EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-272 LHCb-PAPER-2015-041

Measurements of prompt charm production cross-sections in $pp$ collisions at
$\sqrt{s}=13$ TeV

The LHCb collaboration†††Authors are listed at the end of this paper.

Production cross-sections of prompt charm mesons are measured with the first
data from $pp$ collisions at the LHC at a centre-of-mass energy of
$13\text{\,}\mathrm{TeV}$. The data sample corresponds to an integrated
luminosity of $4.98\pm 0.19\text{\,}{\mathrm{pb}}^{-1}$ collected by the LHCb
experiment. The production cross-sections of $D^{0}$, $D^{+}$, $D_{s}^{+}$,
and $D^{*+}$ mesons are measured in bins of charm meson transverse momentum,
$p_{\mathrm{T}}$, and rapidity, $y$, and cover the range
$0<p_{\mathrm{T}}<$15\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
and $2.0<y<4.5$. The inclusive cross-sections for the four mesons, including
charge conjugation, within the range of
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
are found to be

$\displaystyle\begin{array}[]{lcr}\sigma(\mbox{$pp\to D^{0}X$})&=&$2072\pm
2\pm 124\text{\,}\mathrm{\SIUnitSymbolMicro b}$,\\\ \sigma(\mbox{$pp\to
D^{+}X$})&=&$834\pm 2\pm\phantom{1}78\text{\,}\mathrm{\SIUnitSymbolMicro
b}$,\\\ \sigma(\mbox{$pp\to D_{s}^{+}X$})&=&$353\pm
9\pm\phantom{1}76\text{\,}\mathrm{\SIUnitSymbolMicro b}$,\\\
\sigma(\mbox{$pp\to D^{*+}X$})&=&$784\pm
4\pm\phantom{1}87\text{\,}\mathrm{\SIUnitSymbolMicro b}$,\\\ \end{array}$

where the uncertainties are due to statistical and systematic uncertainties,
respectively.

Published in JHEP 03 (2016) 159

Errata published in JHEP 09 (2016) 013 and JHEP 05 (2017) 074‡‡‡The contents
of the errata are reflected in this manuscript.

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

Measurements of charm production cross-sections in proton-proton collisions
are important tests of the predictions of perturbative quantum chromodynamics
[1, 2, 3]. Predictions of charm meson cross-sections have been made at next-
to-leading order using the generalized mass variable flavour number scheme
(GMVFNS) [4, 5, 6, 7, 8, 3] and at fixed order with next-to-leading-log
resummation (FONLL) [1, 9, 10, 11, 12, 2]. These are based on a factorisation
approach, where the cross-sections are calculated as a convolution of three
terms: the parton distribution functions of the incoming protons; the partonic
hard scattering rate, estimated as a perturbative series in the coupling
constant of the strong interaction; and a fragmentation function that
parametrises the hadronisation of the charm quark into a given type of charm
hadron. The range of $y$ and $p_{\mathrm{T}}$ accessible to LHCb enables
quantum chromodynamics calculations to be tested in a region where the
momentum fraction, $x$, of the initial state partons can reach values below
$10^{-4}$. In this region the uncertainties on the gluon parton density
functions are large, exceeding 30$\%$ [1, 13], and LHCb measurements can be
used to constrain them. For example, the predictions provided in Ref. [1] have
made direct use of these constraints from LHCb data, taking as input a set of
parton density functions that is weighted to match the LHCb measurements at
$\sqrt{s}=$7\text{\,}\mathrm{TeV}$$.

The charm production cross-sections are also important in evaluating the rate
of high-energy neutrinos created from the decay of charm hadrons produced in
cosmic ray interactions with atmospheric nuclei [14, 1]. Such neutrinos
constitute an important background for experiments such as IceCube [15]
searching for neutrinos produced from astrophysical sources. The previous
measurements from LHCb at $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ [16] permit the
evaluation of this background for incoming cosmic rays with energy of
$26\text{\,}\mathrm{\mathrm{\,Pe\kern-1.00006ptV}}$. In this paper
measurements at $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ are presented, probing a
new kinematic region that corresponds to a primary cosmic ray energy of
$90\text{\,}\mathrm{\mathrm{\,Pe\kern-1.00006ptV}}$.

Measurements of the charm production cross-sections have been performed in
different kinematic regions and centre-of-mass energies. Measurements by the
CDF experiment cover the central rapidity region $|y|<1$ and transverse
momenta, $p_{\mathrm{T}}$, between
$5.5\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ and
$20\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ at
$\sqrt{s}=$1.96\text{\,}\mathrm{TeV}$$ in $p\overline{p}$ collisions [17]. At
the Large Hadron Collider (LHC), charm cross-sections in $pp$ collisions have
been measured in the $|y|<0.5$ region for
$p_{\mathrm{T}}>$1\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$ at
$\sqrt{s}=$2.76\text{\,}\mathrm{TeV}$$ and $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$
by the ALICE experiment [18, 19, 20]. The LHCb experiment has recorded the
world’s largest dataset of charm hadrons to date and this has led to numerous
high-precision measurements of their production and decay properties. LHCb
measured the cross-sections in the forward region $2.0<y<4.5$ for
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
at $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ [16].

Charm mesons produced at the $pp$ collision point, either directly or as decay
products of excited charm resonances, are referred to as promptly produced. No
attempt is made to distinguish between these two sources. This paper presents
measurements of the cross-sections for the prompt production of $D^{0}$,
$D^{+}$, $D_{s}^{+}$, and $D^{*}(2010)^{+}$ (henceforth denoted as $D^{*+}$)
mesons, based on data corresponding to an integrated luminosity of $4.98\pm
0.19\text{\,}{\mathrm{pb}}^{-1}$. Charm mesons produced through the decays of
$b$ hadrons are referred to as secondary charm, and are considered as a
background process.

Section 2 describes the detector, data acquisition conditions, and the
simulation; this is followed by a detailed account of the data analysis in
Sec. 3. The differential cross-section results are given in Sec. 4, followed
by a discussion of systematic uncertainties in Sec. 5. Section 6 presents the
measurements of integrated cross-sections and of the ratios of the cross-
sections measured at $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ to those at
$7\text{\,}\mathrm{TeV}$. The theory predictions and their comparison with the
results of this paper are discussed in Sec. 7. Sec. 8 provides a summary.

##  2 Detector and simulation

The LHCb detector [21, 22] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes placed downstream of the
magnet. The tracking system provides a measurement of momentum of charged
particles with a relative uncertainty that varies from 0.5% at low momentum to
1.0% at $200\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$. The
minimum distance of a track to a primary vertex, the impact parameter (IP), is
measured with a resolution of
$(15+29/p_{\mathrm{T}})\,$\mathrm{\SIUnitSymbolMicro m}$$, where
$p_{\mathrm{T}}$ is the component of the momentum transverse to the beam, in
$\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$. Different types of charged
hadrons are distinguished by information from two ring-imaging Cherenkov
detectors. Photons, electrons and hadrons are identified by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers.

The online event selection is performed by a trigger. This consists of a
hardware stage, which for this analysis randomly selects a pre-defined
fraction of all beam-beam crossings, followed by a software stage. This
analysis benefits from a new scheme for the LHCb software trigger introduced
for LHC Run 2. Alignment and calibration is performed in near real-time [23]
and updated constants are made available for the trigger. The same alignment
and calibration information is propagated to the offline reconstruction,
ensuring consistent and high-quality particle identification (PID) information
between the trigger and offline software. The larger timing budget available
in the trigger compared to LHCb Run 1 also results in the convergence of the
online and offline track reconstruction, such that offline performance is
achieved in the trigger. The identical performance of the online and offline
reconstruction offers the opportunity to perform physics analyses directly
using candidates reconstructed in the trigger [24]. The storage of only the
triggered candidates enables a reduction in the event size by an order of
magnitude.

In the simulation, $pp$ collisions are generated with Pythia [25] using a
specific LHCb configuration [26]. Decays of hadronic particles are described
by EvtGen [27] in which final-state radiation is generated with Photos [28].
The implementation of the interaction of the generated particles with the
detector, and its response, uses the Geant4 toolkit [29, *Agostinelli:2002hh]
as described in Ref. [31].

##  3 Analysis strategy

The analysis is based on fully reconstructed decays of charm mesons in the
following decay modes: $D^{0}\to K^{-}\pi^{+}$, $D^{+}\to
K^{-}\pi^{+}\pi^{+}$, $D^{*+}\to D^{0}(\to K^{-}\pi^{+})\pi^{+}$,
$D_{s}^{+}\to(K^{-}K^{+})_{\phi}\pi^{+}$, and their charge conjugates. The
$D^{0}\to K^{-}\pi^{+}$ sample contains the sum of the Cabibbo-favoured decays
$D^{0}\to K^{-}\pi^{+}$ and the doubly Cabibbo-suppressed decays ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}^{0}\to K^{-}\pi^{+}$, but for
simplicity the combined sample is referred to by its dominant component. The
$D_{s}^{+}\to(K^{-}K^{+})_{\phi}\pi^{+}$ sample comprises $D_{s}^{+}\to
K^{-}K^{+}\pi^{+}$ decays where the invariant mass of the $K^{-}K^{+}$ pair is
required to be within
$\pm$20\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$$ of the
nominal $\phi(1020)$ mass. To allow cross-checks of the main results, the
following decays are also reconstructed: $D^{+}\to K^{-}K^{+}\pi^{+}$,
$D^{*+}\to D^{0}(K^{-}\pi^{+}\pi^{-}\pi^{+})\pi^{+}$, and $D_{s}^{+}\to
K^{-}K^{+}\pi^{+}$, where the $D_{s}^{+}\to K^{-}K^{+}\pi^{+}$ sample here
excludes candidates used in the $D_{s}^{+}\to(K^{-}K^{+})_{\phi}\pi^{+}$
measurement. All decay modes are inclusive with respect to final state
radiation.

The cross-sections are measured in two-dimensional bins of $p_{\mathrm{T}}$
and $y$ of the reconstructed mesons, where $p_{\mathrm{T}}$ and $y$ are
measured in the $pp$ centre-of-mass frame. The bin widths are $0.5$ in $y$
covering a range of $2.0<y<4.5$,
$1\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ in $p_{\mathrm{T}}$
for
$0<p_{\mathrm{T}}<$1\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$,
$0.5\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ in
$p_{\mathrm{T}}$ for
$1<p_{\mathrm{T}}<$3\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$,
and $1\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ in
$p_{\mathrm{T}}$ for
$3<p_{\mathrm{T}}<$15\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$.

###  3.1 Selection criteria

The selection of candidates is optimised independently for each decay mode.
For $D^{0}\to K^{-}\pi^{+}$ decays the same criteria are used for both the
$D^{0}$ and $D^{*+}$ cross-section measurements. All events are required to
contain at least one reconstructed primary ($pp$) interaction vertex (PV). All
final-state kaons and pions from the decays of $D^{0}$, $D^{+}$ and
$D_{s}^{+}$ are required to be identified with high purity within the momentum
and rapidity coverage of the LHCb PID system, i.e. momentum between 3 and
$100\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ and pseudorapidity
between 2 and 5.

The corresponding tracks must be of good quality and satisfy
$p_{\mathrm{T}}>200$ or
$250\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c}}$, depending on the
decay mode. At least one track must satisfy
$p_{\mathrm{T}}>$800\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c}}$$,
while for three-body decays, one track has to satisfy
$p_{\mathrm{T}}>$1000\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c}}$$
and at least two tracks must have
$p_{\mathrm{T}}>$400\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c}}$$.
The lifetimes of the weakly decaying charm mesons are sufficiently long for
the final-state particles to originate from a point away from the PV, and this
characteristic is exploited by requiring that all final-state particles from
these mesons are inconsistent with having originated from the PV.

When combining tracks to form $D^{0}$, $D^{+}$, and $D_{s}^{+}$ meson
candidates, requirements are made to ensure that the tracks are consistent
with originating from a common decay vertex and that this vertex is
significantly displaced from the PV. Additionally, the angle between the
particle’s momentum vector and the vector connecting the PV to the decay
vertex of the $D^{0}$ ($D^{+}$ and $D_{s}^{+}$) candidate must not exceed
$17(35)\,$\mathrm{mrad}$$. Candidate $D^{*+}\to D^{0}\pi^{+}$ decays are
formed by the combination of a $D^{0}$ candidate and a pion candidate, which
are required to form a good quality vertex. The $D^{0}$ candidates contained
in the $D^{*+}$ sample are a subset of those used in the measurement of the
$D^{0}$ cross-section.

###  3.2 Selection efficiencies

The efficiencies for triggering, reconstructing and selecting signal decays
are factorised into components that are measured in independent studies. These
are the efficiency for decays to occur in the detector acceptance, for the
final-state particles to be reconstructed, and for the decay to be selected.
To determine the efficiency of each of these components, the full event
simulation is used, except for the PID selection efficiencies, where a data-
driven approach is adopted: the efficiency with which pions and kaons are
selected is measured using high-purity, independent calibration samples of
pions and kaons from $D^{*+}\to D^{0}(\to K^{-}\pi^{+})\pi^{+}$ decays
identified without PID requirements, but with otherwise tighter criteria. The
efficiency in $(p_{\mathrm{T}},y)$ bins for each charm meson decay mode is
obtained with a weighting procedure to align the calibration and signal
samples for the variables with respect to which the PID selection efficiency
varies. These variables are the track momentum, track pseudorapidity, and the
number of hits in the scintillating-pad detector as a measure of the detector
occupancy. The signal distributions for this weighting are determined with the
sPlot technique [32] with $\ln{\chi^{2}_{\rm IP}}$ as the discriminating
variable, where $\chi^{2}_{\rm IP}$ is defined as the difference in $\chi^{2}$
of the PV reconstructed with and without the particle under consideration.

A correction factor is used to account for the difference between the tracking
efficiencies measured in data and simulation as described in Ref. [33]. This
factor is computed in bins of track momentum and pseudorapidity and weighted
to the kinematics of a given signal decay in the simulated sample to obtain a
correction factor in each charm meson $(p_{\mathrm{T}},y)$ bin. This
correction factor ranges from 0.98 to 1.16, depending on the decay mode.

###  3.3 Determination of signal yields

The data contain a mixture of prompt signal decays, secondary charm mesons
produced in decays of $b$ hadrons, and combinatorial background. Secondary
charm mesons will, in general, have a greater IP with respect to the PV than
prompt signal, and thus a greater value of $\ln{\chi^{2}_{\rm IP}}$. The
number of prompt signal charm meson decays within each $(p_{\mathrm{T}},y)$
bin is determined with fits to the $\ln{\chi^{2}_{\rm IP}}$ distribution of
the selected samples. These fits are carried out in a signal window in the
invariant mass of the candidates and background templates are obtained from
regions outside the signal window. Fits to the invariant mass distributions
are used to constrain the level of combinatorial background in the subsequent
fits to the $\ln{\chi^{2}_{\rm IP}}$ distributions.

In the case of the $D^{0}$, $D^{+}$, and $D_{s}^{+}$ measurements, the signal
window is defined as $\pm
20\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ around the known
mass of the charm meson [34], corresponding to approximately $2.5$ times the
mass resolution. Background samples are taken from two windows of width
$20\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$, centred
$50\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ below and
$50\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ above the
centre of the signal window. For the $D^{*+}$ measurements, the signal window
is defined in the distribution of the difference between the reconstructed
$D^{*+}$ mass and the reconstructed $D^{0}$ mass,
$\Delta{m}=m(D^{*+})-m(D^{0})$, as $\pm
3\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ around the
nominal $\Delta{m}$ value of
$145.43\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ [34]. The
background sample is taken from the region
$4.5\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ to
$9\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$ above the
nominal $\Delta{m}$ value.

The number of combinatorial background candidates in the signal window of each
decay mode is measured with binned extended maximum likelihood fits to either
the mass or $\Delta{m}$ distribution, performed simultaneously across all
$(p_{\mathrm{T}},y)$ bins for a given decay mode. Prompt and secondary signals
cannot be separated in mass or $\Delta{m}$, so a single signal probability
density function (PDF) is used to describe both components. For the $D^{0}$,
$D^{+}$, and $D_{s}^{+}$ measurements the signal PDF is the sum of a Crystal
Ball function [35] and a Gaussian function, sharing a common mode but allowed
to have different widths, whilst the combinatorial background is modelled as a
first-order polynomial. The signal PDF for the $D^{*+}$ measurement is the sum
of three Gaussian functions with a common mean but different widths. The
combinatorial background component in $\Delta{m}$ is modelled as an
empirically derived threshold function with an exponent $A$ and a turn-on
parameter $\Delta{m}_{0}$, fixed to be the nominal charged pion mass
$\Delta{m}_{0}=$139.57\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$$
[34],

$g(\Delta{m};\Delta{m}_{0},A)={(\Delta{m}-\Delta{m}_{0})}^{A}.$ (1)

Candidates entering the $\Delta{m}$ fit are required to be within the
previously defined $D^{0}$ signal window.

Only candidates within the mass and $\Delta{m}$ signal windows are used in the
$\ln{\chi^{2}_{\rm IP}}$ fits. A Gaussian constraint is applied to the
background yield in each $(p_{\mathrm{T}},y)$ bin, requiring it to be
consistent with the integral of the background PDF in the signal window of the
mass or $\Delta{m}$ fit.

Extended likelihood functions are constructed from one-dimensional PDFs in the
$\ln{\chi^{2}_{\rm IP}}$ observable, with one set of signal and background
PDFs for each $(p_{\mathrm{T}},y)$ bin. The set of these PDFs is fitted
simultaneously to the data in each $(p_{\mathrm{T}},y)$ bin, where all shape
parameters other than the peak value of the prompt signal PDF are shared
between bins.

The signal PDF in $\ln{\chi^{2}_{\rm IP}}$ is a bifurcated Gaussian with
exponential tails, defined as

$f_{\text{S}}(\ln{\chi^{2}_{\rm
IP}};\mu,\sigma,\epsilon,\rho_{L},\rho_{R})=\begin{cases}\exp\left(\frac{\rho_{L}^{2}}{2}+\rho_{L}\frac{\ln{\chi^{2}_{\rm
IP}}-\mu}{(1-\epsilon)\sigma}\right)&\ln{\chi^{2}_{\rm
IP}}<\mu-(\rho_{L}\sigma(1-\epsilon)),\\\
\exp\left(-\left(\frac{\ln{\chi^{2}_{\rm
IP}}-\mu}{\sqrt{2}\sigma(1-\epsilon)}\right)^{2}\right)&\mu-(\rho_{L}\sigma(1-\epsilon))\leq\ln{\chi^{2}_{\rm
IP}}<\mu,\\\ \exp\left(-\left(\frac{\ln{\chi^{2}_{\rm
IP}}-\mu}{\sqrt{2}\sigma(1+\epsilon)}\right)^{2}\right)&\mu\leq\ln{\chi^{2}_{\rm
IP}}<\mu+(\rho_{R}\sigma(1+\epsilon)),\\\
\exp\left(\frac{\rho_{R}^{2}}{2}-\rho_{R}\frac{\ln{\chi^{2}_{\rm
IP}}-\mu}{(1+\epsilon)\sigma}\right)&\ln{\chi^{2}_{\rm
IP}}\geq\mu+(\rho_{R}\sigma(1+\epsilon)),\end{cases}$ (2)

where $\mu$ is the mode of the distribution, $\sigma$ is the average of the
left and right Gaussian widths, $\epsilon$ is the asymmetry of the left and
right Gaussian widths, and $\rho_{L(R)}$ is the exponent for the left (right)
tail. The PDF for secondary charm decays is a Gaussian function.

The tail parameters $\rho_{L}$ and $\rho_{R}$ and the asymmetry parameter
$\epsilon$ of the $\ln{\chi^{2}_{\rm IP}}$ prompt signal PDFs are fixed to
values obtained from unbinned maximum likelihood fits to simulated signal
samples. All other parameters are determined in the fit. The sums of the
simultaneous likelihood fits in each $(p_{\mathrm{T}},y)$ bin are given in
Figures 1–4. The fits generally describe the data well. The systematic
uncertainty due to fit inaccuracies is determined as described in Sec. 5. The
sums of the prompt signal yields, as determined by the fits, are given in
Table 1.

Figure 1: Distributions for selected $D^{0}\to K^{-}\pi^{+}$ candidates:
(left) $K^{-}\pi^{+}$ invariant mass and (right) $\ln{\chi^{2}_{\rm IP}}$ for
a mass window of
$\pm$20\text{\,}\mathrm{{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}}$$ around the
nominal $D^{0}$ mass. The sum of the simultaneous likelihood fits in each
$(p_{\mathrm{T}},y)$ bin is shown, with components as indicated in the
legends.

Figure 2: Distributions for selected $D^{+}\to K^{-}\pi^{+}\pi^{+}$
candidates: (left) $K^{-}\pi^{+}\pi^{+}$ invariant mass and (right)
$\ln{\chi^{2}_{\rm IP}}$ for a mass window of
$\pm$20\text{\,}\mathrm{{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}}$$ around the
nominal $D^{+}$ mass. The sum of the simultaneous likelihood fits in each
$(p_{\mathrm{T}},y)$ bin is shown, with components as indicated in the
legends.

Figure 3: Distributions for selected $D_{s}^{+}\to(K^{-}K^{+})_{\phi}\pi^{+}$
candidates: (left) $K^{+}K^{-}\pi^{+}$ invariant mass and (right)
$\ln{\chi^{2}_{\rm IP}}$ for a mass window of
$\pm$20\text{\,}\mathrm{{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}}$$ around the
nominal $D_{s}^{+}$ mass. The sum of the simultaneous likelihood fits in each
$(p_{\mathrm{T}},y)$ bin is shown, with components as indicated in the
legends.

Figure 4: Distributions for selected $D^{*+}\to D^{0}\pi^{+}$ candidates, with
$D^{0}\to K^{-}\pi^{+}$: (left) $\Delta{m}=m(D^{*+})-m(D^{0})$ for a mass
window of $\pm$20\text{\,}\mathrm{{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}}$$
around the nominal $D^{0}$ mass and (right) $\ln{\chi^{2}_{\rm IP}}$ with an
additional mass window of
$\pm$3\text{\,}\mathrm{{\mathrm{\,Me\kern-0.90005ptV\\!/}c^{2}}}$$ around the
nominal $D^{*+}$\- $D^{0}$ mass difference. The sum of the simultaneous
likelihood fits in each $(p_{\mathrm{T}},y)$ bin is shown, with components as
indicated in the legends.

Table 1: Prompt signal yields in the fully selected dataset, summed over all ($p_{\mathrm{T}}$,$y$) bins in which a measurement is made.  Hadron | Prompt signal yield
---|---
$D^{0}$ | $(25.77\pm 0.02)\times 10^{5}$
$D^{+}$ | $(19.74\pm 0.02)\times 10^{5}$
$D_{s}^{+}$ | $(11.32\pm 0.04)\times 10^{4}$
$D^{*+}$ | $(30.12\pm 0.06)\times 10^{4}$

##  4 Cross-section measurements

The signal yields are used to measure differential cross-sections in bins of
$p_{\mathrm{T}}$ and $y$ in the range $0<p_{\mathrm{T}}<15$
$\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$ and $2.0<y<4.5$. The
differential cross-section for producing the charm meson species $D$ in bin
$i$ is calculated from the relation

$\frac{\text{d}^{2}\sigma_{i}(D)}{\text{d}p_{\mathrm{T}}\,\text{d}y}=\frac{1}{\Delta
p_{\mathrm{T}}\Delta y}\cdot\frac{N_{i}(\mbox{$D\to
f$}+\text{c.c.})}{\varepsilon_{i,\text{tot}}(\mbox{$D\to
f$})\mathcal{B}(\mbox{$D\to f$})\kappa\mathcal{L}_{\text{int}}},$ (3)

where $\Delta p_{\mathrm{T}}$ and $\Delta y$ are the widths in
$p_{\mathrm{T}}$ and $y$ of bin $i$, $N_{i}(\mbox{$D\to f$}+\text{c.c.})$ is
the measured yield of prompt $D$ decays to the final state $f$ in bin $i$ plus
the charge-conjugate decay, $\mathcal{B}(\mbox{$D\to f$})$ is the known
branching fraction of the decay, and $\varepsilon_{i,\text{tot}}(\mbox{$D\to
f$})$ is the total efficiency for observing the signal decay in bin $i$. The
total integrated luminosity collected $\mathcal{L}_{\text{int}}$ is $4.98\pm
0.19\text{\,}{\mathrm{pb}}^{-1}$ and $\kappa=10.7\%$ is the average fraction
of events passed by the prescaled hardware trigger. The integrated luminosity
of the dataset is evaluated with a precision of $3.8\%$ from the number of
visible $pp$ collisions and a constant of proportionality that is measured in
a dedicated calibration dataset. The absolute luminosity for the calibration
dataset is determined from the beam currents, which are measured by LHC
instruments, and the beam profiles and overlap integral, which are measured
with a beam-gas imaging method [36].

The following branching fractions taken from Ref. [34] are used:
$\mathcal{B}(\mbox{$D^{+}\to K^{-}\pi^{+}\pi^{+}$})=(9.13\pm 0.19)\%$,
$\mathcal{B}(\mbox{$D^{*+}\to D^{0}(\to K^{-}\pi^{+})\pi^{+}$})=(2.63\pm
0.04)\%$, and $\mathcal{B}(\mbox{$D^{0}\to K^{\mp}\pi^{\pm}$})=(3.89\pm
0.05)\%$. The last is the sum of Cabibbo-favoured and doubly Cabibbo-
suppressed branching fractions, which agrees to better than 1% with the HFAG
result that accounts for the effects of final-state radiation [37]. For the
$D_{s}^{+}$ measurement the fraction of $D_{s}^{+}\to K^{-}K^{+}\pi^{+}$
decays with a $K^{-}K^{+}$ invariant mass in the range
$1000<m_{K^{-}K^{+}}<$1040\text{\,}\mathrm{{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}}$$
is taken as $(2.24\pm 0.13)\%$ [38].

The measured differential cross-sections are tabulated in Appendix A. These
results agree with the absolute cross-sections measured using the cross-check
modes that are listed in Section 3. Figures 5 and 6 show the $D^{0}$, $D^{+}$,
$D_{s}^{+}$, and $D^{*+}$ cross-section measurements and predictions. The
systematic uncertainties are discussed in Sec. 5 and the theory contributions
are provided in Refs. [1, 2, 3] and described in Sec. 7.

Figure 5: Measurements and predictions for the absolute prompt (top) $D^{0}$,
and (bottom) $D^{+}$ cross-sections at $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$.
Each set of measurements and predictions in a given rapidity bin is offset by
a multiplicative factor $10^{-m}$, where the factor $m$ is shown on the plots.
The boxes indicate the $\pm 1\sigma$ uncertainty band on the theory
predictions. In cases where this band spans more than two orders of magnitude
only its upper edge is indicated.

Figure 6: Measurements and predictions for the absolute prompt (top)
$D_{s}^{+}$, and (bottom) $D^{*+}$ cross-sections at
$\sqrt{s}=$13\text{\,}\mathrm{TeV}$$. Each set of measurements and predictions
in a given rapidity bin is offset by a multiplicative factor $10^{-m}$, where
the factor $m$ is shown on the plots. The boxes indicate the $\pm 1\sigma$
uncertainty band on the theory predictions. In cases where this band spans
more than two orders of magnitude only its upper edge is indicated.

##  5 Systematic uncertainties

Several sources of systematic uncertainty are identified and evaluated
separately for each decay mode and $(p_{\mathrm{T}},y)$ bin. In all cases, the
dominant systematic uncertainties originate from the luminosity and the
estimation of the tracking efficiencies, amounting to 3.9% and 5–10%,
respectively. Uncertainties in the branching fractions give rise to systematic
uncertainties between 1% and 5%, depending on the decay mode. Systematic
uncertainties are also evaluated to account for the modelling in the
simulation, the PID calibration procedure, and the PDF shapes used in the
determination of the signal yields. These sum in quadrature to around 5%.
Table 2 lists the fractional systematic uncertainties for the different decay
modes. Also given are the correlations of each uncertainty between different
$(p_{\mathrm{T}},y)$ bins and between different decay modes. The systematic
uncertainties can be grouped into three categories: those highly correlated
between different decay modes and $(p_{\mathrm{T}},y)$ bins, those that are
only correlated between different bins but independent between decay modes,
and those that are independent between different decay modes and bins.

The systematic uncertainty on the luminosity is identical for all
$(p_{\mathrm{T}},y)$ bins and decay modes. The uncertainty on the tracking
efficiency correction is a strongly correlated contribution. It includes a
per-track uncertainty on the correction factor that originates from the finite
size of the calibration sample, a 0.4% uncertainty stemming from the weighting
in different event multiplicity variables, and an additional 1.1% (1.4%)
uncertainty for kaon (pion) tracks, due to uncertainties on the amount of
material in the detector. The per-track uncertainties are propagated to obtain
uncertainties on the correction factor in each $(p_{\mathrm{T}},y)$ bin of the
charm meson, and are included as systematic uncertainties, resulting in a
5–10% uncertainty on the measured cross-sections, depending on the decay mode.

The finite sizes of the simulated samples limit the statistical precision of
the estimated efficiencies, leading to a systematic uncertainty on the
measured cross-sections. As different simulated samples are used for each
decay mode, the resulting uncertainty is independent between different decay
modes and $(p_{\mathrm{T}},y)$ bins.

Imperfect modelling of variables used in the selection can lead to differences
between data and simulation, giving rise to a biased estimate of selection
efficiencies. The effect is estimated by comparing the efficiencies when using
modified selection criteria. The simulated sample is used to define a tighter
requirement for each variable used in the selection, such that 50% of the
simulated events are accepted. The same requirement is then applied to the
collision data sample, and the signal yield in this subset of the data is
compared to the 50% reduction expected from simulation. The procedure is
performed separately for each variable used in the selection. The sum of the
individual differences, taking the correlations between the variables into
account, is assigned as an uncertainty on the signal yield. The corresponding
uncertainty on the measured cross-sections is evaluated with Eq. 3.

The systematic uncertainties associated with the PID calibration procedure
result from the finite size of the calibration sample and binning effects of
the weighting procedure. The PID efficiency in this calibration sample is
determined in bins of track momentum, track pseudorapidity, and detector
occupancy. The statistical uncertainties of these efficiencies are propagated
to obtain systematic uncertainties on the cross-sections. In the weighting
procedure, it is assumed that the PID efficiencies for all candidates in a
given bin are identical. A systematic uncertainty is assigned to account for
deviations from this approximation by sampling from kernel density estimates
[39] created from the calibration samples, and recomputing the total PID
efficiency with the sampled data using a progressively finer binning. The
efficiency converges to a value that is offset from the value measured with
the nominal binning. This deviation is assigned as a systematic uncertainty on
the PID efficiency. As all decay modes and $(p_{\mathrm{T}},y)$ bins use the
same calibration data, this systematic uncertainty is highly correlated
between different modes and bins.

Lastly, the systematic uncertainty on the signal yield extracted from the fits
is dominated by the uncertainties on the choice of fit model. This is
evaluated by refitting the data with different sets of PDFs that are also
compatible with the data, and assigning a systematic uncertainty based on the
largest deviation in the prompt signal yield.

Table 2: Systematic uncertainties expressed as fractions of the cross-section measurements, in percent. Uncertainties that are computed bin-by-bin are expressed as ranges giving the minimum to maximum values. Ranges for the correlations between $p_{\mathrm{T}}$-$y$ bins and between modes are also given, expressed in percent.  | Uncertainties (%) | Correlations (%)
---|---|---
| $D^{0}$ | $D^{+}$ | $D_{s}^{+}$ | $D^{*+}$ | Bins | Modes
Luminosity | 3.9 | 100 | 100
Tracking | 3–10 | 4–14 | 4–14 | 5–11 | 90–100 | 90–100
Branching fractions | 1.2 | 2.1 | 5.8 | 1.5 | 100 | 0–95
Simulation sample size | 1–26 | 1–39 | 1–55 | 1–23 | 0 | 0
Simulation modelling | 1 | 1 | 0.2 | 0.9 | 0 | 0
PID sample size | 0–2 | 0–1 | 0–2 | 0–1 | 0–100 | 0–100
PID binning | 0–44 | 0–10 | 0–20 | 0-15 | 100 | 100
PDF shapes | 1–6 | 1–5 | 1–2 | 1–2 | - | -

##  6 Production ratios and integrated cross-sections

###  6.1 Production ratios

The predicted ratios of prompt charm production cross-sections between
different centre-of-mass energies are devoid of several theoretical
uncertainties [1, 2, 3] that are inherent in the corresponding absolute cross-
sections. Using the present results obtained at
$\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ and the corresponding results from LHCb
data at $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ [16], these ratios, $R_{13/7}$,
are measured for $D^{0}$, $D^{+}$, $D_{s}^{+}$, and $D^{*+}$ mesons. The
$\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ measurements are rebinned to match the
binning used in the $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ results and the
production ratios are presented for
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
and $2.0<y<4.5$ in Appendix B. In the calculation of the uncertainties the
branching fraction uncertainties cancel, and correlations of $30\%$ and $50\%$
are assumed for the uncertainties of luminosity and tracking, respectively.
All other uncertainties are assumed to be uncorrelated. Figure 7 shows the
measured ratios compared with predictions from theory calculations [1, 2, 3].

###  6.2 Integrated cross-sections

Integrated production cross-sections, $\sigma(D)$, for each charm meson are
computed as the sum of the per-bin measurements, where the uncertainty on the
sum takes into account the correlations between bins discussed in Section 5.
For $D_{s}^{+}$ and $D^{*+}$ mesons, the kinematic region considered is
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
and $2.0<y<4.5$ due to insufficient data below
$p_{\mathrm{T}}=$1\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$,
while for $D^{0}$ and $D^{+}$ the same kinematic region as for the ratio
measurements is used. The upper limit is chosen to coincide with that of the
measurements at $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$.

The $D^{0}$ and $D^{*+}$ cross-section results contain bins in which a
measurement was not possible and which require a correction that is based on
theory calculations. A multiplicative correction factor is computed as the
ratio between the predicted integrated cross-section within the considered
kinematic region and the sum of all per-bin cross-section predictions for bins
for which a measurement exists. This method is based on the POWHEG+NNPDF3.0L
predictions [1] for $D^{0}$ and the FONLL predictions [2] for $D^{*+}$. The
uncertainty on the extrapolation factor is taken as the difference between
factors computed using the upper and lower bounds of the theory predictions
and is propagated to the integrated cross-sections as a systematic
uncertainty. Table 3 gives the integrated cross-sections for $D^{0}$, $D^{+}$,
$D_{s}^{+}$, and $D^{*+}$ mesons.

The ratios of the cross-sections, with the $D^{0}$ and $D^{+}$ results re-
evaluated in the kinematic region of the $D_{s}^{+}$ and $D^{*+}$
measurements, can be compared with the ratios of the cross-sections measured
at $e^{+}e^{-}$ colliders operating at a centre-of-mass energy close to the
$\Upsilon(4S)$ resonance [40, 41, 42]. A more precise comparison is made here
by computing the ratios of cross-section-times-branching-fractions,
$\sigma(D)\times\mathcal{B}(\mbox{$D\to f$})$, where the final states $f$ are
the same between the LHCb measurements and those made at $e^{+}e^{-}$
experiments. Differential ratios are shown in Fig. 8 and tabulated results and
remaining figures are presented in Appendix C. They exhibit a $p_{\mathrm{T}}$
dependence that is consistent with heavier particles having a harder
$p_{\mathrm{T}}$ spectrum.

The integrated charm cross-section, $\sigma(\mbox{$pp\to c\overline{}cX$})$,
is calculated as $\sigma(D)/(2f(\mbox{$c\to D$}))$ for each decay mode. The
term $f(\mbox{$c\to D$})$ is the quark to hadron transition probability, and
the factor 2 accounts for the inclusion of charge conjugate states in the
measurement. The transition probabilities have been computed using
measurements at $e^{+}e^{-}$ colliders operating at a centre-of-mass energy
close to the $\Upsilon(4S)$ resonance [43] to be $f(\mbox{$c\to
D^{0}$})=0.565\pm 0.032$, $f(\mbox{$c\to D^{+}$})=0.246\pm 0.020$,
$f(\mbox{$c\to D_{s}^{+}$})=0.080\pm 0.017$, and $f(\mbox{$c\to
D^{*+}$})=0.224\pm 0.028$. The fragmentation fraction $f(\mbox{$c\to D^{0}$})$
has an overlapping contribution from $f(\mbox{$c\to D^{*+}$})$.

The combination of the $D^{0}$ and $D^{+}$ measurements, based on the Blue
method [44], gives

$\sigma(\mbox{$pp\to
c\overline{}cX$})_{p_{\mathrm{T}}\,<\,8\,$\mathrm{{\mathrm{\,Ge\kern-0.70004ptV\\!/}c}}$,\,2.0\,<\,y\,<\,4.5}=$2369\pm
3\pm 152\pm 118\text{\,}\mathrm{\SIUnitSymbolMicro b}$,$

where the uncertainties are due to statistical, systematic and fragmentation
fraction uncertainties, respectively. A comparison with predictions is given
in Fig. 9. The same figure also shows a comparison of $\sigma(\mbox{$pp\to
c\overline{}cX$})$ for
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
based on the measurements of all four mesons. Ratios of the integrated cross-
section-time-branching-fraction measurements are given in Table 4.

Table 3: Prompt charm production cross-sections in the kinematic ranges given.
The computation of the extrapolation factors is described in the text. The
first uncertainty on the cross-section is statistical, and the second is
systematic and includes the contribution from the extrapolation factor. No
extrapolation factor is given for $D^{+}_{(s)}$ as a measurement is available
in every bin of the integrated phase space.

Extrapolation factor Cross-section ($\mathrm{\SIUnitSymbolMicro b}$) $D^{0}$
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2<y<4.5$ $1.0014\pm 0.0024$ $2709\pm\phantom{1}2\pm 165$ $D^{+}$
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2<y<4.5$ $1.049\pm 0.031$ $1102\pm\phantom{1}5\pm 111$ $D^{0}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2<y<4.5$ $1.0018\pm 0.0025$ $2072\pm\phantom{1}2\pm 124$ $D^{+}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2<y<4.5$ — $834\pm\phantom{1}2\pm\phantom{1}78$ $D_{s}^{+}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2<y<4.5$ — $353\pm\phantom{1}9\pm\phantom{1}76$ $D^{*+}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2<y<4.5$ $1.102\pm 0.081$ $784\pm\phantom{1}4\pm\phantom{1}87$ $D^{0}$
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2.5<y<4$ — $1720\pm\phantom{1}1\pm\phantom{1}98$ $D^{+}$
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2.5<y<4$ — $706\pm\phantom{1}4\pm\phantom{1}66$ $D^{0}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2.5<y<4$ — $1313\pm\phantom{1}1\pm\phantom{1}73$ $D^{+}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2.5<y<4$ — $527\pm\phantom{1}1\pm\phantom{1}45$ $D_{s}^{+}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2.5<y<4$ — $227\pm\phantom{1}2\pm\phantom{1}24$ $D^{*+}$
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{\giga\kern-1.99997pt\per\kern-1.49994pt}$$
$2.5<y<4$ — $493\pm\phantom{1}2\pm\phantom{1}41$

Table 4: Ratios of integrated cross-section-times-branching-fraction
measurements in the kinematic range
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$$
and $2<y<4.5$. The first uncertainty on the ratio is statistical and the
second is systematic. The notation $\sigma(\mbox{$D\to f$})$ is shorthand for
$\sigma(D)\times\mathcal{B}(\mbox{$D\to f$})$.

Quantity Measurement $\sigma(\mbox{$D^{+}\to
K^{-}\pi^{+}\pi^{+}$})/\sigma(\mbox{$D^{0}\to K^{-}\pi^{+}$})$
$\phantom{1}0.950^{+\phantom{1}0.003}_{-\phantom{1}0.003}$${}^{+\phantom{1}0.040}_{-\phantom{1}0.040}$
$\sigma(D_{s}^{+}\to[K^{-}K^{+}]_{\phi}\pi^{+})/\sigma(\mbox{$D^{0}\to
K^{-}\pi^{+}$})$ $0.0991^{+0.0026}_{-0.0026}$${}^{+0.0053}_{-0.0079}$
$\sigma(D^{*+}\to[K^{-}\pi^{+}]_{D^{0}}\pi^{+})/\sigma(\mbox{$D^{0}\to
K^{-}\pi^{+}$})$
$\phantom{1}0.256^{+\phantom{1}0.001}_{-\phantom{1}0.001}$${}^{+\phantom{1}0.021}_{-\phantom{1}0.021}$
$\sigma(D_{s}^{+}\to[K^{-}K^{+}]_{\phi}\pi^{+})/\sigma(\mbox{$D^{+}\to
K^{-}\pi^{+}\pi^{+}$})$ $0.1043^{+0.0028}_{-0.0028}$${}^{+0.0038}_{-0.0066}$
$\sigma(D^{*+}\to[K^{-}\pi^{+}]_{D^{0}}\pi^{+})/\sigma(\mbox{$D^{+}\to
K^{-}\pi^{+}\pi^{+}$})$
$\phantom{1}0.270^{+\phantom{1}0.002}_{-\phantom{1}0.002}$${}^{+\phantom{1}0.023}_{-\phantom{1}0.022}$
$\sigma(D_{s}^{+}\to[K^{-}K^{+}]_{\phi}\pi^{+})/\sigma(D^{*+}\to[K^{-}\pi^{+}]_{D^{0}}\pi^{+})$
$\phantom{1}0.390^{+\phantom{1}0.010}_{-\phantom{1}0.010}$${}^{+\phantom{1}0.038}_{-\phantom{1}0.045}$

Figure 7: Measurements and predictions of the prompt $D^{0}$, $D^{+}$,
$D_{s}^{+}$, and $D^{*+}$ cross-section ratios. The dash-dotted lines indicate
the unit ratio for each of the rapidity intervals and the dashed lines
indicate a ratio of two. Each set of measurements and predictions in a given
rapidity bin is offset by an additive constant $m$, which is shown on the
plot. No prediction is available for the $D_{s}^{+}$ ratio.

Figure 8: Ratios of cross-section-times-branching-fraction measurements of
(top) $D^{+}$, (middle) $D_{s}^{+}$, and (bottom) $D^{*+}$ mesons with respect
to the $D^{0}$ measurements. The bands indicate the corresponding ratios
computed using measurements from $e^{+}e^{-}$ collider experiments [40, 41,
42]. The ratios are given as a function of $p_{\mathrm{T}}$ and different
symbols indicate different ranges in $y$. The notation $\sigma(\mbox{$D\to
f$})$ is shorthand for $\sigma(D)\times\mathcal{B}(\mbox{$D\to f$})$.

##  7 Comparison to theory

Theoretical calculations for charm meson production cross-sections in $pp$
collisions at $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ have been provided in Refs.
[1] (POWHEG+NNPDF3.0L), [2] (FONLL), and [3] (GMVFNS). All three sets of
calculations are performed at NLO precision, and each includes estimates of
theoretical uncertainties due to the renormalisation and factorisation scales.
The theoretical uncertainties provided with the FONLL and POWHEG+NNPDF3.0L
predictions also include contributions due to uncertainties in the effective
charm quark mass and the parton distribution functions.

The FONLL predictions are provided in the form of $D^{0}$, $D^{+}$, and
$D^{*+}$ production cross-sections for $pp$ collisions at
$\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ for each bin in a subdivision of the
phase space,
$p_{\mathrm{T}}<$30\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
and $2.0<y<4.5$. Ratios of these cross-sections to those computed for $pp$
collisions at $7\text{\,}\mathrm{TeV}$ are also supplied. The calculations use
the NNPDF3.0 NLO [45] parton densities. These FONLL calculations of the meson
differential production cross-sections assume $f(\mbox{$c\to D$})=1$ and are
multiplied by the transition probabilities measured at $e^{+}e^{-}$ colliders
for comparison to the current measurements. No dedicated FONLL cross-section
calculation for $D_{s}^{+}$ production is available.

Figure 9: Integrated cross-sections (black diamonds), their average (black
circle and blue band) and theory predictions (red squares) [1, 2] are shown
(left) based on the $D^{0}$ and $D^{+}$ for
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$$
and (right) for measurements based on all four mesons for
$1<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$$.
The “absolute” predictions are based on calculations of the
$13\text{\,}\mathrm{TeV}$ cross-section, while the “scaled” predictions are
based on calculations of the $13$ to $7\text{\,}\mathrm{TeV}$ ratio multiplied
with the LHCb measurement at $7\text{\,}\mathrm{TeV}$ [16].

The POWHEG+NNPDF3.0L predictions are also provided in the form of $D^{0}$ and
$D^{+}$ production cross-sections for $pp$ collisions at
$\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ for each bin in a subdivision of the
phase space,
$p_{\mathrm{T}}<$30\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
and $2.0<y<4.5$. Ratios of $13$ to $7\text{\,}\mathrm{TeV}$ cross-sections are
given as well. They are obtained with Powheg [46] matched to Pythia8 [47]
parton showers and an improved version of the NNPDF3.0 NLO parton distribution
function set designated NNPDF3.0+LHCb [1]. To produce this improved set, the
authors of Ref. [1] weight the NNPDF3.0 NLO set in order to match FONLL
calculations to LHCb’s charm cross-section measurements at
$7\text{\,}\mathrm{TeV}$ [16]. This results in a significant improvement in
the uncertainties for the gluon distribution function at small momentum
fraction $x$. Two predictions for the integrated cross-section are provided,
one an absolute calculation, identical to that for the differential cross-
sections, and the other scaled from the $7\text{\,}\mathrm{TeV}$ measurement.

The GMVFNS calculations include theoretical predictions for all mesons studied
in this analysis. Results are provided for
$3<p_{\mathrm{T}}<$30\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$.
Here the CT10 [48] set of parton distributions is used. The GMVFNS theoretical
framework includes the convolution with fragmentation functions describing the
transition $c\to H_{c}$ that are normalised to the respective total transition
probabilities [7, 49]. The fragmentation functions are taken from a fit to
production measurements at $e^{+}e^{-}$ colliders, where no attempt is made to
separate direct production and feed-down from higher resonances.

In general, the data shown in Figures 5 and 6 agree with the predicted shapes
of the cross-sections at $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ for all three
sets of calculations. The central values of the measurements generally lie
above those of the POWHEG+NNPDF3.0L and FONLL predictions, albeit within the
uncertainties provided. The GMVFNS predictions provide the best description of
the data, although the cross-section measurements decrease with
$p_{\mathrm{T}}$ at a higher rate than the predictions. Similar behaviour is
observed for the $\sqrt{s}=$7\text{\,}\mathrm{TeV}$$ measurement [16], where
only central values are shown for the FONLL prediction which give lower cross-
sections than the data.

The predictions are in agreement with the data for the ratios of cross-
sections at $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ and $7\text{\,}\mathrm{TeV}$,
shown in Figure 7, though consistently at the upper limit of the predicted
values.

The absolute predictions for the integrated cross-sections show agreement with
data within their large uncertainties, with central values below the
measurements. The scaled POWHEG+NNPDF3.0L prediction, which has smaller
uncertainties than the absolute prediction, agrees with the data. The
measurements are consistent with a linear scaling of the cross-section with
the collision energy.

##  8 Summary

A measurement of charm production in $pp$ collisions at a centre-of-mass
energy of $\sqrt{s}=$13\text{\,}\mathrm{TeV}$$ has been performed with data
collected with the LHCb detector. The shapes of the differential cross-
sections for $D^{0}$, $D^{+}$, $D^{*+}$, and $D_{s}^{+}$ mesons are found to
be in agreement with NLO predictions while the predicted central values
generally lie below the data, albeit mostly within uncertainties. The ratios
of the production cross-sections for centre-of-mass energies of
$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$ and
$7\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$ have been measured and also show
consistency with theoretical predictions. The $c\overline{}c$ cross-section
for production of a charm meson in $pp$ collisions at
$\sqrt{s}=$13\text{\,}\mathrm{T}\mathrm{e}\mathrm{V}$$ and in the range
$0<p_{\mathrm{T}}<$8\text{\,}\mathrm{{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}}$$
and $2<y<4.5$ is $2369\pm 3\pm 152\pm 118\text{\,}\mathrm{\SIUnitSymbolMicro
b}$.

## Acknowledgements

The authors would like to thank R. Gauld, J. Rojo, L. Rottoli, and J. Talbert
for the provision of the POWHEG+NNPDF3.0L numbers; M. Cacciari, M.L. Mangano,
and P. Nason for the FONLL predictions; and H. Spiesberger, B.A. Kniehl, G.
Kramer, and I. Schienbein for the GMVFNS calculations. We express our
gratitude to our colleagues in the CERN accelerator departments for the
excellent performance of the LHC. We thank the technical and administrative
staff at the LHCb institutes. We acknowledge support from CERN and from the
national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China);
CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM and NWO
(The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO
(Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); NSF (USA). We acknowledge the computing resources that are
provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF
(The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI (Russia), CSCS
(Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC
(USA). We are indebted to the communities behind the multiple open source
software packages on which we depend. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from AvH
Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC
(European Union), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU,
Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), The
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

Appendices

##  Appendix A Absolute cross-sections

Tables A–A give the numerical results for the differential cross-sections.

Table 5: Differential production cross-sections,
$\text{d}^{2}\sigma/(\text{d}p_{\mathrm{T}}\,\text{d}y)$, in
$$\mathrm{\SIUnitSymbolMicro
b}$/($\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$)$ for prompt
$D^{0}+{\kern 1.79997pt\overline{\kern-1.79997ptD}{}}^{0}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. $y$ $p_{\text{T}}$ [MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$
$[3.5,4]$ $[4,4.5]$ $[0,1000]$ $254$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$
${}^{31}_{27}$ $277.3$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$
${}^{21.4}_{24.8}$ $281.1$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$
${}^{19.4}_{17.4}$ $256$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{16}_{14}$
$206$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{16}_{14}$ $[1000,1500]$
$433$ ${}^{+}_{-}$ ${}^{3}_{3}$ ${}^{+}_{-}$ ${}^{50}_{45}$ $457$ ${}^{+}_{-}$
${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{32}_{37}$ $454$ ${}^{+}_{-}$ ${}^{1}_{1}$
${}^{+}_{-}$ ${}^{28}_{27}$ $409$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$
${}^{25}_{23}$ $337$ ${}^{+}_{-}$ ${}^{3}_{3}$ ${}^{+}_{-}$ ${}^{25}_{22}$
$[1500,2000]$ $388$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{40}_{37}$
$409$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{30}_{26}$ $380$ ${}^{+}_{-}$
${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{23}_{22}$ $344$ ${}^{+}_{-}$ ${}^{1}_{1}$
${}^{+}_{-}$ ${}^{21}_{19}$ $265$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$
${}^{18}_{17}$ $[2000,2500]$ $296$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$
${}^{24}_{28}$ $314.4$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$
${}^{21.1}_{18.7}$ $292.5$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$
${}^{17.4}_{15.8}$ $259$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{16}_{14}$
$190$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{11}_{12}$ $[2500,3000]$
$228$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{17}_{20}$ $228.9$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{14.7}_{13.2}$ $208.8$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{12.6}_{10.4}$ $175.0$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{11.3}_{\phantom{0}9.5}$
$129.6$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{8.3}_{8.9}$
$[3000,3500]$ $161.3$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$
${}^{11.4}_{13.0}$ $156.1$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$
${}^{9.6}_{8.7}$ $137.3$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$
${}^{8.1}_{6.9}$ $121.4$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$
${}^{8.5}_{6.9}$ $85.6$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$
${}^{6.3}_{6.4}$ $[3500,4000]$ $109.7$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$
${}^{+}_{-}$ ${}^{7.3}_{8.2}$ $111.0$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$
${}^{+}_{-}$ ${}^{6.6}_{6.0}$ $93.5$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$
${}^{+}_{-}$ ${}^{5.5}_{4.7}$ $82.7$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$
${}^{+}_{-}$ ${}^{5.5}_{4.9}$ $58.0$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$
${}^{+}_{-}$ ${}^{5.9}_{5.5}$ $[4000,5000]$ $66.5$ ${}^{+}_{-}$
${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{4.7}_{4.2}$ $64.5$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{3.9}_{3.3}$ $54.5$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{3.2}_{2.7}$ $45.9$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{2.5}_{2.7}$ $26.1$ ${}^{+}_{-}$
${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{3.6}_{3.0}$ $[5000,6000]$ $35.5$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{2.6}_{2.1}$ $31.5$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.8}_{1.6}$ $27.1$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.5}_{1.6}$ $20.8$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.3}_{1.2}$ $10.9$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{2.5}_{1.8}$ $[6000,7000]$
$18.5$ ${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.3}_{1.2}$ $17.20$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.96}_{0.92}$ $14.40$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.82}_{0.85}$ $10.20$
${}^{+}_{-}$ ${}^{0.12}_{0.12}$ ${}^{+}_{-}$ ${}^{0.87}_{0.81}$ $3.4$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{2.4}_{1.3}$ $[7000,8000]$
$10.15$ ${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.72}_{0.63}$ $9.71$
${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.60}_{0.52}$ $7.88$
${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.42}_{0.48}$ $4.94$
${}^{+}_{-}$ ${}^{0.10}_{0.10}$ ${}^{+}_{-}$ ${}^{0.71}_{0.58}$ $[8000,9000]$
$6.11$ ${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.46}_{0.39}$ $5.72$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.38}_{0.32}$ $4.49$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.27}_{0.29}$ $2.88$
${}^{+}_{-}$ ${}^{0.11}_{0.11}$ ${}^{+}_{-}$ ${}^{0.57}_{0.44}$ $[9000,10000]$
$3.92$ ${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.26}_{0.22}$ $3.48$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.21}_{0.15}$ $2.75$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.16}_{0.13}$ $1.53$
${}^{+}_{-}$ ${}^{0.11}_{0.11}$ ${}^{+}_{-}$ ${}^{0.49}_{0.28}$
$[10000,11000]$ $2.48$ ${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$
${}^{0.18}_{0.16}$ $2.18$ ${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$
${}^{0.14}_{0.09}$ $1.62$ ${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$
${}^{0.12}_{0.09}$ $0.77$ ${}^{+}_{-}$ ${}^{0.13}_{0.13}$ ${}^{+}_{-}$
${}^{0.33}_{0.16}$ $[11000,12000]$ $1.59$ ${}^{+}_{-}$ ${}^{0.04}_{0.04}$
${}^{+}_{-}$ ${}^{0.14}_{0.10}$ $1.49$ ${}^{+}_{-}$ ${}^{0.03}_{0.03}$
${}^{+}_{-}$ ${}^{0.10}_{0.06}$ $1.025$ ${}^{+}_{-}$ ${}^{0.034}_{0.034}$
${}^{+}_{-}$ ${}^{0.083}_{0.056}$ $[12000,13000]$ $1.01$ ${}^{+}_{-}$
${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.12}_{0.08}$ $1.031$ ${}^{+}_{-}$
${}^{0.026}_{0.026}$ ${}^{+}_{-}$ ${}^{0.078}_{0.037}$ $0.716$ ${}^{+}_{-}$
${}^{0.034}_{0.034}$ ${}^{+}_{-}$ ${}^{0.060}_{0.048}$ $[13000,14000]$ $0.746$
${}^{+}_{-}$ ${}^{0.026}_{0.026}$ ${}^{+}_{-}$ ${}^{0.089}_{0.055}$ $0.718$
${}^{+}_{-}$ ${}^{0.023}_{0.023}$ ${}^{+}_{-}$ ${}^{0.060}_{0.025}$ $0.447$
${}^{+}_{-}$ ${}^{0.031}_{0.031}$ ${}^{+}_{-}$ ${}^{0.075}_{0.045}$
$[14000,15000]$ $0.498$ ${}^{+}_{-}$ ${}^{0.022}_{0.022}$ ${}^{+}_{-}$
${}^{0.058}_{0.030}$ $0.495$ ${}^{+}_{-}$ ${}^{0.020}_{0.020}$ ${}^{+}_{-}$
${}^{0.048}_{0.022}$ $0.268$ ${}^{+}_{-}$ ${}^{0.031}_{0.031}$ ${}^{+}_{-}$
${}^{0.053}_{0.031}$

Table 6: Differential production cross-sections,
$\text{d}^{2}\sigma/(\text{d}p_{\mathrm{T}}\,\text{d}y)$, in
$$\mathrm{\SIUnitSymbolMicro
b}$/($\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$)$ for prompt
$D^{+}+D^{-}$ mesons in bins of $(p_{\mathrm{T}},y)$. The first uncertainty is
statistical, and the second is the total systematic. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[0,1000]$ $156$
${}^{+}_{-}$ ${}^{6}_{6}$ ${}^{+}_{-}$ ${}^{38}_{32}$ $107$ ${}^{+}_{-}$
${}^{3}_{3}$ ${}^{+}_{-}$ ${}^{15}_{14}$ $97$ ${}^{+}_{-}$ ${}^{3}_{3}$
${}^{+}_{-}$ ${}^{13}_{13}$ $72$ ${}^{+}_{-}$ ${}^{5}_{5}$ ${}^{+}_{-}$
${}^{16}_{14}$ $[1000,1500]$ $182$ ${}^{+}_{-}$ ${}^{7}_{7}$ ${}^{+}_{-}$
${}^{47}_{42}$ $170$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{31}_{22}$
$184$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{19}_{18}$ $158$ ${}^{+}_{-}$
${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{15}_{14}$ $137$ ${}^{+}_{-}$ ${}^{3}_{3}$
${}^{+}_{-}$ ${}^{16}_{15}$ $[1500,2000]$ $146$ ${}^{+}_{-}$ ${}^{2}_{2}$
${}^{+}_{-}$ ${}^{27}_{23}$ $149.5$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$
${}^{23.0}_{16.6}$ $153.5$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$
${}^{13.7}_{14.2}$ $133.6$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$
${}^{11.4}_{10.4}$ $107.1$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$
${}^{9.6}_{9.1}$ $[2000,2500]$ $111$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$
${}^{18}_{16}$ $126.1$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$
${}^{16.4}_{12.9}$ $115.4$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$
${}^{9.5}_{9.7}$ $97.4$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$
${}^{7.8}_{7.2}$ $78.9$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$
${}^{6.3}_{6.1}$ $[2500,3000]$ $86.1$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$
${}^{+}_{-}$ ${}^{13.1}_{12.3}$ $94.0$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$
${}^{+}_{-}$ ${}^{\phantom{0}8.8}_{10.0}$ $83.5$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$
${}^{+}_{-}$ ${}^{6.5}_{6.5}$ $72.1$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$
${}^{+}_{-}$ ${}^{5.4}_{5.1}$ $53.2$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$
${}^{+}_{-}$ ${}^{4.4}_{4.0}$ $[3000,3500]$ $62.3$ ${}^{+}_{-}$
${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{8.8}_{8.6}$ $66.7$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{6.0}_{6.6}$ $59.3$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{4.6}_{4.3}$ $49.7$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{3.8}_{3.4}$ $35.0$ ${}^{+}_{-}$
${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{2.7}_{2.7}$ $[3500,4000]$ $42.4$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{5.5}_{5.6}$ $46.4$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{4.2}_{4.2}$ $42.0$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{3.3}_{2.9}$ $33.3$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{2.7}_{2.2}$ $22.6$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.7}_{1.8}$ $[4000,5000]$
$29.2$ ${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{3.2}_{3.7}$ $28.22$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{2.35}_{2.34}$ $23.36$
${}^{+}_{-}$ ${}^{0.08}_{0.08}$ ${}^{+}_{-}$ ${}^{1.83}_{1.48}$ $19.29$
${}^{+}_{-}$ ${}^{0.08}_{0.08}$ ${}^{+}_{-}$ ${}^{1.51}_{1.26}$ $13.9$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{0.9}_{1.1}$ $[5000,6000]$
$15.1$ ${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.5}_{1.7}$ $14.49$
${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{1.18}_{1.10}$ $12.18$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.94}_{0.78}$ $9.44$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.71}_{0.63}$ $6.87$
${}^{+}_{-}$ ${}^{0.11}_{0.11}$ ${}^{+}_{-}$ ${}^{0.60}_{0.64}$ $[6000,7000]$
$8.34$ ${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.76}_{0.84}$ $7.39$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.59}_{0.54}$ $6.30$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.49}_{0.40}$ $4.89$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.32}_{0.37}$ $3.03$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.32}_{0.30}$ $[7000,8000]$
$4.98$ ${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.47}_{0.46}$ $4.24$
${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.33}_{0.31}$ $3.51$
${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.28}_{0.23}$ $2.56$
${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.18}_{0.21}$ $2.31$
${}^{+}_{-}$ ${}^{0.13}_{0.13}$ ${}^{+}_{-}$ ${}^{0.53}_{0.47}$ $[8000,9000]$
$3.11$ ${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.31}_{0.25}$ $2.63$
${}^{+}_{-}$ ${}^{0.02}_{0.02}$ ${}^{+}_{-}$ ${}^{0.21}_{0.19}$ $2.16$
${}^{+}_{-}$ ${}^{0.02}_{0.02}$ ${}^{+}_{-}$ ${}^{0.17}_{0.14}$ $1.40$
${}^{+}_{-}$ ${}^{0.02}_{0.02}$ ${}^{+}_{-}$ ${}^{0.12}_{0.13}$ $1.17$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.46}_{0.47}$ $[9000,10000]$
$1.46$ ${}^{+}_{-}$ ${}^{0.02}_{0.02}$ ${}^{+}_{-}$ ${}^{0.13}_{0.11}$ $1.35$
${}^{+}_{-}$ ${}^{0.01}_{0.01}$ ${}^{+}_{-}$ ${}^{0.11}_{0.09}$ $1.192$
${}^{+}_{-}$ ${}^{0.015}_{0.015}$ ${}^{+}_{-}$ ${}^{0.083}_{0.083}$ $0.928$
${}^{+}_{-}$ ${}^{0.025}_{0.025}$ ${}^{+}_{-}$ ${}^{0.096}_{0.087}$
$[10000,11000]$ $1.144$ ${}^{+}_{-}$ ${}^{0.020}_{0.020}$ ${}^{+}_{-}$
${}^{0.098}_{0.081}$ $0.970$ ${}^{+}_{-}$ ${}^{0.013}_{0.013}$ ${}^{+}_{-}$
${}^{0.072}_{0.061}$ $0.784$ ${}^{+}_{-}$ ${}^{0.013}_{0.013}$ ${}^{+}_{-}$
${}^{0.050}_{0.052}$ $0.477$ ${}^{+}_{-}$ ${}^{0.020}_{0.020}$ ${}^{+}_{-}$
${}^{0.057}_{0.044}$ $[11000,12000]$ $0.774$ ${}^{+}_{-}$ ${}^{0.016}_{0.016}$
${}^{+}_{-}$ ${}^{0.070}_{0.054}$ $0.641$ ${}^{+}_{-}$ ${}^{0.011}_{0.011}$
${}^{+}_{-}$ ${}^{0.050}_{0.037}$ $0.520$ ${}^{+}_{-}$ ${}^{0.011}_{0.011}$
${}^{+}_{-}$ ${}^{0.035}_{0.034}$ $0.301$ ${}^{+}_{-}$ ${}^{0.017}_{0.017}$
${}^{+}_{-}$ ${}^{0.031}_{0.021}$ $[12000,13000]$ $0.513$ ${}^{+}_{-}$
${}^{0.012}_{0.012}$ ${}^{+}_{-}$ ${}^{0.049}_{0.033}$ $0.443$ ${}^{+}_{-}$
${}^{0.009}_{0.009}$ ${}^{+}_{-}$ ${}^{0.036}_{0.025}$ $0.336$ ${}^{+}_{-}$
${}^{0.009}_{0.009}$ ${}^{+}_{-}$ ${}^{0.024}_{0.021}$ $0.185$ ${}^{+}_{-}$
${}^{0.011}_{0.011}$ ${}^{+}_{-}$ ${}^{0.034}_{0.021}$ $[13000,14000]$ $0.362$
${}^{+}_{-}$ ${}^{0.010}_{0.010}$ ${}^{+}_{-}$ ${}^{0.037}_{0.023}$ $0.298$
${}^{+}_{-}$ ${}^{0.007}_{0.007}$ ${}^{+}_{-}$ ${}^{0.028}_{0.015}$ $0.238$
${}^{+}_{-}$ ${}^{0.008}_{0.008}$ ${}^{+}_{-}$ ${}^{0.019}_{0.014}$ $0.096$
${}^{+}_{-}$ ${}^{0.009}_{0.009}$ ${}^{+}_{-}$ ${}^{0.015}_{0.006}$
$[14000,15000]$ $0.250$ ${}^{+}_{-}$ ${}^{0.008}_{0.008}$ ${}^{+}_{-}$
${}^{0.028}_{0.014}$ $0.212$ ${}^{+}_{-}$ ${}^{0.006}_{0.006}$ ${}^{+}_{-}$
${}^{0.022}_{0.009}$ $0.162$ ${}^{+}_{-}$ ${}^{0.007}_{0.007}$ ${}^{+}_{-}$
${}^{0.017}_{0.007}$

Table 7: Differential production cross-sections,
$\text{d}^{2}\sigma/(\text{d}p_{\mathrm{T}}\,\text{d}y)$, in
$$\mathrm{\SIUnitSymbolMicro
b}$/($\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$)$ for prompt
$D_{s}^{+}+D_{s}^{-}$ mesons in bins of $(p_{\mathrm{T}},y)$. The first
uncertainty is statistical, and the second is the total systematic. $y$
$p_{\text{T}}$ [MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$
$[1000,1500]$ $31$ ${}^{+}_{-}$ ${}^{8}_{8}$ ${}^{+}_{-}$ ${}^{15}_{13}$ $60$
${}^{+}_{-}$ ${}^{4}_{4}$ ${}^{+}_{-}$ ${}^{21}_{13}$ $70$ ${}^{+}_{-}$
${}^{4}_{4}$ ${}^{+}_{-}$ ${}^{13}_{13}$ $55$ ${}^{+}_{-}$ ${}^{5}_{5}$
${}^{+}_{-}$ ${}^{14}_{11}$ $110$ ${}^{+}_{-}$ ${}^{36}_{36}$ ${}^{+}_{-}$
${}^{34}_{72}$ $[1500,2000]$ $47$ ${}^{+}_{-}$ ${}^{3}_{3}$ ${}^{+}_{-}$
${}^{13}_{10}$ $63$ ${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{14}_{10}$
$62.1$ ${}^{+}_{-}$ ${}^{1.6}_{1.6}$ ${}^{+}_{-}$ ${}^{7.5}_{7.2}$ $61.2$
${}^{+}_{-}$ ${}^{2.2}_{2.2}$ ${}^{+}_{-}$ ${}^{8.5}_{7.2}$ $29.8$
${}^{+}_{-}$ ${}^{3.1}_{3.1}$ ${}^{+}_{-}$ ${}^{5.9}_{5.5}$ $[2000,2500]$ $48$
${}^{+}_{-}$ ${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{11}_{\phantom{0}9}$ $52.2$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{8.4}_{5.8}$ $56.1$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{6.2}_{5.6}$ $47.1$
${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{5.3}_{4.7}$ $26.9$
${}^{+}_{-}$ ${}^{1.8}_{1.8}$ ${}^{+}_{-}$ ${}^{4.2}_{3.7}$ $[2500,3000]$
$38.2$ ${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{7.8}_{6.5}$ $44.1$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{4.9}_{5.5}$ $38.3$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{4.2}_{3.3}$ $33.9$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{3.5}_{3.2}$ $23.7$
${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{3.2}_{3.1}$ $[3000,3500]$
$27.1$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{4.9}_{4.2}$ $30.1$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{3.2}_{3.4}$ $27.0$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{2.9}_{2.3}$ $22.4$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{2.3}_{2.1}$ $13.9$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.7}_{1.6}$ $[3500,4000]$
$21.2$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{3.6}_{3.0}$ $20.9$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{2.2}_{2.2}$ $19.0$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{2.0}_{1.6}$ $16.6$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.7}_{1.5}$ $10.7$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.5}_{1.3}$ $[4000,5000]$
$12.4$ ${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.8}_{1.6}$ $13.4$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.4}_{1.3}$ $10.7$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.1}_{0.9}$ $9.60$
${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.93}_{0.87}$ $6.36$
${}^{+}_{-}$ ${}^{0.28}_{0.28}$ ${}^{+}_{-}$ ${}^{0.78}_{0.61}$ $[5000,6000]$
$7.7$ ${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{0.9}_{1.0}$ $7.11$
${}^{+}_{-}$ ${}^{0.11}_{0.11}$ ${}^{+}_{-}$ ${}^{0.79}_{0.59}$ $5.89$
${}^{+}_{-}$ ${}^{0.10}_{0.10}$ ${}^{+}_{-}$ ${}^{0.58}_{0.49}$ $4.62$
${}^{+}_{-}$ ${}^{0.10}_{0.10}$ ${}^{+}_{-}$ ${}^{0.54}_{0.41}$ $3.10$
${}^{+}_{-}$ ${}^{0.20}_{0.20}$ ${}^{+}_{-}$ ${}^{0.45}_{0.40}$ $[6000,7000]$
$3.83$ ${}^{+}_{-}$ ${}^{0.10}_{0.10}$ ${}^{+}_{-}$ ${}^{0.44}_{0.46}$ $3.85$
${}^{+}_{-}$ ${}^{0.08}_{0.08}$ ${}^{+}_{-}$ ${}^{0.41}_{0.34}$ $3.03$
${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.31}_{0.27}$ $2.10$
${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.25}_{0.20}$ $1.39$
${}^{+}_{-}$ ${}^{0.16}_{0.16}$ ${}^{+}_{-}$ ${}^{0.25}_{0.21}$ $[7000,8000]$
$2.43$ ${}^{+}_{-}$ ${}^{0.08}_{0.08}$ ${}^{+}_{-}$ ${}^{0.32}_{0.26}$ $1.79$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.18}_{0.17}$ $1.60$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.18}_{0.14}$ $1.33$
${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.18}_{0.14}$ $0.68$
${}^{+}_{-}$ ${}^{0.18}_{0.18}$ ${}^{+}_{-}$ ${}^{0.18}_{0.18}$ $[8000,9000]$
$1.33$ ${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.17}_{0.14}$ $1.19$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.13}_{0.12}$ $1.22$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.16}_{0.12}$ $0.72$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.10}_{0.09}$ $[9000,10000]$
$0.754$ ${}^{+}_{-}$ ${}^{0.036}_{0.036}$ ${}^{+}_{-}$ ${}^{0.097}_{0.067}$
$0.639$ ${}^{+}_{-}$ ${}^{0.026}_{0.026}$ ${}^{+}_{-}$ ${}^{0.069}_{0.054}$
$0.588$ ${}^{+}_{-}$ ${}^{0.027}_{0.027}$ ${}^{+}_{-}$ ${}^{0.066}_{0.050}$
$0.433$ ${}^{+}_{-}$ ${}^{0.041}_{0.041}$ ${}^{+}_{-}$ ${}^{0.053}_{0.044}$
$[10000,11000]$ $0.553$ ${}^{+}_{-}$ ${}^{0.032}_{0.032}$ ${}^{+}_{-}$
${}^{0.063}_{0.037}$ $0.450$ ${}^{+}_{-}$ ${}^{0.023}_{0.023}$ ${}^{+}_{-}$
${}^{0.045}_{0.031}$ $0.346$ ${}^{+}_{-}$ ${}^{0.022}_{0.022}$ ${}^{+}_{-}$
${}^{0.043}_{0.023}$ $0.192$ ${}^{+}_{-}$ ${}^{0.033}_{0.033}$ ${}^{+}_{-}$
${}^{0.025}_{0.010}$ $[11000,12000]$ $0.331$ ${}^{+}_{-}$ ${}^{0.025}_{0.025}$
${}^{+}_{-}$ ${}^{0.038}_{0.023}$ $0.289$ ${}^{+}_{-}$ ${}^{0.018}_{0.018}$
${}^{+}_{-}$ ${}^{0.031}_{0.017}$ $0.240$ ${}^{+}_{-}$ ${}^{0.018}_{0.018}$
${}^{+}_{-}$ ${}^{0.028}_{0.012}$ $[12000,13000]$ $0.247$ ${}^{+}_{-}$
${}^{0.020}_{0.020}$ ${}^{+}_{-}$ ${}^{0.030}_{0.016}$ $0.164$ ${}^{+}_{-}$
${}^{0.014}_{0.014}$ ${}^{+}_{-}$ ${}^{0.020}_{0.008}$ $0.169$ ${}^{+}_{-}$
${}^{0.016}_{0.016}$ ${}^{+}_{-}$ ${}^{0.022}_{0.006}$ $[13000,14000]$ $0.137$
${}^{+}_{-}$ ${}^{0.016}_{0.016}$ ${}^{+}_{-}$ ${}^{0.019}_{0.009}$ $0.159$
${}^{+}_{-}$ ${}^{0.014}_{0.014}$ ${}^{+}_{-}$ ${}^{0.022}_{0.006}$ $0.1090$
${}^{+}_{-}$ ${}^{0.0146}_{0.0146}$ ${}^{+}_{-}$ ${}^{0.0212}_{0.0010}$
$[14000,15000]$

Table 8: Differential production cross-sections,
$\text{d}^{2}\sigma/(\text{d}p_{\mathrm{T}}\,\text{d}y)$, in
$$\mathrm{\SIUnitSymbolMicro
b}$/($\mathrm{{\mathrm{\,Ge\kern-0.90005ptV\\!/}c}}$)$ for prompt
$D^{*+}+D^{*-}$ mesons in bins of $(p_{\mathrm{T}},y)$. The first uncertainty
is statistical, and the second is the total systematic. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[0,1000]$ $67$
${}^{+}_{-}$ ${}^{9}_{9}$ ${}^{+}_{-}$ ${}^{20}_{19}$ $[1000,1500]$ $124$
${}^{+}_{-}$ ${}^{5}_{5}$ ${}^{+}_{-}$ ${}^{16}_{17}$ $152$ ${}^{+}_{-}$
${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{13}_{15}$ $123$ ${}^{+}_{-}$ ${}^{2}_{2}$
${}^{+}_{-}$ ${}^{12}_{12}$ $127$ ${}^{+}_{-}$ ${}^{4}_{4}$ ${}^{+}_{-}$
${}^{20}_{16}$ $[1500,2000]$ $159$ ${}^{+}_{-}$ ${}^{3}_{3}$ ${}^{+}_{-}$
${}^{18}_{16}$ $148$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{12}_{14}$
$125$ ${}^{+}_{-}$ ${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{11}_{12}$ $100$ ${}^{+}_{-}$
${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{11}_{\phantom{0}9}$ $[2000,2500]$ $117$
${}^{+}_{-}$ ${}^{11}_{11}$ ${}^{+}_{-}$ ${}^{27}_{29}$ $123$ ${}^{+}_{-}$
${}^{1}_{1}$ ${}^{+}_{-}$ ${}^{15}_{10}$ $118.2$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$
${}^{+}_{-}$ ${}^{\phantom{0}9.4}_{11.1}$ $98.4$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$
${}^{+}_{-}$ ${}^{9.2}_{8.2}$ $71.3$ ${}^{+}_{-}$ ${}^{1.3}_{1.3}$
${}^{+}_{-}$ ${}^{8.1}_{7.1}$ $[2500,3000]$ $90$ ${}^{+}_{-}$ ${}^{3}_{3}$
${}^{+}_{-}$ ${}^{13}_{14}$ $91.7$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$
${}^{8.3}_{9.3}$ $83.2$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$
${}^{7.6}_{6.7}$ $67.3$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$
${}^{6.3}_{5.6}$ $50.9$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$
${}^{4.4}_{4.8}$ $[3000,3500]$ $64.8$ ${}^{+}_{-}$ ${}^{1.6}_{1.6}$
${}^{+}_{-}$ ${}^{7.7}_{9.0}$ $65.2$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$
${}^{+}_{-}$ ${}^{5.6}_{6.6}$ $57.9$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$
${}^{+}_{-}$ ${}^{5.4}_{4.3}$ $45.7$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$
${}^{+}_{-}$ ${}^{4.3}_{3.7}$ $32.8$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$
${}^{+}_{-}$ ${}^{4.2}_{3.7}$ $[3500,4000]$ $46.8$ ${}^{+}_{-}$
${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{5.3}_{6.1}$ $48.9$ ${}^{+}_{-}$
${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{4.2}_{4.9}$ $39.9$ ${}^{+}_{-}$
${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{3.7}_{2.9}$ $33.2$ ${}^{+}_{-}$
${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{3.1}_{2.7}$ $23.9$ ${}^{+}_{-}$
${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.1}_{2.1}$ $[4000,5000]$ $28.2$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{2.8}_{3.3}$ $27.8$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{2.3}_{2.7}$ $22.9$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{2.0}_{1.6}$ $19.1$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.8}_{1.6}$ $11.7$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.5}_{1.3}$ $[5000,6000]$
$14.3$ ${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.4}_{1.6}$ $13.7$
${}^{+}_{-}$ ${}^{0.1}_{0.1}$ ${}^{+}_{-}$ ${}^{1.1}_{1.3}$ $11.96$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{1.02}_{0.88}$ $9.91$
${}^{+}_{-}$ ${}^{0.12}_{0.12}$ ${}^{+}_{-}$ ${}^{0.95}_{0.67}$ $5.1$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.0}_{0.8}$ $[6000,7000]$
$8.45$ ${}^{+}_{-}$ ${}^{0.14}_{0.14}$ ${}^{+}_{-}$ ${}^{0.79}_{0.94}$ $7.83$
${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.64}_{0.73}$ $6.33$
${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.50}_{0.49}$ $4.44$
${}^{+}_{-}$ ${}^{0.08}_{0.08}$ ${}^{+}_{-}$ ${}^{0.35}_{0.35}$ $1.93$
${}^{+}_{-}$ ${}^{0.32}_{0.32}$ ${}^{+}_{-}$ ${}^{0.40}_{0.36}$ $[7000,8000]$
$4.96$ ${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.46}_{0.54}$ $4.25$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.37}_{0.41}$ $3.70$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.32}_{0.27}$ $2.68$
${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.30}_{0.27}$ $[8000,9000]$
$2.91$ ${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.28}_{0.32}$ $2.53$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.22}_{0.23}$ $2.08$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.21}_{0.15}$ $1.19$
${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.21}_{0.15}$ $[9000,10000]$
$1.26$ ${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.12}_{0.13}$ $1.59$
${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.14}_{0.14}$ $1.23$
${}^{+}_{-}$ ${}^{0.03}_{0.03}$ ${}^{+}_{-}$ ${}^{0.10}_{0.09}$ $0.92$
${}^{+}_{-}$ ${}^{0.08}_{0.08}$ ${}^{+}_{-}$ ${}^{0.15}_{0.12}$
$[10000,11000]$ $1.17$ ${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$
${}^{0.10}_{0.11}$ $1.034$ ${}^{+}_{-}$ ${}^{0.025}_{0.025}$ ${}^{+}_{-}$
${}^{0.089}_{0.083}$ $0.830$ ${}^{+}_{-}$ ${}^{0.025}_{0.025}$ ${}^{+}_{-}$
${}^{0.066}_{0.048}$ $0.382$ ${}^{+}_{-}$ ${}^{0.067}_{0.067}$ ${}^{+}_{-}$
${}^{0.079}_{0.067}$ $[11000,12000]$ $0.721$ ${}^{+}_{-}$ ${}^{0.027}_{0.027}$
${}^{+}_{-}$ ${}^{0.065}_{0.069}$ $0.661$ ${}^{+}_{-}$ ${}^{0.020}_{0.020}$
${}^{+}_{-}$ ${}^{0.061}_{0.052}$ $0.472$ ${}^{+}_{-}$ ${}^{0.021}_{0.021}$
${}^{+}_{-}$ ${}^{0.046}_{0.033}$ $[12000,13000]$ $0.494$ ${}^{+}_{-}$
${}^{0.023}_{0.023}$ ${}^{+}_{-}$ ${}^{0.048}_{0.047}$ $0.491$ ${}^{+}_{-}$
${}^{0.017}_{0.017}$ ${}^{+}_{-}$ ${}^{0.047}_{0.036}$ $0.347$ ${}^{+}_{-}$
${}^{0.021}_{0.021}$ ${}^{+}_{-}$ ${}^{0.030}_{0.022}$ $[13000,14000]$ $0.374$
${}^{+}_{-}$ ${}^{0.020}_{0.020}$ ${}^{+}_{-}$ ${}^{0.043}_{0.037}$ $0.292$
${}^{+}_{-}$ ${}^{0.014}_{0.014}$ ${}^{+}_{-}$ ${}^{0.031}_{0.021}$ $0.272$
${}^{+}_{-}$ ${}^{0.022}_{0.022}$ ${}^{+}_{-}$ ${}^{0.033}_{0.020}$
$[14000,15000]$ $0.218$ ${}^{+}_{-}$ ${}^{0.015}_{0.015}$ ${}^{+}_{-}$
${}^{0.034}_{0.024}$ $0.248$ ${}^{+}_{-}$ ${}^{0.014}_{0.014}$ ${}^{+}_{-}$
${}^{0.026}_{0.016}$ $0.110$ ${}^{+}_{-}$ ${}^{0.016}_{0.016}$ ${}^{+}_{-}$
${}^{0.023}_{0.017}$

##  Appendix B Cross-section ratios at different energies

Tables B–12 give the numerical results of the cross-section ratios between
$\sqrt{s}=13$ and $7\text{\,}\mathrm{TeV}$.

Table 9: The ratios of differential production cross-sections, $R_{13/7}$, for
prompt $D^{0}+{\kern 1.79997pt\overline{\kern-1.79997ptD}{}}^{0}$ mesons in
bins of $(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the
second is the total systematic. $y$ $p_{\text{T}}$ [MeV/c] $[2,2.5]$ $[2.5,3]$
$[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[0,1000]$ $1.12$ ${}^{+}_{-}$
${}^{0.06}_{0.05}$ ${}^{+}_{-}$ ${}^{0.19}_{0.15}$ $1.44$ ${}^{+}_{-}$
${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.18}_{0.17}$ $1.54$ ${}^{+}_{-}$
${}^{0.07}_{0.06}$ ${}^{+}_{-}$ ${}^{0.18}_{0.14}$ $1.59$ ${}^{+}_{-}$
${}^{0.09}_{0.08}$ ${}^{+}_{-}$ ${}^{0.18}_{0.14}$ $1.80$ ${}^{+}_{-}$
${}^{0.19}_{0.15}$ ${}^{+}_{-}$ ${}^{0.24}_{0.18}$ $[1000,2000]$ $1.40$
${}^{+}_{-}$ ${}^{0.06}_{0.05}$ ${}^{+}_{-}$ ${}^{0.21}_{0.17}$ $1.48$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.17}_{0.15}$ $1.61$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.17}_{0.15}$ $1.67$
${}^{+}_{-}$ ${}^{0.07}_{0.06}$ ${}^{+}_{-}$ ${}^{0.18}_{0.15}$ $1.85$
${}^{+}_{-}$ ${}^{0.13}_{0.11}$ ${}^{+}_{-}$ ${}^{0.22}_{0.17}$ $[2000,3000]$
$1.53$ ${}^{+}_{-}$ ${}^{0.06}_{0.05}$ ${}^{+}_{-}$ ${}^{0.18}_{0.18}$ $1.65$
${}^{+}_{-}$ ${}^{0.04}_{0.04}$ ${}^{+}_{-}$ ${}^{0.19}_{0.15}$ $1.83$
${}^{+}_{-}$ ${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.20}_{0.16}$ $1.86$
${}^{+}_{-}$ ${}^{0.07}_{0.06}$ ${}^{+}_{-}$ ${}^{0.21}_{0.16}$ $2.00$
${}^{+}_{-}$ ${}^{0.14}_{0.12}$ ${}^{+}_{-}$ ${}^{0.25}_{0.20}$ $[3000,4000]$
$1.62$ ${}^{+}_{-}$ ${}^{0.07}_{0.07}$ ${}^{+}_{-}$ ${}^{0.20}_{0.18}$ $1.92$
${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.21}_{0.17}$ $1.84$
${}^{+}_{-}$ ${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.20}_{0.16}$ $2.25$
${}^{+}_{-}$ ${}^{0.10}_{0.10}$ ${}^{+}_{-}$ ${}^{0.29}_{0.22}$ $2.32$
${}^{+}_{-}$ ${}^{0.21}_{0.18}$ ${}^{+}_{-}$ ${}^{0.35}_{0.26}$ $[4000,5000]$
$1.79$ ${}^{+}_{-}$ ${}^{0.10}_{0.09}$ ${}^{+}_{-}$ ${}^{0.24}_{0.18}$ $2.00$
${}^{+}_{-}$ ${}^{0.09}_{0.08}$ ${}^{+}_{-}$ ${}^{0.25}_{0.19}$ $1.90$
${}^{+}_{-}$ ${}^{0.09}_{0.08}$ ${}^{+}_{-}$ ${}^{0.21}_{0.16}$ $2.32$
${}^{+}_{-}$ ${}^{0.16}_{0.14}$ ${}^{+}_{-}$ ${}^{0.28}_{0.23}$ $2.30$
${}^{+}_{-}$ ${}^{0.41}_{0.31}$ ${}^{+}_{-}$ ${}^{0.51}_{0.31}$ $[5000,6000]$
$1.90$ ${}^{+}_{-}$ ${}^{0.14}_{0.13}$ ${}^{+}_{-}$ ${}^{0.26}_{0.19}$ $1.78$
${}^{+}_{-}$ ${}^{0.10}_{0.09}$ ${}^{+}_{-}$ ${}^{0.23}_{0.17}$ $2.18$
${}^{+}_{-}$ ${}^{0.15}_{0.14}$ ${}^{+}_{-}$ ${}^{0.28}_{0.22}$ $2.14$
${}^{+}_{-}$ ${}^{0.21}_{0.17}$ ${}^{+}_{-}$ ${}^{0.29}_{0.20}$ $1.69$
${}^{+}_{-}$ ${}^{0.73}_{0.40}$ ${}^{+}_{-}$ ${}^{0.72}_{0.29}$ $[6000,7000]$
$1.88$ ${}^{+}_{-}$ ${}^{0.22}_{0.18}$ ${}^{+}_{-}$ ${}^{0.27}_{0.18}$ $2.00$
${}^{+}_{-}$ ${}^{0.19}_{0.16}$ ${}^{+}_{-}$ ${}^{0.27}_{0.20}$ $2.41$
${}^{+}_{-}$ ${}^{0.30}_{0.24}$ ${}^{+}_{-}$ ${}^{0.32}_{0.25}$ $2.19$
${}^{+}_{-}$ ${}^{0.38}_{0.28}$ ${}^{+}_{-}$ ${}^{0.37}_{0.25}$ $[7000,8000]$
$2.17$ ${}^{+}_{-}$ ${}^{0.48}_{0.33}$ ${}^{+}_{-}$ ${}^{0.39}_{0.22}$ $2.01$
${}^{+}_{-}$ ${}^{0.36}_{0.26}$ ${}^{+}_{-}$ ${}^{0.32}_{0.19}$ $3.15$
${}^{+}_{-}$ ${}^{0.87}_{0.56}$ ${}^{+}_{-}$ ${}^{0.51}_{0.33}$ $2.16$
${}^{+}_{-}$ ${}^{0.95}_{0.51}$ ${}^{+}_{-}$ ${}^{0.67}_{0.30}$

Table 10: The ratios of differential production cross-sections, $R_{13/7}$,
for prompt $D^{+}+D^{-}$ mesons in bins of $(p_{\mathrm{T}},y)$. The first
uncertainty is statistical, and the second is the total systematic. $y$
$p_{\text{T}}$ [MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$
$[0,1000]$ $1.85$ ${}^{+}_{-}$ ${}^{0.16}_{0.14}$ ${}^{+}_{-}$
${}^{0.66}_{0.43}$ $1.57$ ${}^{+}_{-}$ ${}^{0.10}_{0.09}$ ${}^{+}_{-}$
${}^{0.46}_{0.31}$ $1.66$ ${}^{+}_{-}$ ${}^{0.13}_{0.11}$ ${}^{+}_{-}$
${}^{0.48}_{0.33}$ $1.50$ ${}^{+}_{-}$ ${}^{0.23}_{0.19}$ ${}^{+}_{-}$
${}^{0.62}_{0.38}$ $[1000,2000]$ $1.48$ ${}^{+}_{-}$ ${}^{0.21}_{0.16}$
${}^{+}_{-}$ ${}^{0.52}_{0.32}$ $1.51$ ${}^{+}_{-}$ ${}^{0.07}_{0.06}$
${}^{+}_{-}$ ${}^{0.43}_{0.26}$ $1.66$ ${}^{+}_{-}$ ${}^{0.06}_{0.05}$
${}^{+}_{-}$ ${}^{0.36}_{0.27}$ $1.61$ ${}^{+}_{-}$ ${}^{0.06}_{0.06}$
${}^{+}_{-}$ ${}^{0.38}_{0.26}$ $1.86$ ${}^{+}_{-}$ ${}^{0.15}_{0.13}$
${}^{+}_{-}$ ${}^{0.53}_{0.33}$ $[2000,3000]$ $1.65$ ${}^{+}_{-}$
${}^{0.14}_{0.12}$ ${}^{+}_{-}$ ${}^{0.42}_{0.30}$ $1.73$ ${}^{+}_{-}$
${}^{0.06}_{0.06}$ ${}^{+}_{-}$ ${}^{0.38}_{0.27}$ $1.71$ ${}^{+}_{-}$
${}^{0.05}_{0.05}$ ${}^{+}_{-}$ ${}^{0.32}_{0.25}$ $1.83$ ${}^{+}_{-}$
${}^{0.07}_{0.06}$ ${}^{+}_{-}$ ${}^{0.37}_{0.26}$ $2.09$ ${}^{+}_{-}$
${}^{0.17}_{0.14}$ ${}^{+}_{-}$ ${}^{0.64}_{0.39}$ $[3000,4000]$ $1.75$
${}^{+}_{-}$ ${}^{0.13}_{0.11}$ ${}^{+}_{-}$ ${}^{0.40}_{0.31}$ $1.80$
${}^{+}_{-}$ ${}^{0.07}_{0.06}$ ${}^{+}_{-}$ ${}^{0.33}_{0.27}$ $1.87$
${}^{+}_{-}$ ${}^{0.07}_{0.06}$ ${}^{+}_{-}$ ${}^{0.32}_{0.24}$ $2.04$
${}^{+}_{-}$ ${}^{0.09}_{0.09}$ ${}^{+}_{-}$ ${}^{0.40}_{0.28}$ $2.47$
${}^{+}_{-}$ ${}^{0.26}_{0.21}$ ${}^{+}_{-}$ ${}^{0.74}_{0.44}$ $[4000,5000]$
$2.01$ ${}^{+}_{-}$ ${}^{0.16}_{0.14}$ ${}^{+}_{-}$ ${}^{0.42}_{0.34}$ $1.90$
${}^{+}_{-}$ ${}^{0.09}_{0.08}$ ${}^{+}_{-}$ ${}^{0.32}_{0.26}$ $1.98$
${}^{+}_{-}$ ${}^{0.10}_{0.09}$ ${}^{+}_{-}$ ${}^{0.35}_{0.24}$ $2.34$
${}^{+}_{-}$ ${}^{0.16}_{0.14}$ ${}^{+}_{-}$ ${}^{0.52}_{0.33}$ $3.00$
${}^{+}_{-}$ ${}^{0.48}_{0.37}$ ${}^{+}_{-}$ ${}^{0.93}_{0.54}$ $[5000,6000]$
$2.24$ ${}^{+}_{-}$ ${}^{0.23}_{0.19}$ ${}^{+}_{-}$ ${}^{0.52}_{0.40}$ $2.07$
${}^{+}_{-}$ ${}^{0.13}_{0.12}$ ${}^{+}_{-}$ ${}^{0.38}_{0.28}$ $2.17$
${}^{+}_{-}$ ${}^{0.15}_{0.13}$ ${}^{+}_{-}$ ${}^{0.38}_{0.26}$ $2.48$
${}^{+}_{-}$ ${}^{0.23}_{0.19}$ ${}^{+}_{-}$ ${}^{0.57}_{0.36}$ $5.4$
${}^{+}_{-}$ ${}^{2.1}_{1.2}$ ${}^{+}_{-}$ ${}^{2.2}_{0.9}$ $[6000,7000]$
$2.16$ ${}^{+}_{-}$ ${}^{0.27}_{0.21}$ ${}^{+}_{-}$ ${}^{0.49}_{0.35}$ $2.14$
${}^{+}_{-}$ ${}^{0.19}_{0.16}$ ${}^{+}_{-}$ ${}^{0.38}_{0.27}$ $1.74$
${}^{+}_{-}$ ${}^{0.15}_{0.13}$ ${}^{+}_{-}$ ${}^{0.48}_{0.29}$ $3.06$
${}^{+}_{-}$ ${}^{0.43}_{0.34}$ ${}^{+}_{-}$ ${}^{0.88}_{0.53}$ $[7000,8000]$
$2.04$ ${}^{+}_{-}$ ${}^{0.33}_{0.25}$ ${}^{+}_{-}$ ${}^{0.53}_{0.33}$ $2.26$
${}^{+}_{-}$ ${}^{0.30}_{0.24}$ ${}^{+}_{-}$ ${}^{0.45}_{0.28}$ $2.51$
${}^{+}_{-}$ ${}^{0.37}_{0.28}$ ${}^{+}_{-}$ ${}^{0.76}_{0.40}$ $4.0$
${}^{+}_{-}$ ${}^{1.1}_{0.7}$ ${}^{+}_{-}$ ${}^{1.4}_{0.7}$

Table 11: The ratios of differential production cross-sections, $R_{13/7}$,
for prompt $D_{s}^{+}+D_{s}^{-}$ mesons in bins of $(p_{\mathrm{T}},y)$. The
first uncertainty is statistical, and the second is the total systematic. $y$
$p_{\text{T}}$ [MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$
$[1000,2000]$ $0.86$ ${}^{+}_{-}$ ${}^{0.47}_{0.23}$ ${}^{+}_{-}$
${}^{0.61}_{0.24}$ $1.51$ ${}^{+}_{-}$ ${}^{0.28}_{0.21}$ ${}^{+}_{-}$
${}^{0.63}_{0.31}$ $2.74$ ${}^{+}_{-}$ ${}^{0.60}_{0.41}$ ${}^{+}_{-}$
${}^{0.97}_{0.53}$ $2.6$ ${}^{+}_{-}$ ${}^{1.0}_{0.6}$ ${}^{+}_{-}$
${}^{1.3}_{0.5}$ $[2000,3000]$ $3.6$ ${}^{+}_{-}$ ${}^{1.6}_{0.8}$
${}^{+}_{-}$ ${}^{1.9}_{0.8}$ $2.89$ ${}^{+}_{-}$ ${}^{0.47}_{0.35}$
${}^{+}_{-}$ ${}^{0.76}_{0.46}$ $2.28$ ${}^{+}_{-}$ ${}^{0.29}_{0.24}$
${}^{+}_{-}$ ${}^{0.56}_{0.35}$ $2.76$ ${}^{+}_{-}$ ${}^{0.60}_{0.42}$
${}^{+}_{-}$ ${}^{0.79}_{0.43}$ $2.1$ ${}^{+}_{-}$ ${}^{1.3}_{0.6}$
${}^{+}_{-}$ ${}^{1.0}_{0.4}$ $[3000,4000]$ $3.6$ ${}^{+}_{-}$
${}^{1.4}_{0.8}$ ${}^{+}_{-}$ ${}^{1.5}_{0.7}$ $2.29$ ${}^{+}_{-}$
${}^{0.34}_{0.27}$ ${}^{+}_{-}$ ${}^{0.55}_{0.38}$ $2.41$ ${}^{+}_{-}$
${}^{0.40}_{0.30}$ ${}^{+}_{-}$ ${}^{0.69}_{0.37}$ $2.55$ ${}^{+}_{-}$
${}^{0.55}_{0.39}$ ${}^{+}_{-}$ ${}^{0.73}_{0.38}$ $2.9$ ${}^{+}_{-}$
${}^{2.2}_{0.9}$ ${}^{+}_{-}$ ${}^{1.3}_{0.5}$ $[4000,5000]$ $3.5$
${}^{+}_{-}$ ${}^{1.3}_{0.8}$ ${}^{+}_{-}$ ${}^{1.3}_{0.6}$ $3.08$
${}^{+}_{-}$ ${}^{0.63}_{0.45}$ ${}^{+}_{-}$ ${}^{0.77}_{0.44}$ $3.61$
${}^{+}_{-}$ ${}^{0.87}_{0.59}$ ${}^{+}_{-}$ ${}^{0.94}_{0.48}$ $2.96$
${}^{+}_{-}$ ${}^{0.93}_{0.57}$ ${}^{+}_{-}$ ${}^{0.84}_{0.43}$ $[5000,6000]$
$4.2$ ${}^{+}_{-}$ ${}^{2.5}_{1.1}$ ${}^{+}_{-}$ ${}^{1.8}_{0.8}$ $3.21$
${}^{+}_{-}$ ${}^{0.88}_{0.58}$ ${}^{+}_{-}$ ${}^{0.98}_{0.44}$ $3.3$
${}^{+}_{-}$ ${}^{1.0}_{0.7}$ ${}^{+}_{-}$ ${}^{0.9}_{0.4}$ $3.4$ ${}^{+}_{-}$
${}^{1.6}_{0.8}$ ${}^{+}_{-}$ ${}^{1.5}_{0.5}$ $[6000,7000]$ $2.8$
${}^{+}_{-}$ ${}^{1.4}_{0.7}$ ${}^{+}_{-}$ ${}^{1.2}_{0.5}$ $3.8$ ${}^{+}_{-}$
${}^{1.7}_{0.9}$ ${}^{+}_{-}$ ${}^{1.2}_{0.5}$ $2.44$ ${}^{+}_{-}$
${}^{1.00}_{0.55}$ ${}^{+}_{-}$ ${}^{0.78}_{0.33}$ $[7000,8000]$ $2.0$
${}^{+}_{-}$ ${}^{1.1}_{0.5}$ ${}^{+}_{-}$ ${}^{1.1}_{0.4}$ $3.4$ ${}^{+}_{-}$
${}^{2.5}_{1.0}$ ${}^{+}_{-}$ ${}^{1.4}_{0.5}$

Table 12: The ratios of differential production cross-sections, $R_{13/7}$,
for prompt $D^{*+}+D^{*-}$ mesons in bins of $(p_{\mathrm{T}},y)$. The first
uncertainty is statistical, and the second is the total systematic. $y$
$p_{\text{T}}$ [MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$
$[0,1000]$ $0.71$ ${}^{+}_{-}$ ${}^{0.30}_{0.18}$ ${}^{+}_{-}$
${}^{0.33}_{0.20}$ $[1000,2000]$ $1.13$ ${}^{+}_{-}$ ${}^{0.18}_{0.13}$
${}^{+}_{-}$ ${}^{0.24}_{0.16}$ $1.53$ ${}^{+}_{-}$ ${}^{0.10}_{0.09}$
${}^{+}_{-}$ ${}^{0.25}_{0.21}$ $1.58$ ${}^{+}_{-}$ ${}^{0.14}_{0.12}$
${}^{+}_{-}$ ${}^{0.27}_{0.22}$ $1.75$ ${}^{+}_{-}$ ${}^{0.28}_{0.21}$
${}^{+}_{-}$ ${}^{0.39}_{0.22}$ $[2000,3000]$ $1.75$ ${}^{+}_{-}$
${}^{0.18}_{0.15}$ ${}^{+}_{-}$ ${}^{0.34}_{0.22}$ $2.02$ ${}^{+}_{-}$
${}^{0.13}_{0.12}$ ${}^{+}_{-}$ ${}^{0.33}_{0.26}$ $1.72$ ${}^{+}_{-}$
${}^{0.14}_{0.12}$ ${}^{+}_{-}$ ${}^{0.30}_{0.21}$ $1.65$ ${}^{+}_{-}$
${}^{0.24}_{0.19}$ ${}^{+}_{-}$ ${}^{0.33}_{0.22}$ $[3000,4000]$ $1.82$
${}^{+}_{-}$ ${}^{0.46}_{0.31}$ ${}^{+}_{-}$ ${}^{0.40}_{0.28}$ $1.67$
${}^{+}_{-}$ ${}^{0.14}_{0.12}$ ${}^{+}_{-}$ ${}^{0.28}_{0.23}$ $1.76$
${}^{+}_{-}$ ${}^{0.13}_{0.11}$ ${}^{+}_{-}$ ${}^{0.32}_{0.20}$ $1.89$
${}^{+}_{-}$ ${}^{0.18}_{0.15}$ ${}^{+}_{-}$ ${}^{0.37}_{0.24}$ $2.77$
${}^{+}_{-}$ ${}^{0.72}_{0.48}$ ${}^{+}_{-}$ ${}^{0.65}_{0.35}$ $[4000,5000]$
$1.43$ ${}^{+}_{-}$ ${}^{0.28}_{0.20}$ ${}^{+}_{-}$ ${}^{0.29}_{0.22}$ $2.21$
${}^{+}_{-}$ ${}^{0.26}_{0.21}$ ${}^{+}_{-}$ ${}^{0.39}_{0.31}$ $1.85$
${}^{+}_{-}$ ${}^{0.19}_{0.16}$ ${}^{+}_{-}$ ${}^{0.34}_{0.22}$ $2.11$
${}^{+}_{-}$ ${}^{0.28}_{0.22}$ ${}^{+}_{-}$ ${}^{0.42}_{0.27}$ $1.71$
${}^{+}_{-}$ ${}^{0.74}_{0.39}$ ${}^{+}_{-}$ ${}^{0.53}_{0.23}$ $[5000,6000]$
$1.83$ ${}^{+}_{-}$ ${}^{0.50}_{0.32}$ ${}^{+}_{-}$ ${}^{0.37}_{0.26}$ $1.80$
${}^{+}_{-}$ ${}^{0.25}_{0.20}$ ${}^{+}_{-}$ ${}^{0.32}_{0.25}$ $1.74$
${}^{+}_{-}$ ${}^{0.24}_{0.19}$ ${}^{+}_{-}$ ${}^{0.35}_{0.22}$ $2.53$
${}^{+}_{-}$ ${}^{0.55}_{0.39}$ ${}^{+}_{-}$ ${}^{0.59}_{0.27}$ $[6000,7000]$
$1.76$ ${}^{+}_{-}$ ${}^{0.57}_{0.35}$ ${}^{+}_{-}$ ${}^{0.40}_{0.26}$ $2.20$
${}^{+}_{-}$ ${}^{0.48}_{0.34}$ ${}^{+}_{-}$ ${}^{0.46}_{0.30}$ $3.02$
${}^{+}_{-}$ ${}^{0.94}_{0.58}$ ${}^{+}_{-}$ ${}^{0.77}_{0.36}$ $3.3$
${}^{+}_{-}$ ${}^{1.8}_{0.8}$ ${}^{+}_{-}$ ${}^{0.9}_{0.4}$ $[7000,8000]$
$1.42$ ${}^{+}_{-}$ ${}^{0.71}_{0.36}$ ${}^{+}_{-}$ ${}^{0.42}_{0.22}$ $1.93$
${}^{+}_{-}$ ${}^{0.76}_{0.42}$ ${}^{+}_{-}$ ${}^{0.50}_{0.26}$

##  Appendix C Cross-section ratios for different mesons

Figure 10 shows the remaining three ratios of cross-section-times-branching-
fraction measurements for different mesons, completing those shown and
discussed in Sec. 6. The numerical values of these ratios are given in Tables
13–18.

Figure 10: Ratios of cross-section-times-branching-fraction measurements of
(top) $D^{*+}$, and (middle) $D_{s}^{+}$ mesons with respect to $D^{+}$ cross-
sections, and (bottom) $D_{s}^{+}$ over $D^{*+}$ mesons. The bands indicate
the corresponding ratios computed using measurements from $e^{+}e^{-}$
collider experiments [40, 41, 42]. The ratios are given as a function of
$p_{\mathrm{T}}$ and different symbols indicate different ranges in $y$. The
notation $\sigma(\mbox{$D\to f$})$ is shorthand for
$\sigma(D)\times\mathcal{B}(\mbox{$D\to f$})$.

Table 13: The ratios of differential production cross-section-times-branching
fraction measurements for prompt $D^{+}$ and $D^{0}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. All values are given in percent. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[0,1000]$ $132$
${}^{+}_{-}$ ${}^{5}_{5}$ ${}^{+}_{-}$ ${}^{29}_{23}$ $89$ ${}^{+}_{-}$
${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{10}_{10}$ $89$ ${}^{+}_{-}$ ${}^{3}_{3}$
${}^{+}_{-}$ ${}^{10}_{10}$ $82$ ${}^{+}_{-}$ ${}^{5}_{5}$ ${}^{+}_{-}$
${}^{17}_{16}$ $[1000,1500]$ $99$ ${}^{+}_{-}$ ${}^{4}_{4}$ ${}^{+}_{-}$
${}^{20}_{19}$ $87.3$ ${}^{+}_{-}$ ${}^{0.9}_{1.0}$ ${}^{+}_{-}$
${}^{11.8}_{\phantom{0}7.0}$ $95.5$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$
${}^{6.3}_{6.1}$ $91.1$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$
${}^{5.9}_{5.6}$ $95.8$ ${}^{+}_{-}$ ${}^{2.1}_{2.1}$ ${}^{+}_{-}$
${}^{9.2}_{8.8}$ $[1500,2000]$ $88.3$ ${}^{+}_{-}$ ${}^{1.5}_{1.5}$
${}^{+}_{-}$ ${}^{9.9}_{9.1}$ $86.1$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$
${}^{+}_{-}$ ${}^{8.5}_{6.0}$ $95.1$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$
${}^{+}_{-}$ ${}^{4.8}_{5.5}$ $91.3$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$
${}^{+}_{-}$ ${}^{4.6}_{4.5}$ $95.2$ ${}^{+}_{-}$ ${}^{1.4}_{1.4}$
${}^{+}_{-}$ ${}^{6.8}_{6.9}$ $[2000,2500]$ $88.0$ ${}^{+}_{-}$
${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{8.8}_{7.0}$ $94.4$ ${}^{+}_{-}$
${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{7.4}_{5.7}$ $92.9$ ${}^{+}_{-}$
${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{3.7}_{4.6}$ $88.4$ ${}^{+}_{-}$
${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{3.7}_{3.9}$ $98.0$ ${}^{+}_{-}$
${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{6.0}_{5.1}$ $[2500,3000]$ $88.8$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{8.2}_{7.0}$ $96.6$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{4.5}_{6.5}$ $94.1$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{3.5}_{4.3}$ $96.9$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{4.0}_{4.7}$ $96.6$
${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{5.8}_{4.6}$ $[3000,3500]$
$90.9$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{8.1}_{7.4}$ $100.5$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{4.5}_{6.1}$ $101.6$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{3.7}_{4.2}$ $96.3$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{4.2}_{4.8}$ $96.1$
${}^{+}_{-}$ ${}^{1.4}_{1.3}$ ${}^{+}_{-}$ ${}^{6.0}_{5.2}$ $[3500,4000]$
$91.0$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{7.2}_{7.5}$ $98.4$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{4.6}_{5.3}$ $105.7$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{4.2}_{4.1}$ $94.8$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{4.3}_{4.0}$ $91.8$
${}^{+}_{-}$ ${}^{1.5}_{1.5}$ ${}^{+}_{-}$ ${}^{7.2}_{7.2}$ $[4000,5000]$
$103.2$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{5.9}_{8.7}$ $103.0$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{4.3}_{5.0}$ $100.9$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{4.0}_{3.3}$ $98.9$
${}^{+}_{-}$ ${}^{0.7}_{0.6}$ ${}^{+}_{-}$ ${}^{4.6}_{2.7}$ $125$ ${}^{+}_{-}$
${}^{2}_{2}$ ${}^{+}_{-}$ ${}^{13}_{14}$ $[5000,6000]$ $100.2$ ${}^{+}_{-}$
${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{4.9}_{8.1}$ $108.2$ ${}^{+}_{-}$
${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{4.6}_{4.8}$ $105.6$ ${}^{+}_{-}$
${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{4.7}_{3.3}$ $106.6$ ${}^{+}_{-}$
${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{4.6}_{4.2}$ $149$ ${}^{+}_{-}$ ${}^{6}_{6}$
${}^{+}_{-}$ ${}^{26}_{27}$ $[6000,7000]$ $106.0$ ${}^{+}_{-}$
${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{5.5}_{7.6}$ $101.1$ ${}^{+}_{-}$
${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{4.5}_{4.3}$ $103.0$ ${}^{+}_{-}$
${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{5.1}_{3.3}$ $112.8$ ${}^{+}_{-}$
${}^{1.6}_{1.5}$ ${}^{+}_{-}$ ${}^{7.7}_{8.3}$ $210$ ${}^{+}_{-}$
${}^{40}_{30}$ ${}^{+}_{-}$ ${}^{130}_{\phantom{0}90}$ $[7000,8000]$ $115.5$
${}^{+}_{-}$ ${}^{1.6}_{1.5}$ ${}^{+}_{-}$ ${}^{6.9}_{7.8}$ $102.8$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{4.7}_{4.7}$ $104.8$
${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{6.1}_{3.6}$ $122$ ${}^{+}_{-}$
${}^{3}_{3}$ ${}^{+}_{-}$ ${}^{12}_{14}$ $[8000,9000]$ $119.5$ ${}^{+}_{-}$
${}^{2.0}_{1.9}$ ${}^{+}_{-}$ ${}^{8.5}_{7.6}$ $108.2$ ${}^{+}_{-}$
${}^{1.4}_{1.4}$ ${}^{+}_{-}$ ${}^{5.6}_{5.7}$ $113.0$ ${}^{+}_{-}$
${}^{1.7}_{1.7}$ ${}^{+}_{-}$ ${}^{7.2}_{5.0}$ $114$ ${}^{+}_{-}$ ${}^{5}_{5}$
${}^{+}_{-}$ ${}^{17}_{17}$ $[9000,10000]$ $87.8$ ${}^{+}_{-}$
${}^{1.8}_{1.7}$ ${}^{+}_{-}$ ${}^{4.8}_{4.2}$ $91.0$ ${}^{+}_{-}$
${}^{1.5}_{1.5}$ ${}^{+}_{-}$ ${}^{3.5}_{3.8}$ $102.0$ ${}^{+}_{-}$
${}^{2.1}_{2.0}$ ${}^{+}_{-}$ ${}^{3.2}_{4.4}$ $143$ ${}^{+}_{-}$
${}^{12}_{11}$ ${}^{+}_{-}$ ${}^{24}_{28}$ $[10000,11000]$ $108.4$
${}^{+}_{-}$ ${}^{2.7}_{2.7}$ ${}^{+}_{-}$ ${}^{5.3}_{4.5}$ $104.7$
${}^{+}_{-}$ ${}^{2.2}_{2.2}$ ${}^{+}_{-}$ ${}^{2.7}_{4.1}$ $113.7$
${}^{+}_{-}$ ${}^{3.2}_{3.1}$ ${}^{+}_{-}$ ${}^{4.2}_{6.8}$ $146$ ${}^{+}_{-}$
${}^{32}_{23}$ ${}^{+}_{-}$ ${}^{32}_{32}$ $[11000,12000]$ $114.9$
${}^{+}_{-}$ ${}^{3.6}_{3.4}$ ${}^{+}_{-}$ ${}^{5.5}_{5.2}$ $101.4$
${}^{+}_{-}$ ${}^{2.7}_{2.6}$ ${}^{+}_{-}$ ${}^{2.6}_{3.8}$ $119.3$
${}^{+}_{-}$ ${}^{4.9}_{4.4}$ ${}^{+}_{-}$ ${}^{4.8}_{7.3}$ $[12000,13000]$
$119.2$ ${}^{+}_{-}$ ${}^{4.6}_{4.5}$ ${}^{+}_{-}$ ${}^{7.2}_{6.9}$ $101.0$
${}^{+}_{-}$ ${}^{3.4}_{3.2}$ ${}^{+}_{-}$ ${}^{2.8}_{4.2}$ $110.4$
${}^{+}_{-}$ ${}^{6.3}_{6.0}$ ${}^{+}_{-}$ ${}^{6.8}_{6.6}$ $[13000,14000]$
$114.2$ ${}^{+}_{-}$ ${}^{5.3}_{5.0}$ ${}^{+}_{-}$ ${}^{6.6}_{6.5}$ $97.8$
${}^{+}_{-}$ ${}^{4.0}_{3.9}$ ${}^{+}_{-}$ ${}^{4.2}_{4.0}$ $125$ ${}^{+}_{-}$
${}^{10}_{\phantom{0}9}$ ${}^{+}_{-}$ ${}^{15}_{16}$ $[14000,15000]$ $118.1$
${}^{+}_{-}$ ${}^{6.9}_{6.3}$ ${}^{+}_{-}$ ${}^{7.2}_{5.7}$ $100.9$
${}^{+}_{-}$ ${}^{5.2}_{4.9}$ ${}^{+}_{-}$ ${}^{5.9}_{3.8}$ $142$ ${}^{+}_{-}$
${}^{20}_{16}$ ${}^{+}_{-}$ ${}^{25}_{18}$

Table 14: The ratios of differential production cross-section-times-branching-
fraction measurements for prompt $D_{s}^{+}$ and $D^{0}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. All values are given in percent. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[1000,1500]$ $4.1$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{1.8}_{1.6}$ $7.6$ ${}^{+}_{-}$
${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{2.3}_{1.4}$ $8.9$ ${}^{+}_{-}$
${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.4}_{1.4}$ $7.7$ ${}^{+}_{-}$
${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{1.9}_{1.5}$ $19$ ${}^{+}_{-}$ ${}^{6}_{6}$
${}^{+}_{-}$ ${}^{\phantom{0}5}_{12}$ $[1500,2000]$ $7.0$ ${}^{+}_{-}$
${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.5}_{1.2}$ $9.0$ ${}^{+}_{-}$
${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.5}_{1.1}$ $9.43$ ${}^{+}_{-}$
${}^{0.24}_{0.24}$ ${}^{+}_{-}$ ${}^{0.72}_{0.78}$ $10.3$ ${}^{+}_{-}$
${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ $6.5$ ${}^{+}_{-}$
${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.1}_{1.1}$ $[2000,2500]$ $9.3$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.6}_{1.2}$ $9.59$
${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.99}_{0.65}$ $11.07$
${}^{+}_{-}$ ${}^{0.19}_{0.19}$ ${}^{+}_{-}$ ${}^{0.66}_{0.70}$ $10.50$
${}^{+}_{-}$ ${}^{0.25}_{0.25}$ ${}^{+}_{-}$ ${}^{0.71}_{0.74}$ $8.2$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.1}_{1.0}$ $[2500,3000]$
$9.7$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.4}_{1.1}$ $11.12$
${}^{+}_{-}$ ${}^{0.16}_{0.16}$ ${}^{+}_{-}$ ${}^{0.58}_{0.90}$ $10.59$
${}^{+}_{-}$ ${}^{0.15}_{0.15}$ ${}^{+}_{-}$ ${}^{0.61}_{0.50}$ $11.19$
${}^{+}_{-}$ ${}^{0.22}_{0.23}$ ${}^{+}_{-}$ ${}^{0.65}_{0.73}$ $10.6$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.1}_{1.1}$ $[3000,3500]$
$9.7$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.2}_{1.0}$ $11.13$
${}^{+}_{-}$ ${}^{0.16}_{0.17}$ ${}^{+}_{-}$ ${}^{0.57}_{0.78}$ $11.36$
${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.62}_{0.51}$ $10.66$
${}^{+}_{-}$ ${}^{0.22}_{0.21}$ ${}^{+}_{-}$ ${}^{0.62}_{0.70}$ $9.40$
${}^{+}_{-}$ ${}^{0.46}_{0.46}$ ${}^{+}_{-}$ ${}^{0.96}_{0.87}$ $[3500,4000]$
$11.2$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.2}_{1.0}$ $10.88$
${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.55}_{0.72}$ $11.72$
${}^{+}_{-}$ ${}^{0.19}_{0.19}$ ${}^{+}_{-}$ ${}^{0.60}_{0.54}$ $11.58$
${}^{+}_{-}$ ${}^{0.25}_{0.25}$ ${}^{+}_{-}$ ${}^{0.73}_{0.71}$ $10.6$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.3}_{1.1}$ $[4000,5000]$
$10.80$ ${}^{+}_{-}$ ${}^{0.22}_{0.21}$ ${}^{+}_{-}$ ${}^{0.90}_{0.97}$
$12.01$ ${}^{+}_{-}$ ${}^{0.15}_{0.15}$ ${}^{+}_{-}$ ${}^{0.60}_{0.61}$
$11.37$ ${}^{+}_{-}$ ${}^{0.15}_{0.15}$ ${}^{+}_{-}$ ${}^{0.48}_{0.42}$
$12.08$ ${}^{+}_{-}$ ${}^{0.22}_{0.22}$ ${}^{+}_{-}$ ${}^{0.57}_{0.54}$ $14.0$
${}^{+}_{-}$ ${}^{0.7}_{0.6}$ ${}^{+}_{-}$ ${}^{2.1}_{1.7}$ $[5000,6000]$
$12.5$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{0.8}_{1.2}$ $13.02$
${}^{+}_{-}$ ${}^{0.21}_{0.20}$ ${}^{+}_{-}$ ${}^{0.77}_{0.58}$ $12.53$
${}^{+}_{-}$ ${}^{0.22}_{0.22}$ ${}^{+}_{-}$ ${}^{0.65}_{0.51}$ $12.79$
${}^{+}_{-}$ ${}^{0.30}_{0.29}$ ${}^{+}_{-}$ ${}^{0.88}_{0.67}$ $16.5$
${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{2.8}_{2.7}$ $[6000,7000]$
$11.95$ ${}^{+}_{-}$ ${}^{0.33}_{0.33}$ ${}^{+}_{-}$ ${}^{0.81}_{1.00}$
$12.94$ ${}^{+}_{-}$ ${}^{0.27}_{0.26}$ ${}^{+}_{-}$ ${}^{0.77}_{0.62}$
$12.15$ ${}^{+}_{-}$ ${}^{0.28}_{0.27}$ ${}^{+}_{-}$ ${}^{0.73}_{0.59}$
$11.86$ ${}^{+}_{-}$ ${}^{0.40}_{0.39}$ ${}^{+}_{-}$ ${}^{0.96}_{0.66}$ $23$
${}^{+}_{-}$ ${}^{5}_{4}$ ${}^{+}_{-}$ ${}^{15}_{10}$ $[7000,8000]$ $13.8$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.2}_{1.1}$ $10.64$
${}^{+}_{-}$ ${}^{0.29}_{0.29}$ ${}^{+}_{-}$ ${}^{0.58}_{0.68}$ $11.71$
${}^{+}_{-}$ ${}^{0.35}_{0.34}$ ${}^{+}_{-}$ ${}^{0.94}_{0.62}$ $15.5$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.2}_{1.8}$ $[8000,9000]$
$12.6$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.3}_{1.1}$ $12.06$
${}^{+}_{-}$ ${}^{0.41}_{0.41}$ ${}^{+}_{-}$ ${}^{0.84}_{0.93}$ $15.7$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.6}_{1.2}$ $14.5$
${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{3.0}_{2.6}$ $[9000,10000]$
$11.11$ ${}^{+}_{-}$ ${}^{0.56}_{0.55}$ ${}^{+}_{-}$ ${}^{0.96}_{0.74}$
$10.60$ ${}^{+}_{-}$ ${}^{0.46}_{0.45}$ ${}^{+}_{-}$ ${}^{0.57}_{0.57}$
$12.35$ ${}^{+}_{-}$ ${}^{0.61}_{0.59}$ ${}^{+}_{-}$ ${}^{0.79}_{0.65}$ $16.3$
${}^{+}_{-}$ ${}^{2.1}_{1.9}$ ${}^{+}_{-}$ ${}^{3.7}_{3.7}$ $[10000,11000]$
$12.84$ ${}^{+}_{-}$ ${}^{0.80}_{0.78}$ ${}^{+}_{-}$ ${}^{0.82}_{0.23}$
$11.92$ ${}^{+}_{-}$ ${}^{0.63}_{0.63}$ ${}^{+}_{-}$ ${}^{0.24}_{0.36}$
$12.30$ ${}^{+}_{-}$ ${}^{0.82}_{0.82}$ ${}^{+}_{-}$ ${}^{0.77}_{0.14}$ $14.5$
${}^{+}_{-}$ ${}^{4.1}_{3.2}$ ${}^{+}_{-}$ ${}^{4.8}_{3.9}$ $[11000,12000]$
$12.05$ ${}^{+}_{-}$ ${}^{0.94}_{0.94}$ ${}^{+}_{-}$ ${}^{0.69}_{0.33}$
$11.21$ ${}^{+}_{-}$ ${}^{0.74}_{0.74}$ ${}^{+}_{-}$ ${}^{0.42}_{0.27}$ $13.5$
${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{1.0}_{0.4}$ $[12000,13000]$
$14.0$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{0.9}_{0.6}$ $9.17$
${}^{+}_{-}$ ${}^{0.81}_{0.80}$ ${}^{+}_{-}$ ${}^{0.43}_{0.25}$ $14.0$
${}^{+}_{-}$ ${}^{1.5}_{1.4}$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ $[13000,14000]$
$10.6$ ${}^{+}_{-}$ ${}^{1.3}_{1.2}$ ${}^{+}_{-}$ ${}^{0.6}_{0.5}$ $12.8$
${}^{+}_{-}$ ${}^{1.2}_{1.1}$ ${}^{+}_{-}$ ${}^{0.8}_{0.3}$ $14.1$
${}^{+}_{-}$ ${}^{2.2}_{2.0}$ ${}^{+}_{-}$ ${}^{1.9}_{0.2}$ $[14000,15000]$

Table 15: The ratios of differential production cross-section-times-branching-
fraction measurements for prompt $D^{*+}$ and $D^{0}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. All values are given in percent. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[0,1000]$ $21.9$
${}^{+}_{-}$ ${}^{3.0}_{3.0}$ ${}^{+}_{-}$ ${}^{6.7}_{6.3}$ $[1000,1500]$
$18.3$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.0}_{2.0}$ $22.6$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.3}_{1.6}$ $20.3$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.4}_{1.5}$ $25.5$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{3.7}_{3.1}$ $[1500,2000]$
$26.3$ ${}^{+}_{-}$ ${}^{0.5}_{0.4}$ ${}^{+}_{-}$ ${}^{1.8}_{1.6}$ $26.4$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.3}_{1.9}$ $24.7$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.5}_{1.9}$ $25.5$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.5}_{2.0}$ $[2000,2500]$
$26.8$ ${}^{+}_{-}$ ${}^{2.4}_{2.4}$ ${}^{+}_{-}$ ${}^{5.7}_{6.0}$ $26.5$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.9}_{1.1}$ $27.4$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.3}_{1.8}$ $25.7$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.6}_{1.6}$ $25.5$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{2.6}_{2.1}$ $[2500,3000]$
$26.8$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{2.9}_{3.1}$ $27.1$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.2}_{1.7}$ $27.0$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.6}_{1.5}$ $26.0$
${}^{+}_{-}$ ${}^{0.2}_{0.3}$ ${}^{+}_{-}$ ${}^{1.7}_{1.7}$ $26.6$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.8}_{2.0}$ $[3000,3500]$
$27.2$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.2}_{2.5}$ $28.3$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.2}_{1.9}$ $28.6$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.7}_{1.4}$ $25.5$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.8}_{1.8}$ $25.9$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.7}_{2.2}$ $[3500,4000]$
$28.9$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.1}_{2.5}$ $29.8$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.4}_{2.1}$ $28.9$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.8}_{1.4}$ $27.2$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.9}_{1.7}$ $27.9$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.7}_{2.7}$ $[4000,5000]$
$28.8$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.4}_{2.3}$ $29.2$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.3}_{2.0}$ $28.5$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.6}_{1.4}$ $28.2$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{2.0}_{1.5}$ $30.3$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{2.3}_{2.2}$ $[5000,6000]$
$27.3$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.3}_{2.3}$ $29.4$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.4}_{2.0}$ $29.9$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.7}_{1.3}$ $32.2$
${}^{+}_{-}$ ${}^{0.4}_{0.5}$ ${}^{+}_{-}$ ${}^{2.3}_{1.6}$ $31.5$
${}^{+}_{-}$ ${}^{2.1}_{2.0}$ ${}^{+}_{-}$ ${}^{4.1}_{3.7}$ $[6000,7000]$
$30.9$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.8}_{2.6}$ $30.8$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.6}_{2.1}$ $29.8$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.7}_{1.5}$ $29.5$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.2}_{2.2}$ $38$ ${}^{+}_{-}$
${}^{10}_{\phantom{0}8}$ ${}^{+}_{-}$ ${}^{24}_{17}$ $[7000,8000]$ $33.1$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.0}_{2.9}$ $29.6$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.7}_{2.3}$ $31.7$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{2.2}_{1.6}$ $36.8$
${}^{+}_{-}$ ${}^{1.3}_{1.2}$ ${}^{+}_{-}$ ${}^{4.4}_{4.3}$ $[8000,9000]$
$32.2$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.2}_{2.9}$ $29.9$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.9}_{2.3}$ $31.4$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.8}_{1.7}$ $28.0$
${}^{+}_{-}$ ${}^{1.8}_{1.7}$ ${}^{+}_{-}$ ${}^{4.1}_{3.4}$ $[9000,10000]$
$21.8$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.2}_{1.7}$ $30.9$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.6}_{2.1}$ $30.2$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{1.6}_{1.5}$ $40.6$
${}^{+}_{-}$ ${}^{4.8}_{4.3}$ ${}^{+}_{-}$ ${}^{6.1}_{7.0}$ $[10000,11000]$
$31.8$ ${}^{+}_{-}$ ${}^{1.2}_{1.1}$ ${}^{+}_{-}$ ${}^{1.6}_{2.2}$ $32.1$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{1.6}_{2.1}$ $34.6$
${}^{+}_{-}$ ${}^{1.4}_{1.3}$ ${}^{+}_{-}$ ${}^{1.8}_{1.8}$ $34$ ${}^{+}_{-}$
${}^{10}_{\phantom{0}8}$ ${}^{+}_{-}$ ${}^{13}_{11}$ $[11000,12000]$ $30.8$
${}^{+}_{-}$ ${}^{1.3}_{1.4}$ ${}^{+}_{-}$ ${}^{1.6}_{2.5}$ $30.1$
${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{1.4}_{2.0}$ $31.2$
${}^{+}_{-}$ ${}^{1.8}_{1.7}$ ${}^{+}_{-}$ ${}^{1.6}_{1.7}$ $[12000,13000]$
$33.0$ ${}^{+}_{-}$ ${}^{1.8}_{1.8}$ ${}^{+}_{-}$ ${}^{2.1}_{3.1}$ $32.2$
${}^{+}_{-}$ ${}^{1.4}_{1.4}$ ${}^{+}_{-}$ ${}^{1.6}_{2.2}$ $32.8$
${}^{+}_{-}$ ${}^{2.5}_{2.4}$ ${}^{+}_{-}$ ${}^{2.2}_{1.8}$ $[13000,14000]$
$34.0$ ${}^{+}_{-}$ ${}^{2.1}_{2.1}$ ${}^{+}_{-}$ ${}^{1.8}_{3.0}$ $27.6$
${}^{+}_{-}$ ${}^{1.6}_{1.6}$ ${}^{+}_{-}$ ${}^{1.5}_{2.0}$ $41.2$
${}^{+}_{-}$ ${}^{4.7}_{4.3}$ ${}^{+}_{-}$ ${}^{3.1}_{3.4}$ $[14000,15000]$
$29.7$ ${}^{+}_{-}$ ${}^{2.5}_{2.4}$ ${}^{+}_{-}$ ${}^{1.9}_{2.4}$ $34.0$
${}^{+}_{-}$ ${}^{2.5}_{2.3}$ ${}^{+}_{-}$ ${}^{2.3}_{2.5}$ $27.8$
${}^{+}_{-}$ ${}^{5.6}_{4.8}$ ${}^{+}_{-}$ ${}^{6.7}_{5.7}$

Table 16: The ratios of differential production cross-section-times-branching-
fraction measurements for prompt $D_{s}^{+}$ and $D^{+}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. All values are given in percent. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[1000,1500]$ $4.1$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{2.0}_{1.7}$ $8.7$ ${}^{+}_{-}$
${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.9}_{1.5}$ $9.3$ ${}^{+}_{-}$
${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.4}_{1.4}$ $8.5$ ${}^{+}_{-}$
${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.0}_{1.6}$ $20$ ${}^{+}_{-}$ ${}^{6}_{6}$
${}^{+}_{-}$ ${}^{\phantom{0}5}_{13}$ $[1500,2000]$ $8.0$ ${}^{+}_{-}$
${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.5}_{1.2}$ $10.42$ ${}^{+}_{-}$
${}^{0.28}_{0.28}$ ${}^{+}_{-}$ ${}^{0.98}_{0.86}$ $9.92$ ${}^{+}_{-}$
${}^{0.25}_{0.25}$ ${}^{+}_{-}$ ${}^{0.68}_{0.67}$ $11.2$ ${}^{+}_{-}$
${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.1}_{1.0}$ $6.8$ ${}^{+}_{-}$
${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ $[2000,2500]$ $10.6$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.4}_{1.1}$ $10.15$
${}^{+}_{-}$ ${}^{0.18}_{0.18}$ ${}^{+}_{-}$ ${}^{0.58}_{0.42}$ $11.93$
${}^{+}_{-}$ ${}^{0.20}_{0.21}$ ${}^{+}_{-}$ ${}^{0.64}_{0.56}$ $11.88$
${}^{+}_{-}$ ${}^{0.28}_{0.28}$ ${}^{+}_{-}$ ${}^{0.76}_{0.76}$ $8.4$
${}^{+}_{-}$ ${}^{0.5}_{0.6}$ ${}^{+}_{-}$ ${}^{1.1}_{1.0}$ $[2500,3000]$
$10.9$ ${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.2}_{0.9}$ $11.51$
${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.44}_{0.52}$ $11.25$
${}^{+}_{-}$ ${}^{0.17}_{0.16}$ ${}^{+}_{-}$ ${}^{0.60}_{0.36}$ $11.55$
${}^{+}_{-}$ ${}^{0.23}_{0.23}$ ${}^{+}_{-}$ ${}^{0.65}_{0.64}$ $10.9$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.1}_{1.2}$ $[3000,3500]$
$10.66$ ${}^{+}_{-}$ ${}^{0.30}_{0.29}$ ${}^{+}_{-}$ ${}^{0.93}_{0.70}$
$11.07$ ${}^{+}_{-}$ ${}^{0.16}_{0.17}$ ${}^{+}_{-}$ ${}^{0.42}_{0.45}$
$11.18$ ${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.56}_{0.39}$
$11.07$ ${}^{+}_{-}$ ${}^{0.22}_{0.22}$ ${}^{+}_{-}$ ${}^{0.59}_{0.58}$ $9.77$
${}^{+}_{-}$ ${}^{0.48}_{0.48}$ ${}^{+}_{-}$ ${}^{0.93}_{0.88}$ $[3500,4000]$
$12.27$ ${}^{+}_{-}$ ${}^{0.33}_{0.33}$ ${}^{+}_{-}$ ${}^{0.95}_{0.67}$
$11.05$ ${}^{+}_{-}$ ${}^{0.17}_{0.17}$ ${}^{+}_{-}$ ${}^{0.43}_{0.49}$
$11.09$ ${}^{+}_{-}$ ${}^{0.18}_{0.18}$ ${}^{+}_{-}$ ${}^{0.54}_{0.46}$
$12.21$ ${}^{+}_{-}$ ${}^{0.27}_{0.26}$ ${}^{+}_{-}$ ${}^{0.69}_{0.69}$ $11.6$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.3}_{1.0}$ $[4000,5000]$
$10.47$ ${}^{+}_{-}$ ${}^{0.21}_{0.21}$ ${}^{+}_{-}$ ${}^{0.66}_{0.41}$
$11.66$ ${}^{+}_{-}$ ${}^{0.15}_{0.15}$ ${}^{+}_{-}$ ${}^{0.46}_{0.36}$
$11.27$ ${}^{+}_{-}$ ${}^{0.15}_{0.15}$ ${}^{+}_{-}$ ${}^{0.42}_{0.42}$
$12.21$ ${}^{+}_{-}$ ${}^{0.22}_{0.22}$ ${}^{+}_{-}$ ${}^{0.45}_{0.63}$ $11.2$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.1}_{0.7}$ $[5000,6000]$
$12.49$ ${}^{+}_{-}$ ${}^{0.29}_{0.29}$ ${}^{+}_{-}$ ${}^{0.70}_{0.65}$
$12.03$ ${}^{+}_{-}$ ${}^{0.19}_{0.19}$ ${}^{+}_{-}$ ${}^{0.62}_{0.41}$
$11.87$ ${}^{+}_{-}$ ${}^{0.20}_{0.20}$ ${}^{+}_{-}$ ${}^{0.51}_{0.54}$
$12.00$ ${}^{+}_{-}$ ${}^{0.28}_{0.27}$ ${}^{+}_{-}$ ${}^{0.81}_{0.63}$ $11.1$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.4}_{1.2}$ $[6000,7000]$
$11.28$ ${}^{+}_{-}$ ${}^{0.31}_{0.31}$ ${}^{+}_{-}$ ${}^{0.71}_{0.65}$
$12.80$ ${}^{+}_{-}$ ${}^{0.26}_{0.26}$ ${}^{+}_{-}$ ${}^{0.70}_{0.57}$
$11.80$ ${}^{+}_{-}$ ${}^{0.27}_{0.27}$ ${}^{+}_{-}$ ${}^{0.62}_{0.66}$
$10.51$ ${}^{+}_{-}$ ${}^{0.34}_{0.33}$ ${}^{+}_{-}$ ${}^{0.99}_{0.62}$ $11.2$
${}^{+}_{-}$ ${}^{1.3}_{1.3}$ ${}^{+}_{-}$ ${}^{2.0}_{1.7}$ $[7000,8000]$
$12.0$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.0}_{0.8}$ $10.35$
${}^{+}_{-}$ ${}^{0.28}_{0.27}$ ${}^{+}_{-}$ ${}^{0.58}_{0.65}$ $11.17$
${}^{+}_{-}$ ${}^{0.33}_{0.33}$ ${}^{+}_{-}$ ${}^{0.74}_{0.69}$ $12.7$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.4}_{0.9}$ $7.2$ ${}^{+}_{-}$
${}^{2.0}_{1.9}$ ${}^{+}_{-}$ ${}^{2.7}_{2.2}$ $[8000,9000]$ $10.53$
${}^{+}_{-}$ ${}^{0.43}_{0.44}$ ${}^{+}_{-}$ ${}^{0.98}_{0.91}$ $11.15$
${}^{+}_{-}$ ${}^{0.38}_{0.38}$ ${}^{+}_{-}$ ${}^{0.81}_{0.83}$ $13.9$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ $12.7$
${}^{+}_{-}$ ${}^{0.9}_{0.8}$ ${}^{+}_{-}$ ${}^{1.8}_{1.3}$ $[9000,10000]$
$12.6$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.1}_{0.8}$ $11.65$
${}^{+}_{-}$ ${}^{0.49}_{0.50}$ ${}^{+}_{-}$ ${}^{0.76}_{0.66}$ $12.11$
${}^{+}_{-}$ ${}^{0.58}_{0.58}$ ${}^{+}_{-}$ ${}^{0.92}_{0.62}$ $11.4$
${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{1.2}_{1.0}$ $[10000,11000]$
$11.98$ ${}^{+}_{-}$ ${}^{0.72}_{0.72}$ ${}^{+}_{-}$ ${}^{0.37}_{0.36}$
$11.38$ ${}^{+}_{-}$ ${}^{0.59}_{0.61}$ ${}^{+}_{-}$ ${}^{0.43}_{0.17}$
$11.07$ ${}^{+}_{-}$ ${}^{0.70}_{0.71}$ ${}^{+}_{-}$ ${}^{0.60}_{0.59}$ $9.9$
${}^{+}_{-}$ ${}^{1.8}_{1.7}$ ${}^{+}_{-}$ ${}^{1.1}_{0.7}$ $[11000,12000]$
$10.58$ ${}^{+}_{-}$ ${}^{0.80}_{0.81}$ ${}^{+}_{-}$ ${}^{0.36}_{0.35}$
$11.05$ ${}^{+}_{-}$ ${}^{0.73}_{0.71}$ ${}^{+}_{-}$ ${}^{0.52}_{0.14}$
$11.57$ ${}^{+}_{-}$ ${}^{0.89}_{0.89}$ ${}^{+}_{-}$ ${}^{0.45}_{0.44}$
$[12000,13000]$ $11.8$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$
${}^{0.6}_{0.2}$ $9.17$ ${}^{+}_{-}$ ${}^{0.79}_{0.78}$ ${}^{+}_{-}$
${}^{0.38}_{0.38}$ $12.6$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$
${}^{0.6}_{0.6}$ $[13000,14000]$ $9.3$ ${}^{+}_{-}$ ${}^{1.1}_{1.1}$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ $13.1$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$
${}^{+}_{-}$ ${}^{0.8}_{0.2}$ $11.7$ ${}^{+}_{-}$ ${}^{1.6}_{1.6}$
${}^{+}_{-}$ ${}^{1.1}_{1.0}$ $[14000,15000]$

Table 17: The ratios of differential production cross-section-times-branching-
fraction for prompt $D^{*+}$ and $D^{+}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. All values are given in percent. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[0,1000]$ $27$
${}^{+}_{-}$ ${}^{4}_{4}$ ${}^{+}_{-}$ ${}^{11}_{\phantom{0}8}$ $[1000,1500]$
$20.9$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{2.5}_{3.3}$ $23.7$
${}^{+}_{-}$ ${}^{0.3}_{0.4}$ ${}^{+}_{-}$ ${}^{1.4}_{1.6}$ $22.3$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.5}_{1.6}$ $26.7$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{4.4}_{3.4}$ $[1500,2000]$
$30.6$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{2.4}_{2.8}$ $27.8$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.3}_{1.6}$ $27.0$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.5}_{1.8}$ $26.8$
${}^{+}_{-}$ ${}^{0.7}_{0.6}$ ${}^{+}_{-}$ ${}^{2.7}_{2.0}$ $[2000,2500]$
$30.4$ ${}^{+}_{-}$ ${}^{2.8}_{2.7}$ ${}^{+}_{-}$ ${}^{6.3}_{7.1}$ $28.0$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.7}_{1.2}$ $29.5$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.2}_{1.4}$ $29.1$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.6}_{1.4}$ $26.0$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{2.4}_{2.1}$ $[2500,3000]$
$30.2$ ${}^{+}_{-}$ ${}^{1.1}_{1.1}$ ${}^{+}_{-}$ ${}^{3.0}_{3.5}$ $28.1$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ $28.7$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.5}_{1.1}$ $26.9$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.6}_{1.4}$ $27.5$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.6}_{1.9}$ $[3000,3500]$
$29.9$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.2}_{2.6}$ $28.1$
${}^{+}_{-}$ ${}^{0.2}_{0.3}$ ${}^{+}_{-}$ ${}^{0.8}_{1.0}$ $28.1$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.5}_{1.0}$ $26.4$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.6}_{1.4}$ $27.0$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.8}_{2.4}$ $[3500,4000]$
$31.7$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.0}_{2.2}$ $30.3$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{0.8}_{1.2}$ $27.3$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.4}_{1.0}$ $28.7$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.7}_{1.6}$ $30.4$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.1}_{2.0}$ $[4000,5000]$
$27.9$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.3}_{1.3}$ $28.3$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{0.7}_{1.2}$ $28.2$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.2}_{1.1}$ $28.5$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.6}_{1.6}$ $24.3$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.7}_{1.9}$ $[5000,6000]$
$27.2$ ${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ $27.2$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{0.8}_{1.3}$ $28.3$
${}^{+}_{-}$ ${}^{0.2}_{0.2}$ ${}^{+}_{-}$ ${}^{1.3}_{1.3}$ $30.2$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.9}_{1.3}$ $21.2$
${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{4.0}_{2.7}$ $[6000,7000]$
$29.2$ ${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.4}_{1.5}$ $30.5$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.1}_{1.6}$ $28.9$
${}^{+}_{-}$ ${}^{0.3}_{0.3}$ ${}^{+}_{-}$ ${}^{1.2}_{1.5}$ $26.1$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.6}_{1.3}$ $18.3$
${}^{+}_{-}$ ${}^{3.0}_{3.0}$ ${}^{+}_{-}$ ${}^{4.0}_{3.4}$ $[7000,8000]$
$28.7$ ${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.4}_{1.9}$ $28.8$
${}^{+}_{-}$ ${}^{0.4}_{0.4}$ ${}^{+}_{-}$ ${}^{1.4}_{1.8}$ $30.3$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.6}_{1.6}$ $30.1$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{3.0}_{2.3}$ $[8000,9000]$
$27.0$ ${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.4}_{2.2}$ $27.7$
${}^{+}_{-}$ ${}^{0.5}_{0.5}$ ${}^{+}_{-}$ ${}^{1.4}_{1.8}$ $27.8$
${}^{+}_{-}$ ${}^{0.6}_{0.5}$ ${}^{+}_{-}$ ${}^{2.1}_{1.6}$ $24.4$
${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{3.8}_{2.4}$ $[9000,10000]$
$24.7$ ${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{1.1}_{1.7}$ $33.9$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.7}_{2.0}$ $29.6$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{1.7}_{1.3}$ $28.4$
${}^{+}_{-}$ ${}^{2.6}_{2.5}$ ${}^{+}_{-}$ ${}^{3.6}_{2.8}$ $[10000,11000]$
$29.3$ ${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{0.6}_{1.5}$ $30.7$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{1.3}_{1.5}$ $30.5$
${}^{+}_{-}$ ${}^{1.1}_{1.0}$ ${}^{+}_{-}$ ${}^{1.4}_{0.3}$ $23.1$
${}^{+}_{-}$ ${}^{4.2}_{4.1}$ ${}^{+}_{-}$ ${}^{4.8}_{4.3}$ $[11000,12000]$
$26.8$ ${}^{+}_{-}$ ${}^{1.2}_{1.1}$ ${}^{+}_{-}$ ${}^{0.8}_{1.6}$ $29.7$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{1.3}_{1.6}$ $26.1$
${}^{+}_{-}$ ${}^{1.3}_{1.3}$ ${}^{+}_{-}$ ${}^{1.9}_{1.2}$ $[12000,13000]$
$27.7$ ${}^{+}_{-}$ ${}^{1.4}_{1.4}$ ${}^{+}_{-}$ ${}^{1.0}_{1.9}$ $31.9$
${}^{+}_{-}$ ${}^{1.3}_{1.3}$ ${}^{+}_{-}$ ${}^{1.5}_{1.7}$ $29.7$
${}^{+}_{-}$ ${}^{2.0}_{2.0}$ ${}^{+}_{-}$ ${}^{1.7}_{1.1}$ $[13000,14000]$
$29.7$ ${}^{+}_{-}$ ${}^{1.8}_{1.7}$ ${}^{+}_{-}$ ${}^{1.2}_{2.3}$ $28.2$
${}^{+}_{-}$ ${}^{1.6}_{1.5}$ ${}^{+}_{-}$ ${}^{1.3}_{1.8}$ $32.8$
${}^{+}_{-}$ ${}^{3.0}_{2.8}$ ${}^{+}_{-}$ ${}^{3.2}_{2.0}$ $[14000,15000]$
$25.1$ ${}^{+}_{-}$ ${}^{2.0}_{1.9}$ ${}^{+}_{-}$ ${}^{1.7}_{2.2}$ $33.7$
${}^{+}_{-}$ ${}^{2.2}_{2.1}$ ${}^{+}_{-}$ ${}^{1.6}_{2.4}$ $19.5$
${}^{+}_{-}$ ${}^{3.0}_{2.9}$ ${}^{+}_{-}$ ${}^{3.2}_{3.3}$

Table 18: The ratios of differential production cross-section-times-branching-
fraction for prompt $D_{s}^{+}$ and $D^{*+}$ mesons in bins of
$(p_{\mathrm{T}},y)$. The first uncertainty is statistical, and the second is
the total systematic. All values are given in percent. $y$ $p_{\text{T}}$
[MeV/c] $[2,2.5]$ $[2.5,3]$ $[3,3.5]$ $[3.5,4]$ $[4,4.5]$ $[1000,1500]$ $41$
${}^{+}_{-}$ ${}^{3}_{3}$ ${}^{+}_{-}$ ${}^{14}_{\phantom{0}8}$ $39.3$
${}^{+}_{-}$ ${}^{2.4}_{2.4}$ ${}^{+}_{-}$ ${}^{6.6}_{5.8}$ $38.3$
${}^{+}_{-}$ ${}^{3.9}_{3.8}$ ${}^{+}_{-}$ ${}^{9.6}_{7.2}$ $74$ ${}^{+}_{-}$
${}^{24}_{24}$ ${}^{+}_{-}$ ${}^{22}_{49}$ $[1500,2000]$ $34.1$ ${}^{+}_{-}$
${}^{1.1}_{1.0}$ ${}^{+}_{-}$ ${}^{5.6}_{4.1}$ $35.7$ ${}^{+}_{-}$
${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{2.9}_{2.4}$ $41.6$ ${}^{+}_{-}$
${}^{1.5}_{1.5}$ ${}^{+}_{-}$ ${}^{5.2}_{4.1}$ $25.4$ ${}^{+}_{-}$
${}^{2.7}_{2.6}$ ${}^{+}_{-}$ ${}^{4.6}_{4.8}$ $[2000,2500]$ $35$ ${}^{+}_{-}$
${}^{4}_{3}$ ${}^{+}_{-}$ ${}^{13}_{\phantom{0}7}$ $36.2$ ${}^{+}_{-}$
${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.7}_{2.5}$ $40.5$ ${}^{+}_{-}$
${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.9}_{2.1}$ $40.8$ ${}^{+}_{-}$
${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{3.3}_{3.3}$ $32.2$ ${}^{+}_{-}$
${}^{2.2}_{2.2}$ ${}^{+}_{-}$ ${}^{5.0}_{4.5}$ $[2500,3000]$ $36.1$
${}^{+}_{-}$ ${}^{1.7}_{1.6}$ ${}^{+}_{-}$ ${}^{6.7}_{4.1}$ $41.0$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{1.8}_{2.1}$ $39.3$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.6}_{2.0}$ $43.0$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{3.4}_{3.4}$ $39.7$
${}^{+}_{-}$ ${}^{2.1}_{2.1}$ ${}^{+}_{-}$ ${}^{4.8}_{4.2}$ $[3000,3500]$
$35.6$ ${}^{+}_{-}$ ${}^{1.3}_{1.3}$ ${}^{+}_{-}$ ${}^{4.9}_{3.1}$ $39.4$
${}^{+}_{-}$ ${}^{0.7}_{0.6}$ ${}^{+}_{-}$ ${}^{1.8}_{1.6}$ $39.8$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.3}_{2.3}$ $41.9$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{3.1}_{3.2}$ $36.2$
${}^{+}_{-}$ ${}^{1.9}_{1.9}$ ${}^{+}_{-}$ ${}^{4.7}_{4.5}$ $[3500,4000]$
$38.7$ ${}^{+}_{-}$ ${}^{1.3}_{1.3}$ ${}^{+}_{-}$ ${}^{4.1}_{2.6}$ $36.4$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{1.9}_{1.5}$ $40.6$
${}^{+}_{-}$ ${}^{0.7}_{0.7}$ ${}^{+}_{-}$ ${}^{2.4}_{2.5}$ $42.5$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{3.5}_{3.3}$ $38.1$
${}^{+}_{-}$ ${}^{2.3}_{2.3}$ ${}^{+}_{-}$ ${}^{4.8}_{3.8}$ $[4000,5000]$
$37.6$ ${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{2.8}_{1.8}$ $41.2$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.4}_{1.2}$ $39.9$
${}^{+}_{-}$ ${}^{0.6}_{0.6}$ ${}^{+}_{-}$ ${}^{2.1}_{2.2}$ $42.9$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.7}_{3.0}$ $46.3$
${}^{+}_{-}$ ${}^{2.4}_{2.3}$ ${}^{+}_{-}$ ${}^{6.4}_{5.2}$ $[5000,6000]$
$45.8$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{2.9}_{2.7}$ $44.2$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{3.4}_{1.5}$ $42.0$
${}^{+}_{-}$ ${}^{0.8}_{0.8}$ ${}^{+}_{-}$ ${}^{2.5}_{2.4}$ $39.7$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{3.1}_{3.1}$ $52.2$
${}^{+}_{-}$ ${}^{4.6}_{4.2}$ ${}^{+}_{-}$ ${}^{7.9}_{7.8}$ $[6000,7000]$
$38.7$ ${}^{+}_{-}$ ${}^{1.2}_{1.2}$ ${}^{+}_{-}$ ${}^{2.9}_{2.3}$ $42.0$
${}^{+}_{-}$ ${}^{0.9}_{0.9}$ ${}^{+}_{-}$ ${}^{3.4}_{2.0}$ $40.8$
${}^{+}_{-}$ ${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{2.9}_{2.5}$ $40.2$
${}^{+}_{-}$ ${}^{1.5}_{1.4}$ ${}^{+}_{-}$ ${}^{3.8}_{2.6}$ $61$ ${}^{+}_{-}$
${}^{14}_{11}$ ${}^{+}_{-}$ ${}^{19}_{12}$ $[7000,8000]$ $41.7$ ${}^{+}_{-}$
${}^{1.6}_{1.6}$ ${}^{+}_{-}$ ${}^{4.5}_{2.6}$ $35.9$ ${}^{+}_{-}$
${}^{1.0}_{1.0}$ ${}^{+}_{-}$ ${}^{3.1}_{2.5}$ $36.9$ ${}^{+}_{-}$
${}^{1.2}_{1.1}$ ${}^{+}_{-}$ ${}^{3.0}_{2.5}$ $42.3$ ${}^{+}_{-}$
${}^{2.3}_{2.2}$ ${}^{+}_{-}$ ${}^{5.5}_{4.2}$ $[8000,9000]$ $39.0$
${}^{+}_{-}$ ${}^{1.8}_{1.7}$ ${}^{+}_{-}$ ${}^{4.6}_{3.1}$ $40.3$
${}^{+}_{-}$ ${}^{1.5}_{1.4}$ ${}^{+}_{-}$ ${}^{3.9}_{3.2}$ $50.0$
${}^{+}_{-}$ ${}^{2.0}_{2.0}$ ${}^{+}_{-}$ ${}^{4.9}_{5.1}$ $51.8$
${}^{+}_{-}$ ${}^{4.2}_{4.0}$ ${}^{+}_{-}$ ${}^{9.3}_{8.5}$ $[9000,10000]$
$51.1$ ${}^{+}_{-}$ ${}^{2.8}_{2.8}$ ${}^{+}_{-}$ ${}^{6.0}_{3.1}$ $34.3$
${}^{+}_{-}$ ${}^{1.5}_{1.5}$ ${}^{+}_{-}$ ${}^{3.1}_{2.2}$ $40.9$
${}^{+}_{-}$ ${}^{2.1}_{2.1}$ ${}^{+}_{-}$ ${}^{3.4}_{2.8}$ $40.2$
${}^{+}_{-}$ ${}^{5.5}_{4.8}$ ${}^{+}_{-}$ ${}^{6.1}_{5.5}$ $[10000,11000]$
$41.4$ ${}^{+}_{-}$ ${}^{2.7}_{2.7}$ ${}^{+}_{-}$ ${}^{2.1}_{2.1}$ $37.1$
${}^{+}_{-}$ ${}^{2.1}_{2.1}$ ${}^{+}_{-}$ ${}^{2.6}_{1.6}$ $35.5$
${}^{+}_{-}$ ${}^{2.5}_{2.5}$ ${}^{+}_{-}$ ${}^{2.8}_{1.2}$ $43$ ${}^{+}_{-}$
${}^{12}_{\phantom{0}9}$ ${}^{+}_{-}$ ${}^{11}_{\phantom{0}5}$ $[11000,12000]$
$40.1$ ${}^{+}_{-}$ ${}^{3.3}_{3.2}$ ${}^{+}_{-}$ ${}^{2.4}_{2.4}$ $37.3$
${}^{+}_{-}$ ${}^{2.6}_{2.6}$ ${}^{+}_{-}$ ${}^{3.0}_{1.3}$ $43.4$
${}^{+}_{-}$ ${}^{3.9}_{3.7}$ ${}^{+}_{-}$ ${}^{3.7}_{1.7}$ $[12000,13000]$
$42.5$ ${}^{+}_{-}$ ${}^{4.1}_{3.8}$ ${}^{+}_{-}$ ${}^{4.3}_{1.2}$ $28.4$
${}^{+}_{-}$ ${}^{2.6}_{2.5}$ ${}^{+}_{-}$ ${}^{2.5}_{0.9}$ $42.6$
${}^{+}_{-}$ ${}^{4.7}_{4.6}$ ${}^{+}_{-}$ ${}^{2.5}_{2.5}$ $[13000,14000]$
$31.4$ ${}^{+}_{-}$ ${}^{4.0}_{3.9}$ ${}^{+}_{-}$ ${}^{3.3}_{1.0}$ $46.5$
${}^{+}_{-}$ ${}^{4.7}_{4.5}$ ${}^{+}_{-}$ ${}^{4.7}_{1.5}$ $35.5$
${}^{+}_{-}$ ${}^{5.5}_{5.4}$ ${}^{+}_{-}$ ${}^{2.8}_{2.7}$ $[14000,15000]$

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LHCb collaboration

R. Aaij38, C. Abellán Beteta40, B. Adeva37, M. Adinolfi46, A. Affolder52, Z.
Ajaltouni5, S. Akar6, J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G.