{\,Te\kern-1.00006ptV}$ and
$\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ [57, 58] within the measured
kinematic range of $p_{\mathrm{T}}<10\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$2.0<y<4.5$, hence $R_{p\mathrm{Pb}}$ is measured in that range. The
uncertainties from the interpolation are incorporated into the systematic
uncertainties in $R_{p\mathrm{Pb}}$. The nuclear modification factor of the
${D}^{0}$ meson as a function of $p_{\mathrm{T}}$ in different $y^{*}$
intervals is displayed in Fig. 2 and the numerical values are given in the
Supplemental Material [52]. The $R_{p\mathrm{Pb}}$ values in finer $y^{*}$
intervals are given in the Supplemental Material [52]. The results are
compared with LHCb ${D}^{0}$ results at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-1.00006ptV}$ [19]
and HELAC-Onia calculations [59, 60, 61] incorporating nPDFs of EPPS16 [62]
and nCTEQ15 [63], which are weighted with ${D}^{0}$ measurements from LHC [19,
24, 25, 26, 27]. The model first fits LHC measured cross-sections in $pp$
collisions for parameterization and then incorporates the nPDFs to account for
the CNM effects [64], without considering other nuclear matter effects. The
uncertainties are dominated by nPDF parameterizations and correspond to a 68%
confidence interval. The nuclear modification factor with
$p_{\mathrm{T}}<5\text{\,Ge\kern-1.00006ptV\\!/}c$ in the forward rapidity
region is also compared with calculations from CGC predictions. For CGC1 [65,
66] the $D$-meson production is calculated with the optical Glauber model to
relate the initial condition of a nucleus to the one of the proton, while for
CGC2 [67] the cross-sections are computed with CGC effective field theory
combined with heavy-quark fragmentation functions. A significant suppression
of the cross-section in $p$Pb collisions with respect to that in $pp$
collisions scaled by the lead mass number is observed, in general agreement
with theoretical expectations. At low $p_{\mathrm{T}}$, the nPDF and CGC1
calculations are slightly higher than the data while the CGC2 calculation
shows a better agreement. The observed suppression in the backward rapidity is
less than that seen for forward rapidities. The $R_{p\mathrm{Pb}}$ values are
lower than the nPDF calculations for
$p_{\mathrm{T}}>6\text{\,Ge\kern-1.00006ptV\\!/}c$. Fig. 3 shows
$R_{p\mathrm{Pb}}$ as a function of $y^{*}$ in two different $p_{\mathrm{T}}$
intervals. The smaller values of $R_{p\mathrm{Pb}}$ compared to theoretical
predictions in the high-$p_{\mathrm{T}}$ interval may indicate that additional
effects exist in the backward rapidity region, which may be related to final-
state energy loss, that are not present at forward rapidity.

Figure 2: Nuclear modification factor as a function of $p_{\mathrm{T}}$ in
different $y^{*}$ intervals for prompt ${{D}^{0}}$ mesons in the (top) forward
and (bottom) backward regions. The error bars show the statistical
uncertainties and the boxes show the systematic uncertainties. The LHCb
results at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-0.90005ptV}$ [19]
and theoretical calculations from Refs. [62, 63, 66, 67] are also shown.
Figure 3: Nuclear modification factor for prompt ${{D}^{0}}$ mesons as a
function of $y^{*}$ in (left) the full-$p_{\mathrm{T}}$ range and (right) the
high-$p_{\mathrm{T}}$ range. The error bars show the statistical uncertainties
and the boxes show the systematic uncertainties. The LHCb results at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-0.90005ptV}$ [19]
and theoretical calculations from Refs. [62, 63, 66, 67] are also shown. On
the left, the $p_{\mathrm{T}}$ range is
$0<p_{\mathrm{T}}<15\text{\,Ge\kern-0.90005ptV\\!/}c$ for the calculations
with nPDFs of EPPS16 and nCTEQ15.

The forward-backward production ratio is defined as

$R_{\mathrm{FB}}(p_{\mathrm{T}},y^{*})\equiv\frac{\mathrm{d}^{2}\sigma(p_{\mathrm{T}},|y^{*}|;y^{*}>0)/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y^{*})}{\mathrm{d}^{2}\sigma(p_{\mathrm{T}},|y^{*}|;y^{*}<0)/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y^{*})}~{},$
(3)

which is calculated in the common $|y^{*}|$ interval of the forward-backward
acceptance, $2.5<|y^{*}|<4$. The measurements of $R_{\mathrm{FB}}$ are shown
as a function of $p_{\mathrm{T}}$ in Fig. 4, along with the LHCb
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-1.00006ptV}$
results [19] and the nPDF calculations. The numerical values for
$R_{\mathrm{FB}}$ are given in the Supplemental Material [52]. The prediction
from first principles considering medium-induced fully coherent energy loss
(FCEL) effect [14] is also shown, without incorporating nPDF effects.
Measurements of $R_{\mathrm{FB}}$ vs. $p_{\mathrm{T}}$ in finer $|y^{*}|$
intervals are shown in the Supplemental Material [52]. Good agreement with
nPDF calculations is found at low $p_{\mathrm{T}}$. However, the data show a
clear rising trend with increasing $p_{\mathrm{T}}$, reaching unity at the
highest $p_{\mathrm{T}}$ values, in contrast to the nPDF calculations of
$R_{\mathrm{FB}}\sim 0.7$, almost independent of $p_{\mathrm{T}}$. This
difference originates from the suppression of high-$p_{\mathrm{T}}$ ${D}^{0}$
mesons in the backward rapidity region, which is also evident in Fig. 2.

Figure 4: Forward-backward production ratio for prompt ${D}^{0}$ mesons as a
function of $p_{\mathrm{T}}$, integrated over the common rapidity range
$2.5<|y^{*}|<4.0$. The error bars show the statistical uncertainties and the
boxes show the systematic uncertainties. The LHCb results at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=5.02\text{\,Te\kern-0.90005ptV}$ [19]
and theoretical calculations from Refs. [62, 63, 14] are also shown.

In summary, the prompt ${{D}^{0}}$ production cross-section is measured at
LHCb in proton-lead collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16\text{\,Te\kern-1.00006ptV}$, in
both forward and backward configurations. The nuclear modification factors and
forward-backward production ratios are measured with high accuracy and show
strong cold nuclear matter effects. A stronger suppression than the
predictions of nPDF calculations is observed for the lowest transverse
momentum region of $p_{\mathrm{T}}<1\text{\,Ge\kern-1.00006ptV\\!/}c$. For the
backward rapidity range of $-3.25<y^{*}<-2.5$, the $R_{p\mathrm{Pb}}$ values
are lower than nPDF calculations at
$p_{\mathrm{T}}>6\text{\,Ge\kern-1.00006ptV\\!/}c$ with a significance of
$2-4$ standard deviations per interval, indicating additional effects that may
be related to final-state energy loss occur at backward rapidity. This Letter
presents the most precise measurement of the prompt ${D}^{0}$ production in
$p$Pb collisions to date. The measurement of $R_{p\mathrm{Pb}}$ provides a
stringent test of nPDFs down to small $x$ regions of $\sim 10^{-6}$.

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## Supplemental Material

### Fit to $M({K}{\pi})$ and $\log_{10}\left(\chi^{2}_{\text{IP}}\right)$
distributions

The fit results for the $M({K}{\pi})$ and
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ distributions in the kinematic
ranges of $2.5<p_{\mathrm{T}}<3.0\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$3.25<y^{*}<3.50$ $(-4.50<y^{*}<-4.25)$ are shown in Fig. 5 (Fig. 6).

Figure 5: Distributions and fit results of (left) $M({K}{\pi})$ and (right)
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ for inclusive ${D}^{0}$ mesons in
the forward data sample in the kinematic range of
$2.5<p_{\mathrm{T}}<3.0\text{\,Ge\kern-0.90005ptV\\!/}c$ and
$3.25<y^{*}<3.50$. For the $\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ fit,
the data are weighted using the sPlot method to subtract the background
component.  Figure 6: Distributions and fit results of (left) $M({K}{\pi})$
and (right) $\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ for inclusive
${D}^{0}$ mesons in the backward data sample in the kinematic range of
$2.5<p_{\mathrm{T}}<3.0\text{\,Ge\kern-0.90005ptV\\!/}c$ and
$-4.50<y^{*}<-4.25$. For the $\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ fit,
the data are weighted using the sPlot method to subtract the background
component.

### Table of systematic uncertainties

The ranges of systematic uncertainties for the forward and backward rapidity
regions are listed in Table 1.

Table 1: Systematic uncertainties considered in this measurement, in %. The range indicates the minimum and the maximum value among the two-dimensional $p_{\mathrm{T}}$ and $y^{*}$ intervals. The systematic uncertainties due to simulation sample size, mass fit and $\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ are uncorrelated across the intervals. The other sources of systematic uncertainties are fully correlated between different intervals.  Uncertainty source | Forward [%] | Backward [%]
---|---|---
Tracking calibration | 3.0 – 4.7 | 3.1 – 10.7
PID | 0.2 – 6.9 | 0.2 – 26.5
Trigger efficiency | 0.0 – 16.5 | 0.0 – 4.7
Multiplicity correction | 0 – 9 | 0 – 16
Luminosity | 2.6 | 2.5
Branching fraction | 0.8 | 0.8
Mass fit | 0.0 – 19.3 | 0.1 – 6.1
$\log_{10}\left(\chi^{2}_{\text{IP}}\right)$ fit | 0.3 – 19.5 | 0.4 – 7.0
Simulation sample size | 1 – 40 | 1 – 26

### Nuclear modification factor in different $y^{*}$ intervals with $\Delta
y^{*}=0.25$

The nuclear modification factor for the forward rapidity regions of
$2.0<y^{*}<4.0$ are shown in Fig. 7 while the backward regions of
$-4.5<y^{*}<-2.5$ are shown in Fig. 8.

Figure 7: Nuclear modification factor as a function of $p_{\mathrm{T}}$ in
different $y^{*}$ intervals for prompt ${{D}^{0}}$ mesons in the forward
regions for $2.0<y^{*}<4.0$. The error bars show the statistical uncertainties
and the boxes show the systematic uncertainties. The theoretical calculations
from Refs. [62, 63, 67, 14] are also shown.  Figure 8: Nuclear modification
factor as a function of $p_{\mathrm{T}}$ in different $y^{*}$ intervals for
prompt ${{D}^{0}}$ mesons in the backward regions for $-4.5<y^{*}<-2.5$. The
error bars show the statistical uncertainties and the boxes show the
systematic uncertainties. The theoretical calculations from Refs. [62, 63, 14]
are also shown.

### Forward-backward ratio in different $|y^{*}|$ intervals

The results for $R_{\mathrm{FB}}$ are presented in Fig. 9 in the kinematic
range of $p_{\mathrm{T}}<15\text{\,Ge\kern-1.00006ptV\\!/}c,2.5<|y^{*}|<4.0$
with $\Delta|y^{*}|=0.25$.

Figure 9: Forward and backward production ratio $R_{\mathrm{FB}}$ for prompt
${D}^{0}$ mesons as a function of $p_{\mathrm{T}}$ in different $|y^{*}|$
intervals. The error bars show the statistical uncertainties and the boxes
show the systematic uncertainties. The theoretical calculations from Refs.
[62, 63] are also shown.

### Tables of numerical values for double-differential cross-section, nuclear
modification factor and forward-backward ratio

The numerical values for double-differential cross-section
$\mathrm{d}^{2}\sigma/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y^{*})$ are listed in
Table 2 and 3 for forward and backward rapidity regions. The numerical values
for nuclear modification factor $R_{p\mathrm{Pb}}$ are listed in Table 4 and 5
for forward and backward rapidity regions. The numerical values for forward-
backward ratio $R_{\mathrm{FB}}$ as a function of $p_{\mathrm{T}}$ integrated
in the rapidity region of $2.5<|y^{*}|<4.0$ are listed in Table 6.

Table 2: Double-differential cross-sections for prompt ${D}^{0}$ mesons in
intervals of $p_{\mathrm{T}}$ and $y^{*}$ in forward rapidity regions. The
first uncertainty is statistical, the second is the component of the
systematic uncertainty that is uncorrelated across intervals and the third is
the correlated component.

$\mathrm{d}^{2}\sigma/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)~{}[\mathrm{mb}/(\text{\,Ge\kern-1.00006ptV\\!/}c)]$
---
$p_{\mathrm{T}}~{}[\text{\,Ge\kern-1.00006ptV\\!/}c]\backslash y^{*}$ | (1.50, 1.75) | (1.75, 2.00) | (2.00, 2.25) | (2.25, 2.50) | (2.50, 2.75)
(0.0,1.0) | $26.049\pm 1.734\pm 1.961\pm 4.494$ | $25.059\pm 0.128\pm 0.594\pm 1.304$ | $25.716\pm 0.090\pm 0.327\pm 1.205$ | $26.194\pm 0.079\pm 0.455\pm 1.208$ | $26.046\pm 0.075\pm 0.607\pm 1.162$
(1.0,1.5) | $47.452\pm 0.229\pm 2.317\pm 4.304$ | $47.375\pm 0.222\pm 0.870\pm 2.639$ | $46.707\pm 0.160\pm 0.630\pm 2.243$ | $45.091\pm 0.137\pm 1.369\pm 2.000$ | $46.465\pm 0.138\pm 0.780\pm 1.999$
(1.5,2.0) | $42.066\pm 0.153\pm 1.760\pm 2.658$ | $44.164\pm 0.188\pm 0.962\pm 2.054$ | $44.574\pm 0.103\pm 0.564\pm 1.952$ | $43.939\pm 0.129\pm 0.876\pm 2.220$ | $41.657\pm 0.120\pm 0.852\pm 1.793$
(2.0,2.5) | $34.993\pm 0.350\pm 1.535\pm 1.662$ | $35.978\pm 0.140\pm 0.653\pm 1.709$ | $36.344\pm 0.112\pm 0.546\pm 1.558$ | $35.023\pm 0.103\pm 0.550\pm 1.541$ | $33.970\pm 0.095\pm 0.659\pm 1.413$
(2.5,3.0) | $26.858\pm 0.227\pm 0.865\pm 1.295$ | $28.324\pm 0.109\pm 0.440\pm 1.250$ | $27.658\pm 0.089\pm 0.358\pm 1.336$ | $26.622\pm 0.080\pm 0.554\pm 1.151$ | $24.771\pm 0.095\pm 0.536\pm 1.062$
(3.0,3.5) | $19.321\pm 0.165\pm 0.615\pm 0.963$ | $19.133\pm 0.155\pm 0.295\pm 0.817$ | $19.185\pm 0.062\pm 0.381\pm 0.828$ | $18.717\pm 0.069\pm 0.251\pm 0.822$ | $17.124\pm 0.076\pm 0.345\pm 0.737$
(3.5,4.0) | $12.973\pm 0.114\pm 0.409\pm 0.563$ | $13.543\pm 0.057\pm 0.282\pm 0.578$ | $13.060\pm 0.059\pm 0.336\pm 0.672$ | $12.918\pm 0.057\pm 0.354\pm 0.542$ | $12.153\pm 0.056\pm 0.248\pm 0.531$
(4.0,4.5) | $9.619\pm 0.098\pm 0.379\pm 0.449$ | $9.947\pm 0.120\pm 0.222\pm 0.432$ | $9.450\pm 0.055\pm 0.189\pm 0.405$ | $8.918\pm 0.057\pm 0.234\pm 0.386$ | $8.350\pm 0.038\pm 0.205\pm 0.360$
(4.5,5.0) | $6.639\pm 0.075\pm 0.323\pm 0.341$ | $7.358\pm 0.039\pm 0.205\pm 0.323$ | $6.747\pm 0.036\pm 0.137\pm 0.292$ | $6.269\pm 0.042\pm 0.170\pm 0.267$ | $5.691\pm 0.036\pm 0.145\pm 0.239$
(5.0,5.5) | $4.851\pm 0.063\pm 0.194\pm 0.212$ | $4.857\pm 0.040\pm 0.151\pm 0.215$ | $4.723\pm 0.032\pm 0.114\pm 0.200$ | $4.430\pm 0.035\pm 0.126\pm 0.194$ | $3.983\pm 0.028\pm 0.105\pm 0.177$
(5.5,6.0) | $3.492\pm 0.051\pm 0.163\pm 0.148$ | $3.726\pm 0.027\pm 0.088\pm 0.168$ | $3.437\pm 0.029\pm 0.088\pm 0.146$ | $3.142\pm 0.025\pm 0.121\pm 0.132$ | $2.877\pm 0.022\pm 0.087\pm 0.130$
(6.0,7.0) | $2.230\pm 0.023\pm 0.104\pm 0.099$ | $2.275\pm 0.022\pm 0.058\pm 0.097$ | $2.196\pm 0.019\pm 0.061\pm 0.097$ | $1.964\pm 0.014\pm 0.053\pm 0.086$ | $1.842\pm 0.013\pm 0.049\pm 0.081$
(7.0,8.0) | $1.395\pm 0.021\pm 0.063\pm 0.060$ | $1.297\pm 0.013\pm 0.037\pm 0.056$ | $1.161\pm 0.014\pm 0.044\pm 0.050$ | $1.188\pm 0.009\pm 0.049\pm 0.053$ | $1.052\pm 0.009\pm 0.032\pm 0.048$
(8.0,9.0) | $0.818\pm 0.013\pm 0.022\pm 0.036$ | $0.764\pm 0.010\pm 0.018\pm 0.032$ | $0.702\pm 0.008\pm 0.014\pm 0.031$ | $0.682\pm 0.008\pm 0.022\pm 0.031$ | $0.605\pm 0.007\pm 0.015\pm 0.028$
(9.0,10.0) | $0.438\pm 0.019\pm 0.032\pm 0.020$ | $0.446\pm 0.007\pm 0.009\pm 0.019$ | $0.394\pm 0.006\pm 0.012\pm 0.018$ | $0.428\pm 0.006\pm 0.010\pm 0.020$ | $0.355\pm 0.006\pm 0.009\pm 0.018$
(10.0,11.0) | $0.284\pm 0.016\pm 0.015\pm 0.013$ | $0.278\pm 0.007\pm 0.010\pm 0.012$ | $0.239\pm 0.005\pm 0.007\pm 0.028$ | $0.276\pm 0.005\pm 0.008\pm 0.014$ | $0.227\pm 0.005\pm 0.008\pm 0.012$
(11.0,12.0) | $0.196\pm 0.009\pm 0.008\pm 0.008$ | $0.168\pm 0.005\pm 0.007\pm 0.008$ | $0.145\pm 0.004\pm 0.005\pm 0.007$ | $0.184\pm 0.005\pm 0.009\pm 0.011$ | $0.143\pm 0.005\pm 0.006\pm 0.008$
(12.0,13.0) | $0.136\pm 0.005\pm 0.006\pm 0.006$ | $0.103\pm 0.005\pm 0.008\pm 0.005$ | $0.098\pm 0.003\pm 0.004\pm 0.005$ | $0.116\pm 0.004\pm 0.006\pm 0.007$ | $0.110\pm 0.004\pm 0.006\pm 0.006$
(13.0,15.0) | $0.074\pm 0.004\pm 0.004\pm 0.004$ | $0.055\pm 0.002\pm 0.003\pm 0.002$ | $0.053\pm 0.002\pm 0.002\pm 0.003$ | $0.069\pm 0.002\pm 0.003\pm 0.005$ | $0.059\pm 0.003\pm 0.004\pm 0.004$
(15.0,30.0) | $(9.1\pm 0.5\pm 0.5\pm 0.5)\times 10^{-3}$ | $(6.8\pm 0.3\pm 0.3\pm 0.3)\times 10^{-3}$ | $(7.4\pm 0.3\pm 0.4\pm 0.8)\times 10^{-3}$ | $(10.7\pm 0.5\pm 0.7\pm 0.9)\times 10^{-3}$ | $(9.3\pm 1.1\pm 1.3\pm 0.7)\times 10^{-3}$
$p_{\mathrm{T}}[\text{\,Ge\kern-1.00006ptV\\!/}c]\backslash y^{*}$ | (2.75, 3.00) | (3.00, 3.25) | (3.25, 3.50) | (3.50, 3.75) | (3.75, 4.00)
(0.0,1.0) | $26.300\pm 0.149\pm 0.840\pm 1.169$ | $26.038\pm 0.083\pm 0.662\pm 1.191$ | $24.968\pm 0.147\pm 1.061\pm 1.189$ | $23.157\pm 0.196\pm 1.842\pm 1.157$ | $20.817\pm 1.548\pm 1.918\pm 1.093$
(1.0,1.5) | $44.909\pm 0.177\pm 1.057\pm 1.965$ | $44.107\pm 0.152\pm 0.649\pm 1.959$ | $39.851\pm 0.269\pm 2.554\pm 1.807$ | $36.184\pm 0.336\pm 1.706\pm 1.688$ | $35.092\pm 0.401\pm 1.848\pm 1.984$
(1.5,2.0) | $41.222\pm 0.124\pm 1.261\pm 1.769$ | $37.934\pm 0.172\pm 0.827\pm 1.668$ | $36.200\pm 0.203\pm 1.124\pm 1.708$ | $32.475\pm 0.262\pm 1.177\pm 1.541$ | $27.126\pm 0.421\pm 1.168\pm 1.492$
(2.0,2.5) | $31.966\pm 0.121\pm 0.963\pm 1.501$ | $28.923\pm 0.127\pm 0.644\pm 1.291$ | $27.061\pm 0.139\pm 0.855\pm 1.342$ | $23.492\pm 0.139\pm 0.796\pm 1.048$ | $20.558\pm 0.243\pm 1.053\pm 1.147$
(2.5,3.0) | $22.247\pm 0.087\pm 0.451\pm 0.977$ | $20.647\pm 0.087\pm 0.412\pm 0.918$ | $18.474\pm 0.097\pm 0.814\pm 0.812$ | $16.646\pm 0.123\pm 0.755\pm 0.779$ | $14.379\pm 0.208\pm 0.637\pm 0.811$
(3.0,3.5) | $15.693\pm 0.070\pm 0.332\pm 0.708$ | $14.210\pm 0.066\pm 0.308\pm 0.631$ | $12.554\pm 0.072\pm 0.365\pm 0.573$ | $11.648\pm 0.101\pm 0.451\pm 0.563$ | $9.117\pm 0.152\pm 0.424\pm 0.501$
(3.5,4.0) | $10.468\pm 0.052\pm 0.246\pm 0.459$ | $9.542\pm 0.048\pm 0.260\pm 0.425$ | $8.336\pm 0.055\pm 0.285\pm 0.370$ | $7.540\pm 0.072\pm 0.303\pm 0.409$ | $6.285\pm 0.185\pm 0.525\pm 0.406$
(4.0,4.5) | $7.317\pm 0.038\pm 0.159\pm 0.317$ | $6.576\pm 0.037\pm 0.174\pm 0.304$ | $5.675\pm 0.043\pm 0.155\pm 0.258$ | $5.108\pm 0.068\pm 0.204\pm 0.253$ | $3.678\pm 0.138\pm 0.273\pm 0.219$
(4.5,5.0) | $5.108\pm 0.030\pm 0.116\pm 0.234$ | $4.799\pm 0.033\pm 0.136\pm 0.216$ | $4.029\pm 0.040\pm 0.121\pm 0.188$ | $3.322\pm 0.061\pm 0.149\pm 0.167$ | $1.971\pm 0.154\pm 0.269\pm 0.139$
(5.0,5.5) | $3.645\pm 0.025\pm 0.088\pm 0.166$ | $3.189\pm 0.026\pm 0.081\pm 0.147$ | $2.725\pm 0.034\pm 0.108\pm 0.139$ | $2.307\pm 0.082\pm 0.158\pm 0.119$ | -
(5.5,6.0) | $2.611\pm 0.021\pm 0.074\pm 0.114$ | $2.296\pm 0.024\pm 0.068\pm 0.111$ | $1.847\pm 0.030\pm 0.077\pm 0.093$ | $1.510\pm 0.094\pm 0.152\pm 0.080$ | -
(6.0,7.0) | $1.656\pm 0.013\pm 0.052\pm 0.073$ | $1.372\pm 0.014\pm 0.056\pm 0.064$ | $0.983\pm 0.023\pm 0.049\pm 0.049$ | $0.717\pm 0.073\pm 0.180\pm 0.039$ | -
(7.0,8.0) | $0.924\pm 0.010\pm 0.033\pm 0.042$ | $0.746\pm 0.012\pm 0.034\pm 0.035$ | $0.493\pm 0.021\pm 0.044\pm 0.030$ | - | -
(8.0,9.0) | $0.533\pm 0.009\pm 0.018\pm 0.025$ | $0.405\pm 0.014\pm 0.025\pm 0.021$ | $0.202\pm 0.028\pm 0.038\pm 0.011$ | - | -
(9.0,10.0) | $0.287\pm 0.008\pm 0.010\pm 0.014$ | $0.243\pm 0.013\pm 0.018\pm 0.013$ | - | - | -
(10.0,11.0) | $0.161\pm 0.007\pm 0.011\pm 0.008$ | $0.129\pm 0.015\pm 0.024\pm 0.008$ | - | - | -
(11.0,12.0) | $0.110\pm 0.008\pm 0.009\pm 0.007$ | - | - | - | -
(12.0,13.0) | $0.079\pm 0.007\pm 0.011\pm 0.005$ | - | - | - | -
(13.0,15.0) | $0.051\pm 0.009\pm 0.017\pm 0.004$ | - | - | - | -
(15.0,30.0) | - | - | - | - | -

Table 3: Double-differential cross-sections for prompt ${D}^{0}$ mesons in
intervals of $p_{\mathrm{T}}$ and $y^{*}$ in backward rapidity regions. The
first uncertainty is statistical, the second is the component of the
systematic uncertainty that is uncorrelated across intervals and the third is
the correlated component.

$\mathrm{d}^{2}\sigma/(\mathrm{d}p_{\mathrm{T}}\mathrm{d}y)~{}[\mathrm{mb}/(\text{\,Ge\kern-1.00006ptV\\!/}c)]$
---
$p_{\mathrm{T}}~{}[\text{\,Ge\kern-1.00006ptV\\!/}c]\backslash y^{*}$ | (-2.75, -2.50) | (-3.00, -2.75) | (-3.25, -3.00) | (-3.50, -3.25) | (-3.75, -3.50)
(0.0,1.0) | $26.423\pm 0.077\pm 1.135\pm 2.046$ | $30.978\pm 0.110\pm 0.658\pm 2.272$ | $31.059\pm 0.086\pm 0.746\pm 1.764$ | $32.488\pm 0.079\pm 0.575\pm 1.859$ | $30.706\pm 0.075\pm 0.555\pm 1.731$
(1.0,1.5) | $50.258\pm 0.329\pm 1.766\pm 3.570$ | $55.180\pm 0.193\pm 1.433\pm 3.295$ | $56.266\pm 0.152\pm 1.055\pm 3.169$ | $55.760\pm 0.139\pm 0.959\pm 2.935$ | $53.809\pm 0.143\pm 0.971\pm 2.852$
(1.5,2.0) | $51.254\pm 0.277\pm 1.579\pm 3.222$ | $51.164\pm 0.162\pm 0.940\pm 2.918$ | $52.039\pm 0.133\pm 1.058\pm 2.768$ | $50.232\pm 0.125\pm 0.751\pm 2.968$ | $47.612\pm 0.121\pm 1.373\pm 2.535$
(2.0,2.5) | $41.615\pm 0.211\pm 1.109\pm 2.506$ | $42.476\pm 0.126\pm 1.047\pm 2.332$ | $41.267\pm 0.099\pm 0.490\pm 2.482$ | $39.322\pm 0.092\pm 0.618\pm 2.022$ | $36.252\pm 0.094\pm 1.045\pm 1.873$
(2.5,3.0) | $27.597\pm 0.140\pm 0.693\pm 1.672$ | $29.397\pm 0.089\pm 0.468\pm 1.603$ | $29.188\pm 0.150\pm 0.490\pm 1.570$ | $27.301\pm 0.062\pm 0.725\pm 1.417$ | $24.672\pm 0.080\pm 0.394\pm 1.389$
(3.0,3.5) | $20.272\pm 0.106\pm 0.478\pm 1.148$ | $20.175\pm 0.079\pm 0.294\pm 1.079$ | $20.078\pm 0.055\pm 0.590\pm 1.055$ | $18.466\pm 0.049\pm 0.464\pm 0.946$ | $16.460\pm 0.056\pm 0.292\pm 0.805$
(3.5,4.0) | $13.875\pm 0.078\pm 0.362\pm 0.737$ | $13.732\pm 0.046\pm 0.269\pm 0.727$ | $13.085\pm 0.079\pm 0.394\pm 0.678$ | $12.130\pm 0.046\pm 0.221\pm 0.637$ | $10.876\pm 0.041\pm 0.303\pm 0.544$
(4.0,4.5) | $9.523\pm 0.109\pm 0.258\pm 0.517$ | $9.049\pm 0.040\pm 0.232\pm 0.515$ | $8.776\pm 0.039\pm 0.182\pm 0.488$ | $8.053\pm 0.034\pm 0.160\pm 0.407$ | $6.978\pm 0.032\pm 0.145\pm 0.359$
(4.5,5.0) | $6.647\pm 0.044\pm 0.182\pm 0.363$ | $6.474\pm 0.043\pm 0.190\pm 0.325$ | $6.065\pm 0.028\pm 0.132\pm 0.294$ | $5.284\pm 0.026\pm 0.124\pm 0.269$ | $4.464\pm 0.022\pm 0.105\pm 0.216$
(5.0,5.5) | $4.622\pm 0.035\pm 0.153\pm 0.247$ | $4.353\pm 0.032\pm 0.106\pm 0.228$ | $3.888\pm 0.030\pm 0.093\pm 0.202$ | $3.662\pm 0.023\pm 0.089\pm 0.184$ | $3.006\pm 0.019\pm 0.091\pm 0.150$
(5.5,6.0) | $3.160\pm 0.041\pm 0.115\pm 0.172$ | $2.878\pm 0.028\pm 0.089\pm 0.158$ | $2.741\pm 0.024\pm 0.086\pm 0.133$ | $2.454\pm 0.017\pm 0.068\pm 0.125$ | $2.209\pm 0.016\pm 0.064\pm 0.114$
(6.0,7.0) | $1.893\pm 0.023\pm 0.098\pm 0.105$ | $1.798\pm 0.015\pm 0.044\pm 0.094$ | $1.669\pm 0.012\pm 0.047\pm 0.084$ | $1.478\pm 0.010\pm 0.037\pm 0.087$ | $1.225\pm 0.009\pm 0.039\pm 0.066$
(7.0,8.0) | $1.021\pm 0.012\pm 0.034\pm 0.055$ | $1.055\pm 0.007\pm 0.030\pm 0.054$ | $0.807\pm 0.009\pm 0.027\pm 0.044$ | $0.824\pm 0.007\pm 0.026\pm 0.054$ | $0.646\pm 0.006\pm 0.021\pm 0.039$
(8.0,9.0) | $0.632\pm 0.014\pm 0.014\pm 0.033$ | $0.562\pm 0.006\pm 0.020\pm 0.029$ | $0.467\pm 0.006\pm 0.011\pm 0.029$ | $0.429\pm 0.005\pm 0.008\pm 0.030$ | $0.355\pm 0.005\pm 0.010\pm 0.022$
(9.0,10.0) | $0.377\pm 0.006\pm 0.010\pm 0.019$ | $0.312\pm 0.006\pm 0.008\pm 0.017$ | $0.266\pm 0.005\pm 0.007\pm 0.017$ | $0.256\pm 0.004\pm 0.007\pm 0.020$ | $0.194\pm 0.004\pm 0.006\pm 0.013$
(10.0,11.0) | $0.241\pm 0.005\pm 0.008\pm 0.013$ | $0.184\pm 0.003\pm 0.006\pm 0.011$ | $0.151\pm 0.003\pm 0.004\pm 0.011$ | $0.157\pm 0.003\pm 0.005\pm 0.014$ | $0.117\pm 0.003\pm 0.008\pm 0.009$
(11.0,12.0) | $0.155\pm 0.009\pm 0.007\pm 0.008$ | $0.118\pm 0.006\pm 0.006\pm 0.008$ | $0.102\pm 0.003\pm 0.004\pm 0.010$ | $0.092\pm 0.003\pm 0.004\pm 0.011$ | $0.080\pm 0.003\pm 0.005\pm 0.006$
(12.0,13.0) | $0.093\pm 0.003\pm 0.007\pm 0.006$ | $0.080\pm 0.003\pm 0.004\pm 0.010$ | $0.067\pm 0.002\pm 0.004\pm 0.008$ | $0.067\pm 0.002\pm 0.003\pm 0.008$ | $0.041\pm 0.002\pm 0.004\pm 0.004$
(13.0,15.0) | $0.056\pm 0.002\pm 0.002\pm 0.005$ | $0.046\pm 0.002\pm 0.003\pm 0.012$ | $0.033\pm 0.001\pm 0.001\pm 0.005$ | $0.033\pm 0.002\pm 0.002\pm 0.005$ | $0.024\pm 0.002\pm 0.003\pm 0.002$
(15.0,30.0) | $(8.6\pm 0.3\pm 0.6\pm 2.4)\times 10^{-3}$ | $(5.5\pm 0.2\pm 0.4\pm 1.5)\times 10^{-3}$ | $(4.6\pm 0.2\pm 0.3\pm 0.9)\times 10^{-3}$ | $(6.1\pm 0.4\pm 0.6\pm 1.1)\times 10^{-3}$ | -
$p_{\mathrm{T}}~{}[\text{\,Ge\kern-1.00006ptV\\!/}c]\backslash y^{*}$ | (-4.00, -3.75) | (-4.25, -4.00) | (-4.50, -4.25) | (-4.75, -4.50) | (-5.00, -4.75)
(0.0,1.0) | $30.648\pm 0.072\pm 0.728\pm 1.785$ | $30.899\pm 0.087\pm 0.480\pm 1.646$ | $30.195\pm 0.102\pm 1.591\pm 1.724$ | $27.540\pm 0.167\pm 2.236\pm 1.559$ | $27.064\pm 0.176\pm 1.855\pm 1.897$
(1.0,1.5) | $50.516\pm 0.149\pm 1.295\pm 2.628$ | $49.920\pm 0.154\pm 1.026\pm 2.753$ | $45.676\pm 0.273\pm 1.648\pm 2.581$ | $39.963\pm 0.244\pm 1.630\pm 2.396$ | $37.309\pm 0.360\pm 2.581\pm 2.781$
(1.5,2.0) | $46.320\pm 0.125\pm 1.204\pm 2.395$ | $42.339\pm 0.125\pm 1.000\pm 2.246$ | $36.955\pm 0.155\pm 1.076\pm 2.017$ | $33.341\pm 0.208\pm 0.936\pm 2.091$ | $29.194\pm 0.518\pm 1.784\pm 2.086$
(2.0,2.5) | $33.509\pm 0.107\pm 0.558\pm 1.718$ | $30.329\pm 0.102\pm 0.515\pm 1.557$ | $27.392\pm 0.119\pm 0.550\pm 1.415$ | $22.942\pm 0.159\pm 0.702\pm 1.405$ | $19.056\pm 0.326\pm 1.006\pm 1.649$
(2.5,3.0) | $21.950\pm 0.069\pm 0.390\pm 1.114$ | $20.166\pm 0.078\pm 0.350\pm 1.076$ | $17.099\pm 0.093\pm 0.526\pm 1.266$ | $13.958\pm 0.096\pm 0.359\pm 0.918$ | $10.073\pm 0.161\pm 0.579\pm 0.860$
(3.0,3.5) | $14.270\pm 0.055\pm 0.262\pm 0.720$ | $12.483\pm 0.054\pm 0.235\pm 0.681$ | $10.923\pm 0.060\pm 0.233\pm 0.656$ | $8.404\pm 0.075\pm 0.256\pm 0.580$ | $5.923\pm 0.129\pm 0.373\pm 0.566$
(3.5,4.0) | $9.224\pm 0.037\pm 0.187\pm 0.462$ | $8.029\pm 0.040\pm 0.239\pm 0.453$ | $6.325\pm 0.044\pm 0.186\pm 0.394$ | $4.711\pm 0.058\pm 0.172\pm 0.368$ | $3.459\pm 0.169\pm 0.395\pm 0.339$
(4.0,4.5) | $5.943\pm 0.029\pm 0.119\pm 0.306$ | $4.791\pm 0.028\pm 0.114\pm 0.295$ | $4.084\pm 0.035\pm 0.116\pm 0.272$ | $2.899\pm 0.050\pm 0.177\pm 0.231$ | $1.790\pm 0.116\pm 0.282\pm 0.188$
(4.5,5.0) | $3.863\pm 0.026\pm 0.098\pm 0.208$ | $3.150\pm 0.024\pm 0.094\pm 0.196$ | $2.502\pm 0.030\pm 0.088\pm 0.165$ | $1.621\pm 0.048\pm 0.135\pm 0.142$ | -
(5.0,5.5) | $2.708\pm 0.019\pm 0.076\pm 0.154$ | $1.993\pm 0.019\pm 0.070\pm 0.131$ | $1.598\pm 0.025\pm 0.082\pm 0.122$ | $1.001\pm 0.072\pm 0.117\pm 0.093$ | -
(5.5,6.0) | $1.722\pm 0.015\pm 0.053\pm 0.098$ | $1.389\pm 0.016\pm 0.052\pm 0.087$ | $0.895\pm 0.021\pm 0.058\pm 0.066$ | $0.458\pm 0.049\pm 0.086\pm 0.040$ | -
(6.0,7.0) | $0.945\pm 0.008\pm 0.031\pm 0.063$ | $0.736\pm 0.010\pm 0.027\pm 0.054$ | $0.550\pm 0.023\pm 0.048\pm 0.046$ | - | -
(7.0,8.0) | $0.489\pm 0.007\pm 0.020\pm 0.032$ | $0.371\pm 0.010\pm 0.026\pm 0.028$ | $0.241\pm 0.023\pm 0.053\pm 0.024$ | - | -
(8.0,9.0) | $0.258\pm 0.005\pm 0.009\pm 0.018$ | $0.153\pm 0.010\pm 0.011\pm 0.012$ | - | - | -
(9.0,10.0) | $0.128\pm 0.006\pm 0.007\pm 0.010$ | $0.083\pm 0.013\pm 0.014\pm 0.007$ | - | - | -
(10.0,11.0) | $0.069\pm 0.004\pm 0.006\pm 0.006$ | - | - | - | -
(11.0,12.0) | $0.033\pm 0.004\pm 0.005\pm 0.003$ | - | - | - | -
(12.0,13.0) | - | - | - | - | -
(13.0,15.0) | - | - | - | - | -
(15.0,30.0) | - | - | - | - | -

Table 4: Nuclear modification factor $R_{p\mathrm{Pb}}$ for prompt ${D}^{0}$
mesons in intervals of $p_{\mathrm{T}}$ and $y^{*}$ for
$p_{\mathrm{T}}<10\text{\,Ge\kern-1.00006ptV\\!/}c$. The first uncertainty is
statistical and the second is the systematic component.

$R_{p\mathrm{Pb}}$
---
$p_{\mathrm{T}}~{}[\text{\,Ge\kern-1.00006ptV\\!/}c]\backslash y^{*}$ | (2.5, 4.0) | (2.0, 2.5) | (2.5, 3.0) | (3.0, 3.5) | (3.5, 4.0)
(0.0,1.0) | $0.546\pm 0.002\pm 0.033$ | $0.485\pm 0.001\pm 0.041$ | $0.525\pm 0.001\pm 0.032$ | $0.556\pm 0.002\pm 0.036$ | $0.561\pm 0.005\pm 0.039$
(1.0,2.0) | $0.596\pm 0.002\pm 0.034$ | $0.557\pm 0.001\pm 0.037$ | $0.591\pm 0.003\pm 0.034$ | $0.611\pm 0.002\pm 0.036$ | $0.585\pm 0.003\pm 0.038$
(2.0,3.0) | $0.637\pm 0.001\pm 0.034$ | $0.648\pm 0.001\pm 0.036$ | $0.637\pm 0.001\pm 0.034$ | $0.648\pm 0.001\pm 0.035$ | $0.624\pm 0.003\pm 0.037$
(3.0,4.0) | $0.671\pm 0.001\pm 0.036$ | $0.679\pm 0.001\pm 0.038$ | $0.676\pm 0.002\pm 0.035$ | $0.673\pm 0.002\pm 0.036$ | $0.659\pm 0.004\pm 0.044$
(4.0,5.0) | $0.706\pm 0.002\pm 0.040$ | $0.697\pm 0.002\pm 0.042$ | $0.719\pm 0.002\pm 0.039$ | $0.710\pm 0.003\pm 0.041$ | $0.681\pm 0.007\pm 0.048$
(5.0,6.0) | $0.719\pm 0.005\pm 0.048$ | $0.718\pm 0.003\pm 0.056$ | $0.722\pm 0.002\pm 0.047$ | $0.737\pm 0.004\pm 0.047$ | $0.688\pm 0.019\pm 0.064$
(6.0,7.0) | $0.710\pm 0.014\pm 0.067$ | $0.721\pm 0.004\pm 0.056$ | $0.769\pm 0.004\pm 0.058$ | $0.725\pm 0.006\pm 0.057$ | $0.568\pm 0.061\pm 0.169$
(7.0,8.0) | $0.752\pm 0.005\pm 0.061$ | $0.777\pm 0.006\pm 0.067$ | $0.783\pm 0.005\pm 0.061$ | $0.709\pm 0.010\pm 0.067$ | -
(8.0,9.0) | $0.768\pm 0.011\pm 0.073$ | $0.717\pm 0.006\pm 0.084$ | $0.832\pm 0.008\pm 0.074$ | $0.683\pm 0.023\pm 0.078$ | -
(9.0,10.0) | $0.784\pm 0.018\pm 0.111$ | $0.687\pm 0.007\pm 0.070$ | $0.764\pm 0.011\pm 0.086$ | $0.814\pm 0.043\pm 0.160$ | -

Table 5: Nuclear modification factor $R_{p\mathrm{Pb}}$ for prompt ${D}^{0}$
mesons in intervals of $p_{\mathrm{T}}$ and $y^{*}$ for
$p_{\mathrm{T}}<10\text{\,Ge\kern-1.00006ptV\\!/}c$. The first uncertainty is
statistical and the second is the systematic component.

$R_{p\mathrm{Pb}}$
---
$p_{\mathrm{T}}~{}[\text{\,Ge\kern-1.00006ptV\\!/}c]\backslash y^{*}$ | (-4.0, -2.5) | (-3.0, -2.5) | (-3.5, -3.0) | (-4.0, -3.5) | (-4.5, -4.0)
(0.0,1.0) | $0.691\pm 0.001\pm 0.049$ | $0.607\pm 0.002\pm 0.047$ | $0.706\pm 0.001\pm 0.049$ | $0.781\pm 0.001\pm 0.054$ | $0.959\pm 0.002\pm 0.080$
(1.0,2.0) | $0.803\pm 0.001\pm 0.053$ | $0.718\pm 0.001\pm 0.052$ | $0.824\pm 0.001\pm 0.054$ | $0.891\pm 0.001\pm 0.057$ | $0.994\pm 0.002\pm 0.068$
(2.0,3.0) | $0.891\pm 0.001\pm 0.056$ | $0.804\pm 0.002\pm 0.056$ | $0.940\pm 0.002\pm 0.056$ | $0.960\pm 0.001\pm 0.058$ | $1.087\pm 0.002\pm 0.075$
(3.0,4.0) | $0.917\pm 0.001\pm 0.053$ | $0.841\pm 0.003\pm 0.051$ | $0.982\pm 0.002\pm 0.056$ | $0.952\pm 0.002\pm 0.057$ | $1.134\pm 0.003\pm 0.099$
(4.0,5.0) | $0.916\pm 0.003\pm 0.056$ | $0.860\pm 0.008\pm 0.054$ | $0.962\pm 0.002\pm 0.058$ | $0.948\pm 0.003\pm 0.062$ | $1.031\pm 0.004\pm 0.139$
(5.0,6.0) | $0.894\pm 0.002\pm 0.062$ | $0.832\pm 0.005\pm 0.061$ | $0.929\pm 0.003\pm 0.060$ | $0.956\pm 0.004\pm 0.072$ | $1.493\pm 0.010\pm 0.403$
(6.0,7.0) | $0.884\pm 0.003\pm 0.074$ | $0.819\pm 0.005\pm 0.064$ | $0.911\pm 0.005\pm 0.073$ | $0.974\pm 0.005\pm 0.111$ | -
(7.0,8.0) | $0.898\pm 0.004\pm 0.086$ | $0.827\pm 0.006\pm 0.067$ | $0.881\pm 0.006\pm 0.084$ | $1.101\pm 0.009\pm 0.158$ | -
(8.0,9.0) | $0.918\pm 0.006\pm 0.118$ | $0.861\pm 0.010\pm 0.079$ | $0.857\pm 0.008\pm 0.091$ | $1.197\pm 0.014\pm 0.352$ | -
(9.0,10.0) | $0.867\pm 0.007\pm 0.123$ | $0.805\pm 0.010\pm 0.091$ | $0.964\pm 0.011\pm 0.181$ | - | -

Table 6: Forward-backward production ratio $R_{\mathrm{FB}}$ for prompt ${D}^{0}$ mesons as a function of $p_{\mathrm{T}}$, integrated over $2.5<|y^{*}|<4.0$. The first uncertainty is statistical, the second is the component of the systematic uncertainty that is uncorrelated across intervals and the third is the correlated component. $p_{\mathrm{T}}~{}[\text{\,Ge\kern-1.00006ptV\\!/}c]$ | $R_{\mathrm{FB}}$
---|---
(0.0,1.0) | $0.808\pm 0.009\pm 0.019\pm 0.051$
(1.0,1.5) | $0.766\pm 0.002\pm 0.014\pm 0.044$
(1.5,2.0) | $0.725\pm 0.002\pm 0.011\pm 0.041$
(2.0,2.5) | $0.708\pm 0.002\pm 0.011\pm 0.039$
(2.5,3.0) | $0.732\pm 0.002\pm 0.011\pm 0.040$
(3.0,3.5) | $0.732\pm 0.002\pm 0.011\pm 0.039$
(3.5,4.0) | $0.745\pm 0.003\pm 0.013\pm 0.040$
(4.0,4.5) | $0.760\pm 0.004\pm 0.012\pm 0.042$
(4.5,5.0) | $0.760\pm 0.006\pm 0.015\pm 0.040$
(5.0,5.5) | $0.811\pm 0.006\pm 0.016\pm 0.044$
(5.5,6.0) | $0.829\pm 0.009\pm 0.020\pm 0.045$
(6.0,7.0) | $0.815\pm 0.010\pm 0.029\pm 0.045$
(7.0,8.0) | $0.868\pm 0.008\pm 0.024\pm 0.051$
(8.0,9.0) | $0.835\pm 0.017\pm 0.027\pm 0.050$
(9.0,10.0) | $0.926\pm 0.019\pm 0.028\pm 0.055$
(10.0,11.0) | $0.896\pm 0.032\pm 0.050\pm 0.060$
(11.0,12.0) | $0.925\pm 0.048\pm 0.051\pm 0.063$
(12.0,13.0) | $1.096\pm 0.056\pm 0.088\pm 0.106$
(13.0,15.0) | $1.078\pm 0.099\pm 0.178\pm 0.181$