EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2020-119 LHCb-PAPER-2020-010

Observation of enhanced double parton scattering in proton-lead collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16\text{\,Te\kern-2.07413ptV}$

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

A study of prompt charm-hadron pair production in proton-lead collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=$ 8.16 TeV is performed using data
corresponding to an integrated luminosity of about $30\text{\,nb}^{-1}$,
collected with the LHCb experiment. Production cross-sections for different
pairs of charm hadrons are measured and kinematic correlations between the two
charm hadrons are investigated. This is the first measurement of associated
production of two charm hadrons in proton-lead collisions. The results confirm
the predicted enhancement of double parton scattering production in proton-
lead collisions compared to the single parton scattering production.

Published in Phys. Rev. Lett. 125 (2020) 212001

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

At high energy hadron colliders, particles are produced in fundamental
collisions of internal partons in the beam projectiles. The underlying parton
densities are described by parton distribution functions (PDFs). A collision
event can produce multiple heavy-flavor hadrons via a single parton scattering
(SPS) or multiple parton scatterings. The latter, generating on average a
larger number of charged tracks, could explain the heavy-flavor production
rate in high-multiplicity events [1, 2, 3, 4]. In a simple model, assuming
that the PDFs of two partons in the same projectile are independent, the
associated production cross-section of final-state particles $A$ and $B$ from
two separate partonic interactions, i.e. a double parton scattering (DPS)
process, is related to the inclusive production cross-section of $A$ and $B$,
$\sigma^{A}$ and $\sigma^{B}$, as [5, 6, 7, 8, 9, 10, 11, 12, 13, 14],

$\sigma_{\mathrm{DPS}}^{AB}=\frac{1}{1+\delta_{AB}}\frac{\sigma^{A}\sigma^{B}}{\sigma_{\mathrm{eff}}}.$
(1)

Here, $\delta_{AB}=1$ if $A$ and $B$ are identical and is zero otherwise, and
$\sigma_{\mathrm{eff}}$ is the so-called effective cross-section. The
parameter $\sigma_{\mathrm{eff}}$ is related to the collision geometry and is
expected to be independent of the final state [15, 16, 17]. In proton-ion
collisions, following the Glauber model [18], SPS production cross-section is
expected to scale with the ion mass number in the absence of nuclear matter
effects. However, DPS production is enhanced compared to a mass number scaling
due to collisions of partons from two different nucleons in the ion, and the
enhancement factor is about three in proton-lead ($p$-Pb) collisions [19, 20,
10, 21, 22, 23, 24, 25].

The production of two open charm hadrons, $D_{1}D_{2}$, and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{D}$ meson pairs is of particular interest
in the study of SPS and DPS processes, as the cross-section is relatively
large and the high charm quark mass permits perturbative calculations even at
low transverse momentum ($p_{\mathrm{T}}$). In this Letter, $D$ and $D_{1,2}$
refer to either a ${{D}^{0}}$, ${{D}^{+}}$ or ${{D}^{+}_{s}}$ meson and the
inclusion of charge conjugate states is implied. Both like-sign
($\mathrm{LS}$) and opposite-sign ($\mathrm{OS}$) open charm hadron pairs are
considered. In an $\mathrm{LS}$ pair the two hadrons have the same charm-quark
flavor, while in an $\mathrm{OS}$ pair they have opposite charm flavors. Pairs
of $\mathrm{OS}$ charm hadrons can be produced from a ${c}{\overline{c}}$ pair
via SPS, thus the kinematics of the two hadrons are correlated, while DPS
produces correlated and uncorrelated $\mathrm{OS}$ pairs. The correlation in
SPS production may be modified in heavy-ion data compared to proton-proton
($pp$) collisions, due to nuclear matter effects [26, 27, 28, 29, 30, 31, 32,
33]. The $\mathrm{OS}$ correlation is predicted to be sensitive to the
properties of the hot medium formed in ultra-relativistic heavy nucleus-
nucleus collisions [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44].

The two hadrons in an $\mathrm{LS}$ pair produced in a DPS process are
expected to be uncorrelated. Studies of $\mathrm{LS}$ pair production and
correlation in different environments help to test the universality of the
parameter $\sigma_{\mathrm{eff}}$ and gain insight into the underlying parton
correlations [45]. Since DPS production involves two parton pairs, it is very
sensitive to the nuclear PDF (nPDF) in proton-ion collisions, including its
possible dependence on the position inside the nucleus [46].

Production of $\mathrm{OS}$ charm and beauty pairs has been studied in fully
reconstructed decays [47, 48, 49, 50, 51] and using partially reconstructed
decays [52, 53, 54, 55, 56, 57, 58, 59], and the hadron and anti-hadron are
found to be correlated; in particular, the azimuthal angle, $\Delta\phi$,
between the two hadron directions projected to the plane transverse to the
beam line favors values close to $\Delta\phi=0$ or $\pi$. Production of
$\mathrm{LS}$ charm pairs, double quarkonium and multiple jets at the Tevatron
and the LHC revealed evidence of DPS signals [60, 61, 51, 62, 63, 64, 65, 66,
67, 68]. The effective cross-section is measured to be in the range of 10 to
$20\text{\,mb}$ for most final states, however, a value as low as
$5\text{\,mb}$ is extracted using double quarkonium production [69, 70, 71].
More measurements are required to resolve this puzzle.

This Letter presents the first measurement of charm pair production in proton-
lead collisions at a nucleon-nucleon center-of-mass energy of
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16\text{\,Te\kern-1.00006ptV}$. The
data were collected with the LHCb experiment at a low interaction rate in two
distinct beam configurations. In the $p\mathrm{Pb}$ configuration, particles
produced in the direction of the proton beam are analysed, while in the
$\mathrm{Pb}p$ configuration particles are analysed in the Pb beam direction.
The $p\mathrm{Pb}$ ($\mathrm{Pb}p$) data correspond to an integrated
luminosity of $12.2\pm 0.3\text{\,nb}^{-1}$ ($18.6\pm 0.5\text{\,nb}^{-1}$).
The detector coordinate system is defined to have the $z$-axis aligned with
the proton beam direction. In the following, particle rapidities ($y$) are
defined in the nucleon-nucleon rest frame.

The LHCb detector is a single-arm forward spectrometer described in detail in
Refs. [72, 73]. The online event selection is performed by a trigger, which
consists of a hardware stage, based on information from the calorimeter and
muon systems, followed by a software stage, which applies a full event
reconstruction. Charm hadrons
($H_{c}\equiv{{D}^{0}},{{D}^{+}},{{D}^{+}_{s}},{{J\mskip-3.0mu/\mskip-2.0mu\psi}}$)
are reconstructed online via the decays
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow{\mu^{+}\mu^{-}}$. The data
samples are selected by the hardware trigger based on the calorimeter activity
for $D$ candidates and based on the muon system for
${J\mskip-3.0mu/\mskip-2.0mu\psi}$ candidates. Candidate pairs are formed by
${{D}^{0}}{{D}^{0}}$, ${{D}^{0}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ and ${{D}^{+}}{{D}^{\pm}}$
combinations (same species), and ${{D}^{0}}{{D}^{\pm}}$,
${{D}^{0}}{{D}^{\pm}_{s}}$, ${{D}^{+}}{{D}^{\pm}_{s}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{D}^{0,+}$ combinations (different
species). Other charm pairs are not considered due to their limited yield in
the data. The tracks used to reconstruct the ${D}$ mesons are required to be
positively identified as kaons or pions and must be separated from every
primary $p$-Pb collision vertex (PV). These tracks are also required to have
$p_{\mathrm{T}}>250\text{\,Me\kern-1.00006ptV\\!/}c$ and at least one track
must have $p_{\mathrm{T}}>500\text{\,Me\kern-1.00006ptV\\!/}c$
($p_{\mathrm{T}}>1000\text{\,Me\kern-1.00006ptV\\!/}c$) for ${{D}^{0}}$
(${{D}^{+}},{{D}^{+}_{s}}$) final states. The tracks are required to form a
vertex of good quality that is separated from every PV. The reconstructed $D$
mesons are required to be consistent with originating from a PV, which favors
prompt production over mesons from beauty-hadron decays (denoted as charm-
from-$b$). The two muons used to reconstruct
${J\mskip-3.0mu/\mskip-2.0mu\psi}$ candidates are required to have
$p_{\mathrm{T}}>500\text{\,Me\kern-1.00006ptV\\!/}c$ and form a good-quality
vertex.

In the offline selection, kaons and pions are required to have momentum
$p>3\text{\,Ge\kern-1.00006ptV\\!/}c$, and muons to have
$p>6\text{\,Ge\kern-1.00006ptV\\!/}c$,
$p_{\mathrm{T}}>750\text{\,Me\kern-1.00006ptV\\!/}c$ and be positively
identified by using information from all subdetectors [74, 75]. The
${{K}^{-}}{{K}^{+}}$ invariant mass from the
${{D}^{+}_{s}}\\!\rightarrow{{K}^{-}}{{K}^{+}}{{\pi}^{+}}$ decay is required
to be within $\pm 20\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ of the known
$\phi(1020)$ mass [76]. A kinematic fit is performed on each charm hadron and
on the pair, constraining them to originate from a PV. Requirements on the fit
qualities strongly reduce charm-from-$b$ contributions but retain more than
99% of prompt pairs.

Results are obtained in a charm-hadron kinematic region
$p_{\mathrm{T}}(H_{c})<12\text{\,Ge\kern-1.00006ptV\\!/}c$ and
$1.7<y(H_{c})<3.7$ ($-4.7<y(H_{c})<-2.7$) for $p\mathrm{Pb}$ ($\mathrm{Pb}p$)
data. For ${D}^{+}$ and ${D}^{+}_{s}$ mesons the requirement
$p_{\mathrm{T}}(H_{c})>2\text{\,Ge\kern-1.00006ptV\\!/}c$ is applied due to
extremely small yields at lower $p_{\mathrm{T}}$. Total cross-sections of
${{D}^{0}}{{D}^{0}}$, ${{D}^{0}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ pair production are also
evaluated in the full LHCb rapidity acceptance, $1.5<y(H_{c})<4$
($-5<y(H_{c})<-2.5$) for $p\mathrm{Pb}$ ($\mathrm{Pb}p$) data, in order to
compare with single charm production [77, 78].

The cross-section for a charm pair is calculated as
$\sigma=N^{\mathrm{corr}}/(\mathcal{L}\times{\mathcal{B}}_{1}\times{\mathcal{B}}_{2})$,
where $\mathcal{L}$ is the integrated luminosity, and $N^{\mathrm{corr}}$ is
the signal yield after efficiency correction and the subtraction of charm-
from-$b$ background. The branching fractions of the two charm-hadron decays,
${\mathcal{B}}_{1,2}$, are taken from Ref. [76] for the ${{D}^{0}}$,
${{D}^{+}}$, ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ decays, and
${\mathcal{B}}({{D}^{+}_{s}}\rightarrow({{K}^{+}}{{K}^{-}})_{\phi}{{\pi}^{+}})=(2.24\pm
0.13)\%$ from Refs. [79, 80]. The raw signal yield is determined from an
unbinned maximum likelihood fit to the distribution of the invariant masses,
$m_{1}$ and $m_{2}$, of the two charm hadrons. The two-dimensional probability
densities comprise four components: signal-signal, background-background,
signal-background and background-signal for the first-second charm hadron in a
pair. The background is mainly from random combinations of tracks. The signal
component for each charm hadron is described by the sum of a Gaussian and a
Crystal Ball function (CB) [81] and the background component by an exponential
function. The distribution for pairs of same-species hadrons is constructed to
be independent of the ordering of $m_{1}$ and $m_{2}$. As an example, the
$(m_{1},m_{2})$ distribution for ${{D}^{0}}{{D}^{0}}$ candidates and its
projection on $m_{1}$ and $m_{2}$ are are shown in Fig. 1 for $p\mathrm{Pb}$
data, with the fit projections overlaid. More distributions are shown in the
Supplemental Material. The raw signal yield is between 100 and 4000 for all
hadron pairs considered.

Figure 1:  (Left) Two-dimensional invariant-mass distributions of
$(m_{1},m_{2})$ for ${{D}^{0}}{{D}^{0}}$ pairs and the projections on (middle)
$m_{1}$ and (right) $m_{2}$ with the fit results superimposed. Shown in the
projection plots are (points with bars) $p\mathrm{Pb}$ data, (solid blue) the
total fit and its four components.

The total detection efficiency for each individual charm hadron is evaluated
from simulated signal decays, properly corrected using control samples of
$p$-Pb collisions. These control samples are used to calibrate track finding
and particle identification (PID) efficiencies [82]. In the simulation,
minimum-bias $p$-Pb collisions are produced using the EPOS generator [83]
according to beam configurations of the data. Charm hadrons are generated in
$pp$ collisions at $\sqrt{s}=8.16\text{\,Te\kern-1.00006ptV}$ using Pythia8
[84, 85] and are embedded into EPOS minimum-bias events. Particle decays are
described by EvtGen [86], while the particle interaction with the detector,
and its response, are implemented using the Geant4 toolkit [87,
*Agostinelli:2002hh] as described in Ref. [89]. The track finding efficiency
in data and simulation is studied with a tag-and-probe method using
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rightarrow{\mu^{+}\mu^{-}}$ decays [90].
Similarly, the PID efficiency is measured using large control samples of
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\rightarrow{\mu^{+}\mu^{-}}$ decays for
${{K}^{-}},{{\pi}^{+}}$ and ${\mu^{-}}$ tracks, in bins of track momentum and
pseudorapidity $(p,\eta)$. The average charged-track multiplicity in
$\mathrm{OS}$ data is similar to the one in the control samples, while for
$\mathrm{LS}$ data it is about 13% higher, which is consistent with a larger
contribution of multiple parton scattering in $\mathrm{LS}$ data [1, 2, 3, 4].
The corresponding difference in detector occupancy results in different
detection efficiencies in $\mathrm{LS}$ and $\mathrm{OS}$ data, which is
evaluated in control samples. Efficiencies from control samples are combined
with simulation to obtain the efficiency for each charm hadron as a function
of $p_{\mathrm{T}}$ and $y$, $\epsilon(p_{\mathrm{T}},y)$, which is used to
determine the efficiency corrected signal yield
$\sum_{i}\frac{w^{i}}{\epsilon_{1}(p_{\mathrm{T}}^{i},y^{i})\epsilon_{2}(p_{\mathrm{T}}^{i},y^{i})}$.
Here $w^{i}$ is the signal sPlot weight [91] used to remove the contribution
of background and is obtained from the fit to the invariant-mass distribution,
and $\epsilon_{1,2}(p_{\mathrm{T}}^{i},y^{i})$ is the efficiency for the first
and second hadron in the $i^{th}$ candidate pair in data. The signal yield is
then corrected for the charm-from-$b$ contamination, which is estimated to be
less than $1\%$ for open charm pairs and $(4\pm 2)\%$ ($(3.0\pm 1.5)\%$) for
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{D}$ pairs in $p\mathrm{Pb}$
($\mathrm{Pb}p$) data.

Several sources of systematic uncertainties are investigated. The variation of
the signal yield is studied with fits to the invariant-mass distribution using
a different signal or background model. A maximum relative variation of 2% is
obtained on the signal yield. The dominant systematic uncertainty arises from
the limited control sample size to determine the track finding efficiency,
which is on average about 5% (10%) per track in $p\mathrm{Pb}$
($\mathrm{Pb}p$) data. An uncertainty of 2% per hadron track is introduced to
account for the loss of particles due to interactions with the detector
material. Due to the small sample size and the choice of $(p,\eta)$ binning
for each track, the PID efficiencies obtained from control samples introduce
an uncertainty of less than 1% on the total efficiency of each charm hadron.
Other contributions include the uncertainty on the total efficiency due to the
size of the simulation sample, the uncertainty on the charm decay branching
fractions, the uncertainty on the luminosity measurements and on the charm-
from-$b$ fraction. These uncertainties are propagated to the cross-section
measurements.

Total cross-sections are determined for all charm pairs. Results are detailed
in the Supplemental Material. For $\mathrm{LS}$ open charm pairs, the
measurements are in good agreement with theoretical calculations including
both SPS and DPS production [24]. The
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ cross-section is found to be
generally higher than SPS production, calculated using the weighted EPPS16
nPDF [92, 93, 94, 95].

Prompt single charm cross-sections in $p\mathrm{Pb}$ data were measured to be
smaller than those of $\mathrm{Pb}p$ data [96, 78], which is explained by
modifications of the nPDF. The same effect would result in even stronger
suppression of DPS production in $p\mathrm{Pb}$ compared to $\mathrm{Pb}p$
data due to the participation of two pairs of partons. For charm pairs, the
cross-section ratio between $p\mathrm{Pb}$ and $\mathrm{Pb}p$ data, the
forward-backward ratio ($R_{\mathrm{FB}}$), is determined for
$2.7<|y(H_{c})|<3.7,p_{\mathrm{T}}(H_{c})>2\text{\,Ge\kern-1.00006ptV\\!/}c$,
to be $0.40\,\pm 0.05\,\pm 0.10$ ($0.61\,\pm 0.04\,\pm 0.12$) averaged over
$\mathrm{LS}$ ($\mathrm{OS}$) open charm pairs, and is $0.26\,\pm 0.06\,\pm
0.04$ for ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{D}$ pairs. Here and in the
following, the first uncertainty is statistical and the second is systematic.
The results indicate reduced production in $p\mathrm{Pb}$ compared to
$\mathrm{Pb}p$ data for both $\mathrm{LS}$ and $\mathrm{OS}$ pairs. The
$R_{\mathrm{FB}}$ of $\mathrm{OS}$ production is compatible with that of
prompt ${D}^{0}$ mesons [96, 78], while that of $\mathrm{LS}$ production is
smaller. The ratio between the $R_{\mathrm{FB}}$ of $\mathrm{LS}$ and
$\mathrm{OS}$ production, $0.66\,\pm 0.09\,\pm 0.03$, is in good agreement
with the $R_{\mathrm{FB}}$ of $\mathrm{OS}$ data and the $R_{\mathrm{FB}}$ of
prompt ${D}^{0}$ production. The measurements favor the interpretation of
$\mathrm{LS}$ production via DPS.

The $\mathrm{LS}$ over $\mathrm{OS}$ cross-section ratio,
$R^{D_{1}D_{2}}\equiv\sigma^{D_{1}D_{2}}/\sigma^{D_{1}{{\kern
1.25995pt\overline{\kern-1.25995ptD}}}_{2}}$, is determined for all studied
${D}_{1}{D}_{2}$ pairs under the
$p_{\mathrm{T}}(D)>2\text{\,Ge\kern-1.00006ptV\\!/}c$ requirement, giving an
average value of $0.308\pm 0.015\pm 0.010$ and $0.391\pm 0.019\pm 0.025$ for
$p\mathrm{Pb}$ and $\mathrm{Pb}p$ data respectively. The measurements agree
with the calculations in Ref. [24] of $0.57^{+0.16}_{-0.41}$ ($p\mathrm{Pb}$)
and $0.52^{+0.17}_{-0.38}$ ($\mathrm{Pb}p$), and are significantly larger than
that in $pp$ collisions where $R^{{{D}^{0}}{{D}^{0}}}=0.109\pm 0.008$ [51],
indicating an enhancement of $\mathrm{LS}$ pair production over $\mathrm{OS}$
pairs in $p$-Pb collisions. The differential results as a function of
$y(H_{c})$ is shown in the Supplemental Material.

The correlations of kinematics between the two charm hadrons in a pair are
investigated from the distributions of the two-charm invariant mass ($m_{DD}$)
and their relative azimuthal angle $\Delta\phi$. The differential cross-
section for each variable is normalized by the total cross-section, such that
the largest systematic uncertainty, the one from the track finding efficiency,
almost completely cancels. As examples, in Fig. 2, the $m_{DD}$ distribution
is shown for ${{D}^{0}}{{D}^{0}}$ and ${{D}^{0}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs without any requirement on
$p_{\mathrm{T}}(D)$. The difference between ${{D}^{0}}{{D}^{0}}$ and
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs is
determined to be more than three (two) standard deviations in $p\mathrm{Pb}$
($\mathrm{Pb}p$) data, studied using a $\chi^{2}$ test. For both
${{D}^{0}}{{D}^{0}}$ and ${{D}^{0}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs, the $m_{DD}$ distribution
is compatible between $p\mathrm{Pb}$ and $\mathrm{Pb}p$ data. The
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pair shows a
similar $m_{DD}$ distribution to that of the Pythia8 simulation, in which the
fraction of inclusive charm production that contains more than one charm pair
within the LHCb acceptance is about 7%.

The $\Delta\phi$ distribution is shown in Fig. 3 for ${{D}^{0}}{{D}^{0}}$ and
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs with and
without the requirement
$p_{\mathrm{T}}({{D}^{0}})>2\text{\,Ge\kern-1.00006ptV\\!/}c$. Without this
condition, the $\Delta\phi$ distribution is almost uniform for both
$\mathrm{LS}$ and $\mathrm{OS}$ pairs, similar to that in Pythia8 simulation.
However, with the
$p_{\mathrm{T}}({{D}^{0}})>2\text{\,Ge\kern-1.00006ptV\\!/}c$ requirement, the
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pair favors
values $\Delta\phi\sim 0$, while that of ${{D}^{0}}{{D}^{0}}$ pairs is still
compatible with being flat, and both show inconsistency with the Pythia8
simulation. In general, the behaviour that $m_{DD}$ distribution in
${{D}^{0}}{{D}^{0}}$ pairs peaks at higher values compared to that of
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs and the
flat ${{D}^{0}}{{D}^{0}}$ $\Delta\phi$ distribution are qualitatively
consistent with a large DPS contribution in $\mathrm{LS}$ pair production.
Distributions of the pair transverse momentum and the two-charm relative
rapidity are found to be compatible in $\mathrm{OS}$ data, $\mathrm{LS}$ data
and the Pythia8 simulation.

Figure 2:  Two-charm hadron invariant-mass distribution of (red)
${{D}^{0}}{{D}^{0}}$ and (blue) ${{D}^{0}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs in (left) $p\mathrm{Pb}$,
(right) $\mathrm{Pb}p$ data and (magenta dashed line) Pythia8 simulation.
Vertical bars (filled box) are statistical (systematic) uncertainties.

Figure 3:  The $\Delta\phi$ distribution for (red) ${{D}^{0}}{{D}^{0}}$ and (blue) ${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs in (left) $p\mathrm{Pb}$, (right) $\mathrm{Pb}p$ data and the (magenta dashed line) Pythia8 simulation, (bottom) with and (top) without the $p_{\mathrm{T}}({{D}^{0}})>2\text{\,Ge\kern-1.00006ptV\\!/}c$ requirement. Vertical bars (filled box) are statistical (systematic) uncertainties.  Table 1:  The effective cross-section $\sigma_{\mathrm{eff},\,p\mathrm{Pb}}$ (in  b) measured using ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ and ${{D}^{0}}{{D}^{0}}$ pair production in $p$-Pb data and the extrapolated values from $pp$ data [80].  Pairs | $-5<y(H_{c})<-2.5$ | $1.5<y(H_{c})<4$ |  $pp$ extrapolation
---|---|---|---
${{D}^{0}}{{D}^{0}}$ | $0.99\pm 0.09\pm 0.09$ | $1.41\pm 0.11\pm 0.10$ | $4.3\pm 0.5$
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ | $0.64\pm 0.10\pm 0.06$ | $0.92\pm 0.22\pm 0.06$ | $3.1\pm 0.3$

The effective cross-section $\sigma_{\mathrm{eff},\,p\mathrm{Pb}}$ is
calculated according to Eq. 1 using the ${{D}^{0}}{{D}^{0}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ cross-sections [6], assuming
solely DPS production, where the prompt ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ and
${D}^{0}$ production are evaluated from LHCb measurements [77, 78]. The
results are displayed in Table 1 with a typical value of order $1\text{\,b}$.
Table 1 (“$pp$ extrapolation”) also provides the $\sigma_{\mathrm{eff},\,pp}$
result [80] scaled by the Pb nucleus mass number 208, which is valid under the
assumption of SPS production and absence of nuclear modification. The result
confirms the expectation that DPS production in $p$-Pb collisions is enhanced
by a factor of three compared to SPS production, consistent with the
expectation from the Glauber model. The $\sigma_{\mathrm{eff},\,p\mathrm{Pb}}$
value measured using ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ production
is smaller than that observed in ${{D}^{0}}{{D}^{0}}$ production, as measured
in $pp$ data [80], which may be due to SPS contamination [97] or more than
expected ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ DPS production. The
$p\mathrm{Pb}$ data shows a higher $\sigma_{\mathrm{eff},\,p\mathrm{Pb}}$
value compared to $\mathrm{Pb}p$ data, which may suggest a complicated
structure of the nPDF, as studied in Ref. [46].

The nuclear modification factor,
$R\equiv\frac{\sigma_{p\mathrm{Pb}}}{208\sigma_{pp}}$, is measured for
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ and ${{D}^{0}}{{D}^{0}}$ pairs
with $R^{H_{c}H_{c}^{\prime}}=R^{H_{c}}\times
R^{H_{c}^{\prime}}\times\frac{208\sigma_{\mathrm{eff},\,pp}}{\sigma_{\mathrm{eff},\,p\mathrm{Pb}}}$,
where $\sigma_{p\mathrm{Pb}}$ and $\sigma_{pp}$ are the cross-sections of
charm pairs in $p$-Pb and $pp$ collisions, respectively. Assuming variations
of $R$ and $\sigma_{\mathrm{eff},\,pp}$ as a function of collision energy are
small for $p_{\mathrm{T}}$-integrated production, using measurements of
$\sigma_{\mathrm{eff},\,pp}$ [51], $R^{{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ [77]
and $R^{{D}^{0}}$ [96], $R^{{{D}^{0}}{{D}^{0}}}=1.3\pm 0.2$ ($4.2\pm 0.8$) and
$R^{{{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}}=1.5\pm 0.5$ ($4.6\pm 1.3$)
for $p\mathrm{Pb}$ ($\mathrm{Pb}p$) data are obtained, where the uncertainties
are the total. The results are about a factor of three larger compared to that
of single ${J\mskip-3.0mu/\mskip-2.0mu\psi}$ or ${D}^{0}$ hadron production
[77, 96].

To summarise, the production of $\mathrm{LS}$ and $\mathrm{OS}$ open charm
hadron pairs as well as ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{D}$ pairs are
studied in $p$-Pb collisions at
$\sqrt{s_{\scriptscriptstyle\text{NN}}}=8.16\text{\,Te\kern-1.00006ptV}$ using
fully reconstructed decays. The cross-section ratio between $\mathrm{LS}$ and
$\mathrm{OS}$ pairs is found to be a factor of three higher than that in $pp$
data. The forward-backward ratio of $\mathrm{OS}$ pairs is compatible with
single charm production, while a smaller value is found for $\mathrm{LS}$
pairs. Distributions of the two-charm invariant mass and relative azimuthal
angle show a difference between $\mathrm{LS}$ and $\mathrm{OS}$ pairs, and the
$\mathrm{LS}$ pairs exhibit a flat relative azimuthal angle distribution
independent of charm hadron $p_{\mathrm{T}}$. The effective cross-section and
nuclear modification factor for ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$
and ${{D}^{0}}{{D}^{0}}$ are in general compatible with the expected
enhancement factor of three for DPS over SPS production ratio from $pp$ to
$p$-Pb collisions. This is the first direct observation of such an enhancement
using $\mathrm{LS}$ charm production in $p$-Pb data. The
$\sigma_{\mathrm{eff},\,p\mathrm{Pb}}$ result is different between
$p\mathrm{Pb}$ and $\mathrm{Pb}p$ data and between
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ and ${{D}^{0}}{{D}^{0}}$ pairs
may suggest additional effects not considered yet, which deserve further
investigation using future LHCb data samples.

## Acknowledgements

We would like to thank Hannu Paukkunen and Huasheng Shao for providing
theoretical predictions and helpful discussions. 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); MOST and NSFC (China);
CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO
(Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE (Russia);
MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United
Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC
(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. Individual groups or members
have received support from AvH Foundation (Germany); EPLANET, Marie
Skłodowska-Curie Actions and ERC (European Union); A*MIDEX, ANR, Labex P2IO
and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Program of
Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China);
RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal
Society and the Leverhulme Trust (United Kingdom).

Supplemental Material

## Invariant mass distributions and fit projections

The invariant mass distributions and the fit projections are shown in Fig. 4
for ${{D}^{0}}{{D}^{0}}$ pairs in $\mathrm{Pb}p$ data, and in Figs. 5 and 6
for ${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ pairs in both $p\mathrm{Pb}$ and
$\mathrm{Pb}p$ data.

Figure 4:  (Left) Two-dimensional invariant-mass distributions of
$(m_{1},m_{2})$ for ${{D}^{0}}{{D}^{0}}$ pairs and the projections on (middle)
$m_{1}$ and (right) $m_{2}$ with the fit results superimposed. Shown in the
projection plots are (points with error bars) $\mathrm{Pb}p$ data, (solid
blue) the total fit and the four fit components.

Figure 5:  (Left) Two-dimensional invariant-mass distributions of
$(m_{1},m_{2})$ for ${{D}^{0}}{{\kern
1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ pairs and the projections on
(middle) $m_{1}$ and (right) $m_{2}$ with the fit results superimposed. Shown
in the projection plots are (points with error bars) data data, (solid blue)
the total fit and the four fit components. The plots in the top (bottom) row
correspond to $p\mathrm{Pb}$ ($\mathrm{Pb}p$) data.

Figure 6:  (Left) Two-dimensional invariant-mass distributions of
$(m_{1}^{{J\mskip-3.0mu/\mskip-2.0mu\psi}},m_{2}^{{D}^{0}})$ for
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ pairs and the projections on
(middle) $m_{1}^{{J\mskip-3.0mu/\mskip-2.0mu\psi}}$ and (right)
$m_{2}^{{D}^{0}}$ with the fit results superimposed. Shown in the projection
plots are (points with error bars) data data, (solid blue) the total fit and
the four fit components. The plots in the top (bottom) row correspond to
$p\mathrm{Pb}$ ($\mathrm{Pb}p$) data.

## Cross-sections and cross-section ratios

The total cross-sections measured in the reduced charm hadron rapidity
($y(H_{c})$) range $1.7<y(H_{c})<3.7$ ($-4.7<y(H_{c})<-2.7$) for
$p\mathrm{Pb}$ ($\mathrm{Pb}p$) are shown in Table 2 under the requirement,
$p_{\mathrm{T}}>0\text{\,Ge\kern-1.00006ptV\\!/}c$ for
${{J\mskip-3.0mu/\mskip-2.0mu\psi}},{{D}^{0}}$ and
$p_{\mathrm{T}}>2\text{\,Ge\kern-1.00006ptV\\!/}c$ for
${{D}^{+}},{{D}^{+}_{s}}$. The cross-section of
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ pair production is compared with
the theoretical calculation of SPS production using the reweighted EPPS16
nuclear PDF [92, 93, 94, 95]. Those with the additional requirement
$p_{\mathrm{T}}({{D}^{0}})>2\text{\,Ge\kern-1.00006ptV\\!/}c$ are shown in
Table 3, and those in full rapidity acceptance for ${{D}^{0}}{{D}^{0}}$,
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ and
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ pairs are shown in Table 4.

Table 2: Total cross-sections of charm pair production (in  mb) in $p\mathrm{Pb}$ and $\mathrm{Pb}p$ data for the $p_{\mathrm{T}}$ requirement on the charm hadron, $p_{\mathrm{T}}>0\text{\,Ge\kern-1.00006ptV\\!/}c$ for ${{J\mskip-3.0mu/\mskip-2.0mu\psi}},{{D}^{0}}$ and $p_{\mathrm{T}}>2\text{\,Ge\kern-1.00006ptV\\!/}c$ for ${{D}^{+}},{{D}^{+}_{s}}$. The rapidity range is for each charm hadron in the pair. The first uncertainty is statistical and the second is systematic. The prediction of SPS ${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ production calculated using the weighted EPPS16 nuclear PDF [92, 93, 94, 95] is also listed for comparison, where the first uncertainty is from uncertainties of scales, feed-down contribution and model parameters, and the second due to nuclear PDF uncertainties.  Quantity | $1.7<y(H_{c})<3.7$ | $-4.7<y(H_{c})<-2.7$
---|---|---
${{D}^{0}}{{D}^{0}}$ | $11.0\pm 0.7\pm 1.2$ | $16.5\pm 1.1\pm 3.5$
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | $34.1\pm 1.2\pm 3.6$ | $35.1\pm 1.3\pm 5.9$
${{D}^{0}}{{D}^{+}}$ | $4.0\pm 0.3\pm 0.6$ | $5.3\pm 0.4\pm 1.7$
${{D}^{0}}{{D}^{-}}$ | $12.7\pm 0.4\pm 1.7$ | $11.6\pm 0.4\pm 2.8$
${{D}^{0}}{{D}^{+}_{s}}$ | $2.1\pm 0.6\pm 0.3$ | $3.6\pm 0.7\pm 1.2$
${{D}^{0}}{{D}^{-}_{s}}$ | $5.4\pm 0.6\pm 0.8$ | $7.1\pm 1.0\pm 1.8$
${{D}^{+}}{{D}^{+}}$ | $0.46\pm 0.05\pm 0.09$ | $0.53\pm 0.08\pm 0.24$
${{D}^{+}}{{D}^{-}}$ | $1.38\pm 0.07\pm 0.22$ | $1.26\pm 0.08\pm 0.42$
${{D}^{+}}{{D}^{-}_{s}}$ | $1.43\pm 0.21\pm 0.25$ | $1.32\pm 0.20\pm 0.44$
${{D}^{+}}{{D}^{+}_{s}}$ | $0.32\pm 0.12\pm 0.05$ | $0.80\pm 0.27\pm 0.40$
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ | $0.46\pm 0.05\pm 0.04$ | $0.57\pm 0.07\pm 0.09$
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{+}}$ | $0.08\pm 0.01\pm 0.01$ | $0.10\pm 0.01\pm 0.02$
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ SPS [92, 93, 94, 95] | $0.051^{+0.467}_{-0.043}{}^{+0.009}_{-0.009}$ | $0.055^{+0.426}_{-0.053}{}^{+0.004}_{-0.003}$
Table 3: Total production cross-sections (in  mb) of open charm pairs involving the ${{D}^{0}}$ meson in $p\mathrm{Pb}$ and $\mathrm{Pb}p$ data with the $p_{\mathrm{T}}({{D}^{0}})>2\text{\,Ge\kern-1.00006ptV\\!/}c$ requirement. The rapidity range is for each charm hadron in the pair. The first uncertainty is statistical and the second is systematic. Predictions for the ${{D}^{0}}\,{{D}^{0}}$ and ${{D}^{0}}\,{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ cross-sections from Ref. [24] are given in the last two rows of the Table.  Pairs | $1.7<y(H_{c})<3.7$ | $-4.7<y(H_{c})<-2.7$
---|---|---
${{D}^{0}}{{D}^{0}}$ | $2.36\pm 0.16\pm 0.24$ | $2.28\pm 0.15\pm 0.33$
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | $7.36\pm 0.28\pm 0.71$ | $6.01\pm 0.24\pm 0.81$
${{D}^{0}}{{D}^{+}}$ | $1.83\pm 0.12\pm 0.26$ | $1.97\pm 0.13\pm 0.54$
${{D}^{0}}{{D}^{-}}$ | $6.27\pm 0.19\pm 0.82$ | $5.06\pm 0.17\pm 1.07$
${{D}^{0}}{{D}^{+}_{s}}$ | $0.84\pm 0.19\pm 0.13$ | $1.46\pm 0.50\pm 0.38$
${{D}^{0}}{{D}^{-}_{s}}$ | $3.03\pm 0.34\pm 0.45$ | $2.38\pm 0.29\pm 0.50$
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ | $0.21\pm 0.02\pm 0.02$ | $0.22\pm 0.02\pm 0.03$
${{D}^{0}}{{D}^{0}}$ [24] | $3.62^{+5.92}_{-3.37}$ | $2.93^{+4.72}_{-2.69}$
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ [24] | $6.34^{+8.66}_{-4.79}$ | $5.59^{+7.41}_{-3.79}$
Table 4: Total cross-sections (in  mb) in $p\mathrm{Pb}$ and $\mathrm{Pb}p$ data for full rapidity acceptance without any $p_{\mathrm{T}}(H_{c})$ requirement. The first uncertainty is statistical and the second is systematic.  Pairs | $1.5<y(H_{c})<4$ | $-5<y(H_{c})<-2.5$
---|---|---
${{D}^{0}}{{D}^{0}}$ | $14.72\pm 1.10\pm 2.25$ | $24.05\pm 2.12\pm 5.19$
${{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | $45.99\pm 2.09\pm 5.04$ | $52.05\pm 2.40\pm 8.91$
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}{{D}^{0}}$ | $\phantom{0}0.51\pm 0.12\pm 0.05$ | $\phantom{0}0.82\pm 0.13\pm 0.14$

In Table 5 and Fig. 7, the ratio between cross-sections of like-sign and
opposite-sign pairs is shown in bins of charm hadron rapidity for
$p_{\mathrm{T}}(H_{c})>2\text{\,Ge\kern-1.00006ptV\\!/}c$.

Table 5:  Ratios of differential cross-sections in bins of charm hadron
rapidity for charm $p_{\mathrm{T}}(H_{c})>2\text{\,Ge\kern-1.00006ptV\\!/}c$.
The average over all the pairs in each rapidity interval is also presented.

Pairs | $-4.7<y(H_{c})<-3.7$ | $-3.7<y(H_{c})<-2.7$ | $1.7<y(H_{c})<2.7$ | $2.7<y(H_{c})<3.7$
---|---|---|---|---
${{D}^{0}}{{D}^{0}}/{{D}^{0}}{{\kern 1.79993pt\overline{\kern-1.79993ptD}}{}^{0}}$ | $0.286\pm 0.067\pm 0.011$ | $0.363\pm 0.040\pm 0.009$ | $0.305\pm 0.041\pm 0.009$ | $0.335\pm 0.060\pm 0.012$
${{D}^{0}}{{D}^{+}}/{{D}^{0}}{{D}^{-}}$ | $0.239\pm 0.046\pm 0.017$ | $0.387\pm 0.047\pm 0.026$ | $0.259\pm 0.045\pm 0.010$ | $0.256\pm 0.037\pm 0.009$
${{D}^{+}}{{D}^{+}}/{{D}^{+}}{{D}^{-}}$ | $0.300\pm 0.090\pm 0.037$ | $0.518\pm 0.157\pm 0.079$ | $0.332\pm 0.070\pm 0.018$ | $0.266\pm 0.061\pm 0.012$
${{D}^{0}}{{D}^{+}_{s}}/{{D}^{0}}{{D}^{-}_{s}}$ | $0.321\pm 0.260\pm 0.043$ | $0.504\pm 0.172\pm 0.028$ | $0.201\pm 0.096\pm 0.006$ | $0.303\pm 0.139\pm 0.014$
${{D}^{+}}{{D}^{+}_{s}}/{{D}^{+}}{{D}^{-}_{s}}$ | $0.291\pm 0.590\pm 0.080$ | $0.582\pm 0.340\pm 0.113$ | $0.143\pm 0.116\pm 0.009$ | $0.234\pm 0.113\pm 0.013$
Average | $0.262\pm 0.035\pm 0.019$ | $0.384\pm 0.029\pm 0.019$ | $0.278\pm 0.026\pm 0.010$ | $0.274\pm 0.027\pm 0.011$

Figure 7:  Ratios of differential cross-sections in bins of charm hadron
rapidity under the $p_{\mathrm{T}}({D})>2\text{\,Ge\kern-1.00006ptV\\!/}c$
requirement. The average over all the pairs listed in Table 5 for each
rapidity interval is also presented. The boxes (bars) correspond to systematic
(statistical) uncertainties. Points are shifted horizontally to improve
visibility.

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LHCb collaboration

R. Aaij31, C. Abellán Beteta49, T. Ackernley59, B. Adeva45, M. Adinolfi53, H.
Afsharnia9, C.A. Aidala83, S. Aiola25, Z. Ajaltouni9, S. Akar64, J.
Albrecht14, F. Alessio47, M. Alexander58, A. Alfonso Albero44, Z. Aliouche61,
G. Alkhazov37, P. Alvarez Cartelle47, A.A. Alves Jr45, S. Amato2, Y. Amhis11,
L. An21, L. Anderlini21, G. Andreassi48, A. Andreianov37, M. Andreotti20, F.
Archilli16, A. Artamonov43, M. Artuso67, K. Arzymatov41, E. Aslanides10, M.
Atzeni49, B. Audurier11, S. Bachmann16, M. Bachmayer48, J.J. Back55, S.
Baker60, P. Baladron Rodriguez45, V. Balagura11,b, W. Baldini20, J. Baptista
Leite1, R.J. Barlow61, S. Barsuk11, W. Barter60, M. Bartolini23,47,i, F.
Baryshnikov80, J.M. Basels13, G. Bassi28, V. Batozskaya35, B. Batsukh67, A.
Battig14, A. Bay48, M. Becker14, F. Bedeschi28, I. Bediaga1, A. Beiter67, V.
Belavin41, S. Belin26, V. Bellee48, K. Belous43, I. Belov39, I. Belyaev38, G.
Bencivenni22, E. Ben-Haim12, A. Berezhnoy39, R. Bernet49, D. Berninghoff16,
H.C. Bernstein67, C. Bertella47, E. Bertholet12, A. Bertolin27, C.
Betancourt49, F. Betti19,e, M.O. Bettler54, Ia. Bezshyiko49, S. Bhasin53, J.
Bhom33, L. Bian72, M.S. Bieker14, S. Bifani52, P. Billoir12, M. Birch60,
F.C.R. Bishop54, A. Bizzeti21,u, M. Bjørn62, M.P. Blago47, T. Blake55, F.
Blanc48, S. Blusk67, D. Bobulska58, V. Bocci30, J.A. Boelhauve14, O. Boente
Garcia45, T. Boettcher63, A. Boldyrev81, A. Bondar42,x, N. Bondar37,47, S.
Borghi61, M. Borisyak41, M. Borsato16, J.T. Borsuk33, S.A. Bouchiba48, T.J.V.
Bowcock59, A. Boyer47, C. Bozzi20, M.J. Bradley60, S. Braun65, A. Brea
Rodriguez45, M. Brodski47, J. Brodzicka33, A. Brossa Gonzalo55, D. Brundu26,
E. Buchanan53, A. Buonaura49, C. Burr47, A. Bursche26, A. Butkevich40, J.S.
Butter31, J. Buytaert47, W. Byczynski47, S. Cadeddu26, H. Cai72, R.
Calabrese20,g, L. Calefice14, L. Calero Diaz22, S. Cali22, R. Calladine52, M.
Calvi24,j, M. Calvo Gomez44,m, P. Camargo Magalhaes53, A. Camboni44, P.
Campana22, D.H. Campora Perez47, A.F. Campoverde Quezada5, S. Capelli24,j, L.
Capriotti19,e, A. Carbone19,e, G. Carboni29, R. Cardinale23,i, A. Cardini26,
I. Carli6, P. Carniti24,j, K. Carvalho Akiba31, A. Casais Vidal45, G. Casse59,
M. Cattaneo47, G. Cavallero47, S. Celani48, R. Cenci28, J. Cerasoli10, A.J.
Chadwick59, M.G. Chapman53, M. Charles12, Ph. Charpentier47, G.
Chatzikonstantinidis52, C.A. Chavez Barajas59, M. Chefdeville8, C. Chen3, S.
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Kudryavtsev42,x, H.S. Kuindersma31, G.J. Kunde66, T. Kvaratskheliya38, D.
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Lane61, R. Lane53, G. Lanfranchi22, C. Langenbruch13, J. Langer14, O.
Lantwin49,80, T. Latham55, F. Lazzari28,v, R. Le Gac10, S.H. Lee83, R.
Lefèvre9, A. Leflat39,47, S. Legotin80, O. Leroy10, T. Lesiak33, B.
Leverington16, H. Li71, L. Li62, P. Li16, X. Li66, Y. Li6, Y. Li6, Z. Li67, X.
Liang67, T. Lin60, R. Lindner47, V. Lisovskyi14, R. Litvinov26, G. Liu71, H.
Liu5, S. Liu6, X. Liu3, A. Loi26, J. Lomba Castro45, I. Longstaff58, J.H.
Lopes2, G. Loustau49, G.H. Lovell54, Y. Lu6, D. Lucchesi27,o, S. Luchuk40, M.
Lucio Martinez31, V. Lukashenko31, Y. Luo3, A. Lupato61, E. Luppi20,g, O.
Lupton55, A. Lusiani28,t, X. Lyu5, L. Ma6, S. Maccolini19,e, F. Machefert11,
F. Maciuc36, V. Macko48, P. Mackowiak14, S. Maddrell-Mander53, O. Madejczyk34,
L.R. Madhan Mohan53, O. Maev37, A. Maevskiy81, D. Maisuzenko37, M.W.
Majewski34, S. Malde62, B. Malecki47, A. Malinin79, T. Maltsev42,x, H.
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S. Mariani21,47,h, C. Marin Benito11, M. Marinangeli48, P. Marino48, J.
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K.R. Mattioli83, A. Mauri49, E. Maurice11,b, J. Mauricio44, M. Mazurek35, M.
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K. Petridis53, A. Petrolini23,i, A. Petrov79, S. Petrucci57, M. Petruzzo25, A.
Philippov41, L. Pica28, M. Piccini76, B. Pietrzyk8, G. Pietrzyk48, M. Pili62,
D. Pinci30, J. Pinzino47, F. Pisani47, A. Piucci16, Resmi P.K10, V.
Placinta36, S. Playfer57, J. Plews52, M. Plo Casasus45, F. Polci12, M. Poli
Lener22, M. Poliakova67, A. Poluektov10, N. Polukhina80,c, I. Polyakov67, E.
Polycarpo2, G.J. Pomery53, S. Ponce47, A. Popov43, D. Popov5,47, S. Popov41,
S. Poslavskii43, K. Prasanth33, L. Promberger47, C. Prouve45, V. Pugatch51, A.
Puig Navarro49, H. Pullen62, G. Punzi28,p, W. Qian5, J. Qin5, R. Quagliani12,
B. Quintana8, N.V. Raab17, R.I. Rabadan Trejo10, B. Rachwal34, J.H.
Rademacker53, M. Rama28, M. Ramos Pernas45, M.S. Rangel2, F. Ratnikov41,81, G.
Raven32, M. Reboud8, F. Redi48, F. Reiss12, C. Remon Alepuz46, Z. Ren3, V.
Renaudin62, R. Ribatti28, S. Ricciardi56, D.S. Richards56, K. Rinnert59, P.
Robbe11, A. Robert12, G. Robertson57, A.B. Rodrigues48, E. Rodrigues59, J.A.
Rodriguez Lopez73, M. Roehrken47, A. Rollings62, P. Roloff47, V.
Romanovskiy43, M. Romero Lamas45, A. Romero Vidal45, J.D. Roth83, M.
Rotondo22, M.S. Rudolph67, T. Ruf47, J. Ruiz Vidal46, A. Ryzhikov81, J.
Ryzka34, J.J. Saborido Silva45, N. Sagidova37, N. Sahoo55, B. Saitta26,f, D.
Sanchez Gonzalo44, C. Sanchez Gras31, C. Sanchez Mayordomo46, R.
Santacesaria30, C. Santamarina Rios45, M. Santimaria22, E. Santovetti29,k, D.
Saranin80, G. Sarpis61, M. Sarpis74, A. Sarti30, C. Satriano30,s, A. Satta29,
M. Saur5, D. Savrina38,39, H. Sazak9, L.G. Scantlebury Smead62, S. Schael13,
M. Schellenberg14, M. Schiller58, H. Schindler47, M. Schmelling15, T.
Schmelzer14, B. Schmidt47, O. Schneider48, A. Schopper47, H.F. Schreiner64, M.
Schubiger31, S. Schulte48, M.H. Schune11, R. Schwemmer47, B. Sciascia22, A.
Sciubba30, S. Sellam68, A. Semennikov38, M. Senghi Soares32, A. Sergi52,47, N.
Serra49, J. Serrano10, L. Sestini27, A. Seuthe14, P. Seyfert47, D.M.
Shangase83, M. Shapkin43, I. Shchemerov80, L. Shchutska48, T. Shears59, L.
Shekhtman42,x, Z. Shen4, V. Shevchenko79, E.B. Shields24,j, E. Shmanin80, J.D.
Shupperd67, B.G. Siddi20, R. Silva Coutinho49, L. Silva de Oliveira2, G.
Simi27, S. Simone18,d, I. Skiba20,g, N. Skidmore74, T. Skwarnicki67, M.W.
Slater52, J.C. Smallwood62, J.G. Smeaton54, A. Smetkina38, E. Smith13, M.
Smith60, A. Snoch31, M. Soares19, L. Soares Lavra9, M.D. Sokoloff64, F.J.P.
Soler58, A. Solovev37, I. Solovyev37, F.L. Souza De Almeida2, B. Souza De
Paula2, B. Spaan14, E. Spadaro Norella25,q, P. Spradlin58, F. Stagni47, M.
Stahl64, S. Stahl47, P. Stefko48, O. Steinkamp49,80, S. Stemmle16, O.
Stenyakin43, H. Stevens14, S. Stone67, M.E. Stramaglia48, M. Straticiuc36, D.
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1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
5University of Chinese Academy of Sciences, Beijing, China
6Institute Of High Energy Physics (IHEP), Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
13I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
14Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
15Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
16Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
17School of Physics, University College Dublin, Dublin, Ireland
18INFN Sezione di Bari, Bari, Italy
19INFN Sezione di Bologna, Bologna, Italy
20INFN Sezione di Ferrara, Ferrara, Italy
21INFN Sezione di Firenze, Firenze, Italy
22INFN Laboratori Nazionali di Frascati, Frascati, Italy
23INFN Sezione di Genova, Genova, Italy
24INFN Sezione di Milano-Bicocca, Milano, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Cagliari, Monserrato, Italy
27Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
28INFN Sezione di Pisa, Pisa, Italy
29INFN Sezione di Roma Tor Vergata, Roma, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
32Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
33Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35National Center for Nuclear Research (NCBJ), Warsaw, Poland
36Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
37Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
38Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
39Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
40Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
41Yandex School of Data Analysis, Moscow, Russia
42Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
43Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
44ICCUB, Universitat de Barcelona, Barcelona, Spain
45Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
46Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
47European Organization for Nuclear Research (CERN), Geneva, Switzerland
48Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
49Physik-Institut, Universität Zürich, Zürich, Switzerland
50NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
51Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
52University of Birmingham, Birmingham, United Kingdom
53H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
54Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
55Department of Physics, University of Warwick, Coventry, United Kingdom
56STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
57School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
58School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
59Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
60Imperial College London, London, United Kingdom
61Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
62Department of Physics, University of Oxford, Oxford, United Kingdom
63Massachusetts Institute of Technology, Cambridge, MA, United States
64University of Cincinnati, Cincinnati, OH, United States
65University of Maryland, College Park, MD, United States
66Los Alamos National Laboratory (LANL), Los Alamos, United States
67Syracuse University, Syracuse, NY, United States
68Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria,
associated to 2
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 55
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Guangdong Provencial Key Laboratory of Nuclear Science, Institute of Quantum
Matter, South China Normal University, Guangzhou, China, associated to 3
72School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
73Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 12
74Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 16
75Institut für Physik, Universität Rostock, Rostock, Germany, associated to 16
76INFN Sezione di Perugia, Perugia, Italy, associated to 20
77Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 31
78Universiteit Maastricht, Maastricht, Netherlands, associated to 31
79National Research Centre Kurchatov Institute, Moscow, Russia, associated to
38
80National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 38
81National Research University Higher School of Economics, Moscow, Russia,
associated to 41
82National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
38
83University of Michigan, Ann Arbor, United States, associated to 67

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Firenze, Firenze, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mDS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vUniversità di Siena, Siena, Italy
wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
xNovosibirsk State University, Novosibirsk, Russia
yINFN Sezione di Trieste, Trieste, Italy
zUniversidad Nacional Autonoma de Honduras, Tegucigalpa, Honduras