EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-176 LHCb-PAPER-2021-029

Study of $Z$ bosons produced

in association with charm

in the forward region

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

Events containing a $Z$ boson and a charm jet are studied for the first time
in the forward region of proton-proton collisions. The data sample used
corresponds to an integrated luminosity of 6$\text{\,fb}^{-1}$ collected at a
center-of-mass energy of $13\text{\,Te\kern-1.00006ptV}$ with the LHCb
detector. In events with a $Z$ boson and a jet, the fraction of charm jets is
determined in intervals of $Z$-boson rapidity in the range $2.0<y({Z})<4.5$. A
sizable enhancement is observed in the forward-most $y({Z})$ interval, which
could be indicative of a valence-like intrinsic-charm component in the proton
wave function.

Published as Physical Review Letters 128 (2022) 082001

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

The possibility that the proton wave function may contain a
$|uudc\bar{c}\rangle$ component, referred to as intrinsic charm (IC), in
addition to the charm content that arises due to perturbative gluon radiation,
i.e. $g\\!\rightarrow\\!c\bar{c}$ splitting, has been debated for decades (for
a recent review, see Ref. [1]). The light front QCD calculations of Refs. [2,
3], referred to as the BHPS model, predict that non-perturbative IC manifests
as valence-like charm content in the parton distribution functions (PDFs) of
the proton; whereas, if the $c$-quark content is entirely perturbative in
nature, the charm PDF resembles that of the gluon and sharply decreases at
large momentum fractions, $x$. (Charge conjugation is implied throughout this
Letter, e.g., charm refers to both the $c$ and $\bar{c}$ quarks.)
Understanding the role that non-perturbative dynamics play inside the nucleon
is a fundamental goal of nuclear physics [4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15]. Furthermore, the existence of IC would have many phenomenological
consequences. For example, IC would alter both the rate and kinematics of $c$
hadrons produced by cosmic-ray proton interactions in the atmosphere, which
are an important source of background in studies of astrophysical neutrinos
[16, 17, 18, 19, 20, 21]. The cross sections of many processes at the LHC and
other accelerators would also be affected [22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32].

Measurements of $c$-hadron production in deep inelastic scattering [33] and in
fixed-target experiments [34], where the typical momentum transfers were
$Q\lesssim 10\text{\,Ge\kern-1.00006ptV}$ (natural units are used throughout
this Letter), have been interpreted both as evidence for [35, 36] and against
[37] the percent-level IC content predicted by BHPS. Even though such
experiments are in principle sensitive to valence-like $c$-quark content,
interpreting these low-$Q$ data is challenging since it requires careful
theoretical treatment of nonperturbative hadronic and nuclear effects. Recent
global PDF analyses, which also include measurements from the LHC, are
inconclusive and can only exclude IC carrying more than a few percent of the
momentum of the proton [38, 39].

Reference [29] proposed probing IC by studying events containing a $Z$ boson
and a charm jet, ${Z}c$, in the forward region of proton-proton ($pp$)
collisions at the LHC. The ratio of production cross sections
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle
j$}}\equiv\sigma({Z}c)/\sigma({Z}j)$, where ${Z}j$ refers to events containing
a $Z$ boson and any type of jet, was chosen because it is less sensitive than
$\sigma({Z}c)$ to experimental and theoretical uncertainties. Since ${Z}c$
production is inherently at large $Q$, above the electroweak scale, hadronic
effects are small. A leading-order ${Z}c$ production mechanism is
$gc\\!\rightarrow Zc$ scattering (see Fig. 1), where in the forward region one
of the initial partons must have large $x$, hence ${Z}c$ production probes the
valence-like region (Fig. S4 of the Supplemental Material shows the $x$
regions probed). Using next-to-leading-order (NLO) Standard Model (SM)
calculations, Fig. 2 illustrates that a percent-level valence-like IC
contribution would produce a clear enhancement in
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ for
large (more forward) values of $Z$ rapidity, $y({Z})$; whereas only small
effects are expected in the central region where all previous measurements of
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ were
made [40, 41].

Figure 1: Leading-order Feynman diagrams for $gc\\!\rightarrow Zc$ production.
Figure 2: NLO SM predictions [29] for
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
without IC [42], allowing for potential IC [39], and with the valence-like IC
predicted by BHPS with a mean momentum fraction of 1% [38]. The fiducial
region from Ref. [41] is used for $y({Z})<2$; otherwise the fiducial region of
this analysis is employed. The broadening of the error band that arises in the
forward region, when allowing for IC, is due to the lack of sensitivity to
valence-like IC from previous experiments. More details on these calculations
are provided in the Supplemental Material [43]. The error bands shown for the
first two predictions display the 68% confidence-level regions. Only the
central value is shown for BHPS due to the charm PDF being fixed.

This Letter presents the first measurement of
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ in
the forward region of $pp$ collisions. The data sample used corresponds to an
integrated luminosity of 6$\text{\,fb}^{-1}$ collected at a center-of-mass
energy of $\sqrt{s}=13\text{\,Te\kern-1.00006ptV}$ with the LHCb detector. The
$Z$ bosons are reconstructed using the ${Z}\\!\rightarrow\\!\mu^{+}\mu^{-}$
decay, where henceforth all ${Z}/\gamma^{*}\rightarrow\mu^{+}\mu^{-}$
production in the mass range
$60<m(\mu^{+}\mu^{-})<120\text{\,Ge\kern-1.00006ptV}$ is labeled
${Z}\\!\rightarrow\\!\mu^{+}\mu^{-}$. The analysis is performed using jets
clustered with the anti-$k_{\rm T}$ algorithm [44] using a distance parameter
$R=0.5$. The fiducial region is defined in terms of the transverse momentum,
$p_{\mathrm{T}}$, pseudorapidity, $\eta$, and azimuthal angle, $\phi$, of the
muon and jet momenta, and includes a requirement on $\Delta
R(\mu,j)\equiv\sqrt{\Delta\eta(\mu,j)^{2}+\Delta\phi(\mu,j)^{2}}$ to ensure
that the muons and jets are well separated, which suppresses backgrounds from
QCD multijet events and electroweak processes like $W+$jet production. Charm
jets are the subset for which there is a promptly produced and weakly decaying
$c$ hadron within the jet. The fiducial region is defined in Table 1. If
multiple jets satisfy these criteria, the one with the highest
$p_{\mathrm{T}}$ is selected. No requirement is placed on the maximum number
of jets in the event.

Table 1:  Definition of the fiducial region. $Z$ bosons |  $p_{\mathrm{T}}(\mu)>20\text{\,Ge\kern-1.00006ptV}$, $2.0<\eta(\mu)<4.5$, $60<m(\mu^{+}\mu^{-})<120\text{\,Ge\kern-1.00006ptV}$
---|---
Jets |  $20<p_{\mathrm{T}}(j)<100\text{\,Ge\kern-1.00006ptV}$, $2.2<\eta(j)<4.2$
Charm jets |  $p_{\mathrm{T}}(c$ hadron$)>5\text{\,Ge\kern-1.00006ptV}$, $\Delta R(j,c$ hadron$)<0.5$
Events | $\Delta R(\mu,j)>0.5$

The quantity
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ is
measured in intervals of $y({Z})$ as
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle
j$}}=N(c$-tag$)/[\varepsilon(c$-tag$)N(j)]$, where $N(c$-tag$)$ is the
observed ${Z}c$ yield, $\varepsilon(c$-tag$)$ is the $c$-tagging efficiency,
and $N(j)$ is the total ${Z}j$ yield. The integrated luminosity does not enter
this expression because
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
involves a ratio of production cross sections. In addition, the muon and jet
reconstruction efficiencies largely cancel in the ratio due to the similarity
of the $Z$-boson and jet kinematics in ${Z}c$ and ${Z}j$ production. The
$c$-tagging algorithm, which is described in detail in Ref. [45], looks for a
displaced-vertex (DV) signature inside the jet cone that is indicative of the
weak decay of a $c$ hadron.

The LHCb detector is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, described in detail in Refs. [46, 47].
Simulated data samples are used to evaluate the detector response for jet
reconstruction, including the $c$-tagging efficiency, and to validate the
analysis. In the simulation, $pp$ collisions are generated using Pythia [48,
*Sjostrand:2006za] with a specific LHCb configuration [50]. Decays of unstable
particles are described by EvtGen [51], in which final-state QED radiation is
generated using Photos [52]. The interaction of the generated particles with
the detector, and its response, are implemented using the Geant4 toolkit [53,
*Agostinelli:2002hh] as described in Ref. [55].

The online event selection is performed by a trigger [56, 57] consisting of a
hardware stage using information from the calorimeter and muon systems,
followed by a software stage that performs a full event reconstruction. At the
hardware stage, events are required to have a muon with
${p_{\mathrm{T}}(\mu)>6\text{\,Ge\kern-1.00006ptV}}$. In the software stage,
the muon track is required to be of good quality and to have
${p_{\mathrm{T}}(\mu)>10\text{\,Ge\kern-1.00006ptV}}$. The offline selection
builds ${Z}\\!\rightarrow\\!\mu^{+}\mu^{-}$ candidates from two oppositely
charged muon tracks that must be in the fiducial region defined in Table 1 and
consistent with originating directly from the same $pp$ collision.

Jet reconstruction is performed offline by clustering charged and neutral
particle-flow candidates [58] using the anti-$k_{\rm T}$ clustering algorithm
as implemented in FastJet [59]. Reconstructed jets with
$15<p_{\mathrm{T}}(j)<100\text{\,Ge\kern-1.00006ptV}$ and $2.2<\eta(j)<4.2$
are kept for further analysis. Jets with
$15<p_{\mathrm{T}}(j)<20\text{\,Ge\kern-1.00006ptV}$, which are outside of the
fiducial region, are retained for use when unfolding the detector response.
The $\eta(j)$ requirement, which is included in the fiducial region and was
first used in Refs. [60, 61, 62], ensures a nearly uniform $c$-tagging
efficiency of about 24%, with minimal $p_{\mathrm{T}}(j)$ or $\eta(j)$
dependence. The fiducial requirement $\Delta R(\mu,j)>0.5$ is applied to
reconstructed jets. Finally, the highest-$p_{\mathrm{T}}$ jet satisfying these
criteria from the same $pp$ collision as the $Z$ boson is selected. After
applying all requirements, 68 694 ${Z}j$ candidates remain in the dataset.

The effects of the detector response on the measured jet momenta are accounted
for using an unfolding procedure. This involves first determining the
reconstructed ${Z}c$ and ${Z}j$ yields in intervals of
$[y({Z}),p_{\mathrm{T}}(j)]$. The non-$Z$ background is neglected for both
${Z}c$ and ${Z}j$ candidates because it is less than 1% and largely cancels in
the $\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
ratio. The $c$-jet yields are determined using the DV-based tagging approach
described in detail in the following paragraphs. Interval migration is
accounted for by unfolding the $p_{\mathrm{T}}(j)$ distributions of the ${Z}c$
and ${Z}j$ yields in each $y({Z})$ interval independently using an iterative
Bayesian procedure [63, 64]. The ${Z}c$ yields are then corrected for
$c$-tagging inefficiency. Finally, the unfolded $[y({Z}),p_{\mathrm{T}}(j)]$
distributions are integrated for
$p_{\mathrm{T}}(j)>20\text{\,Ge\kern-1.00006ptV}$ to obtain the ${Z}c$ and
${Z}j$ yields used to determine the
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
ratios. The analysis employs three $y({Z})$ intervals with ranges 2.00–2.75,
2.75–3.50, and 3.50–4.50, and four $p_{\mathrm{T}}(j)$ intervals ranging
15–20, 20–30, 30–50, and 50–100 GeV, where after unfolding the yields in the
three highest $p_{\mathrm{T}}(j)$ intervals are summed to obtain
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$.

The signature of a $c$ jet is the presence of a long-lived $c$ hadron that
carries a sizable fraction of the jet energy. The tagging of $c$ jets is
performed using DVs formed from the decays of such $c$ hadrons. The choice of
using DVs and not single-track or other non-DV-based jet properties, e.g. the
number of particles in the jet, is driven by the need for a small
misidentification probability of light-parton jets. Furthermore, the
properties of DVs from $c$-hadron decays are known to be well modeled by
simulation, which means that only small corrections using control samples are
required. Since DVs can also be formed from the decays of $b$ hadrons or due
to artifacts of the reconstruction, the DV-tagged charm yields are obtained by
fitting the distributions of DV features with good discrimination power
between $c$, $b$, and light-parton jets.

The tracks used as inputs to the DV-tagger algorithm are required to have
$p_{\mathrm{T}}>0.5\text{\,Ge\kern-1.00006ptV}$ and to be inconsistent with
originating directly from a $pp$ interaction point. A DV is associated to a
jet when $\Delta R<0.5$ between the jet axis and the DV direction of flight,
defined by the vector from the $pp$ interaction point to the DV position.
Requirements that reject strange-hadron decays and particles formed in
interactions with material [65] are placed on the mass, $m({\rm DV})$, and
momentum, $p({\rm DV})$, of the particles that form the DV, along with the DV
position. In addition, only DVs with at most four tracks are used, since
higher-multiplicity DVs are almost exclusively due to $b$-hadron decays. More
details about the $c$-tagging algorithm are provided in Ref. [45].

Two DV properties are used to separate charm jets from beauty and light-parton
jets: the number of tracks in the DV, $N_{\rm trk}({\rm DV})$, and the
corrected mass, $m_{\rm cor}({\rm DV})\equiv\sqrt{m({\rm DV})^{2}+[p({\rm
DV})\sin{\theta}]^{2}}+p({\rm DV})\sin{\theta}$, where $\theta$ is the angle
between the momentum and the flight direction of the DV. The corrected mass,
which is the minimum mass the long-lived hadron can have that is consistent
with the flight direction, peaks near the typical $c$-hadron mass for $c$
jets, and consequently provides excellent discrimination against other jet
types. The DV track multiplicity provides additional discrimination against
$b$ jets, since $b$-hadron decays often produce many displaced tracks. These
two distributions are fitted simultaneously to obtain the DV-tagged $c$-jet
yields. The probability density functions, referred to as templates, for $c$,
$b$, and light-parton jets are obtained from calibration data samples that are
each highly enriched in a given jet flavor [45]. Figure 3 shows the $m_{\rm
cor}({\rm DV})$ and $N_{\rm trk}({\rm DV})$ distributions for all DV-tagged
candidates in the ${Z}j$ data sample reconstructed in the fiducial region,
along with the fit projections; such fits are performed in each
$[y({Z}),p_{\mathrm{T}}(j)]$ interval to obtain the reconstructed ${Z}c$
yields.

Figure 3: Distributions of (left) $m_{\rm cor}({\rm DV})$ and (right) $N_{\rm
trk}({\rm DV})$ for all DV-tagged candidates in the ${Z}j$ data sample
reconstructed in the fiducial region with the projections of the fit results
superimposed.

The effects of $p_{\mathrm{T}}(j)$ interval migration are corrected for using
the unfolding procedure. The detector response is studied using the
$p_{\mathrm{T}}$-balance distribution $p_{\mathrm{T}}(j)/p_{\mathrm{T}}(Z)$
for ${Z}j$ candidates that are nearly back-to-back in the transverse plane,
using the same technique as in Refs. [58, 66]. Small adjustments are applied
to the $p_{\mathrm{T}}(j)$ scale and resolution in simulation to obtain the
best agreement with data. In addition, for the ${Z}c$ and ${Z}j$ samples the
$p_{\mathrm{T}}(j)$ and $p_{\mathrm{T}}({\rm DV})$ distributions in simulation
are adjusted to match those observed in data. The unfolding matrix for jets
that contain a reconstructed DV is shown in Fig. 4, while the corresponding
matrix for inclusive ${Z}j$ production is provided in the Supplemental
Material [43].

Figure 4: The detector-response matrix for $c$-tagged jets. The shading
represents the interval-to-interval migration probabilities ranging from
(white) 0 to (black) 1. Numerical labels are only shown for values greater
than 1%. Jets with true (reconstructed) $p_{\mathrm{T}}(j)$ in the 20–100 GeV
region but for which the reconstructed (true) $p_{\mathrm{T}}(j)$ is either
below 15 GeV or above 100 GeV are included in the unfolding but not shown
graphically.

The dominant systematic uncertainty is due to limited knowledge of the
$c$-tagging efficiency, which is measured in $p_{\mathrm{T}}(j)$ intervals
using data in Ref. [45] and briefly summarized here. Scale factors that
correct for discrepancies between data and simulation are determined using a
tag-and-probe approach on a dijet calibration sample. A stringent requirement
is applied to the tag jet which enriches the probe-jet sample in charm
content. The DV-tagged $c$-jet yield in the probe sample is obtained in the
same way the ${Z}c$ yield is determined in this analysis, namely by fitting
the $m_{\rm cor}({\rm DV})$ and $N_{\rm trk}({\rm DV})$ distributions for DV-
tagged probe jets. The total number of $c$ jets in the probe sample is
obtained by fully reconstructing the
${{D}^{0}}\rightarrow{{K}^{-}}{{\pi}^{+}}$ and
${{D}^{+}}\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{+}}$ decays, obtaining the
prompt-charm yields by fitting the $D$-meson mass and impact-parameter
distributions, then correcting these yields for the detector response, decay
branching fractions [67], and $c$-hadron fragmentation fractions [68]. The
$c$-tagging efficiency is the ratio of the DV-tagged and total $c$-jet probe-
sample yields. The scale factors that correct the $c$-tagging efficiency in
simulation are determined to be $1.03\pm 0.06$, $1.01\pm 0.08$, and $1.09\pm
0.17$ in the 20–30, 30–50, and 50–100 GeV $p_{\mathrm{T}}(j)$ intervals,
respectively, with corresponding $c$-tagging efficiencies of $(23.9\pm
1.4)\%$, $(24.4\pm 1.9)\%$, and $(23.6\pm 4.1)\%$. These uncertainties, which
include all statistical and systematic contributions, are propagated to the
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
results producing 6–7% relative uncertainties in each $y({Z})$ interval.

Other sources of smaller systematic uncertainty are also considered. First,
variations of the $m_{\rm cor}({\rm DV})$ and $N_{\rm trk}({\rm DV})$
templates are studied, which arise from using different strategies to model
the backgrounds in the highly enriched calibration data samples. However, the
shifts observed in the ${Z}c$ yields largely cancel with the corresponding
shifts seen in $\varepsilon(c$-tag$)$. The residual differences of 3–4% in
each $y({Z})$ interval are assigned as systematic uncertainties. The ratio of
the jet-reconstruction efficiency for $c$ and inclusive jets is consistent
with unity in all kinematic intervals in simulation, with a 1% systematic
uncertainty assigned due to the limited sample sizes. Finally, the statistical
precision of the back-to-back ${Z}j$ sample used to determine the
$p_{\mathrm{T}}(j)$ scale and resolution is propagated through the unfolding
procedure resulting in a 1% relative systematic uncertainty on
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$. The
systematic uncertainties are summarized in Table 2.

Table 2:  Relative systematic uncertainties on $\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$, where ranges indicate that the value depends on the $y({Z})$ intervals. Source | Relative Uncertainty
---|---
$c$ tagging | 6–7%
DV-fit templates | 3–4%
Jet reconstruction | 1%
Jet $p_{\mathrm{T}}$ scale & resolution | 1%
Total | 8%

Figure 5 shows the measured
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
distribution in intervals of $y({Z})$; the numerical results are provided in
Table 3, and additional results are reported in the Supplemental Material
[43]. The measured
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
values are compared to NLO SM calculations [29] based on Refs. [69, 70, 71,
72, 73, 74, 75], which are validated against additional predictions [72, 73,
76, 77] and updated here to use more recent PDFs [42, 38, 39, 78, 79]. While
$Zc$ predictions at NNLO in QCD are not available, $Zb$ predictions are [80],
and similar methods should be applicable. The NNPDF analysis provides results
where the charm PDF is allowed to vary, both in size and in shape [39]. The
sizable uncertainties that arise in the forward region are due to the lack of
sensitivity to valence-like IC from previous experiments. Reference [38]
updated the CT14 analysis [81] to include the IC content predicted by BHPS [2,
3], which results in the enhancement at forward $y({Z})$ shown previously in
Fig. 2. These predictions have smaller uncertainties because the size and
shape of the IC contribution are fixed, i.e. the IC contribution is assumed to
be known, hence does not contribute to the uncertainty on
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$.
More details on the theory calculations, along with predictions based on other
PDFs [82, 83, 84], are provided in the Supplemental Material [43].

Figure 5: Measured $\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ distribution (gray bands) for three intervals of forward $Z$ rapidity, compared to NLO SM predictions [29] without IC [42], with the charm PDF shape allowed to vary (hence, permitting IC) [39, 78], and with IC as predicted by BHPS with a mean momentum fraction of 1% [38]. The predictions are offset in each interval to improve visibility. Table 3:  Numerical results for the $\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ measurements, where the first uncertainty is statistical and the second is systematic. $y({Z})$ |  $\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ (%)
---|---
2.00–2.75 | $6.84\pm 0.54\pm 0.51$
2.75–3.50 | $4.05\pm 0.32\pm 0.31$
3.50–4.50 | $4.80\pm 0.50\pm 0.39$
2.00–4.50 | $4.98\pm 0.25\pm 0.35$

The observed
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
values are consistent with both the no-IC and IC hypotheses in the first two
$y({Z})$ intervals; however, this is not the case in the forward-most interval
where the ratio of the observed to no-IC-expected values is $1.85\pm 0.25$. As
illustrated in Fig. 2, this is precisely the $y({Z})$ region where valence-
like IC would cause a large enhancement. Indeed, Fig. 5 shows that, after
including the IC PDF shape predicted by BHPS with a mean momentum fraction of
1%, the theory predictions are consistent with the data. Incorporating these
novel forward
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
results into a global analysis should strongly constrain the large-$x$ charm
PDF, both in size and in shape. While the large enhancement in the forward-
most $y({Z})$ interval is suggestive of valence-like IC, no definitive
statements can be made until the
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
results are included in a global PDF analysis.

In conclusion, events containing a $Z$ boson and a charm jet are studied for
the first time in the forward region of $pp$ collisions. The data sample used
corresponds to an integrated luminosity of 6$\text{\,fb}^{-1}$ collected at a
center-of-mass energy of $13\text{\,Te\kern-1.00006ptV}$ with the LHCb
detector. The ratio
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ is
measured in intervals of $y({Z})$ and compared to NLO SM calculations. The
observed spectrum exhibits a sizable enhancement at forward $Z$ rapidities,
consistent with the effect expected if the proton wave function contains the
$|uudc\bar{c}\rangle$ component predicted by BHPS. However, conclusions about
whether the proton contains valence-like intrinsic charm can only be drawn
after incorporating these results into global PDF analyses.

## Acknowledgements

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); MICINN (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 NERSC (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 ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, IPhU and Labex P2IO, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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Supplemental Material for LHCb-PAPER-2021-029

Study of $Z$ bosons produced in association with charm in the forward region

### Theory Predictions

The NLO SM calculations of Ref. [29] are updated here to use more recent PDFs
[42, 38, 39, 78, 79, 82, 83, 84]. These predictions are made using the $Zj$
PowhegBox matrix element [69] interfaced to the Pythia 8 parton shower [70]
using Powheg matching [71]. These predictions were cross-checked against
results produced with the aMC@NLO matrix element generator [72] interfaced to
the Pythia 8 parton shower using FxFx matching [73]. Hadronization was
performed with the Pythia 8 event generator, while hadrons were decayed with
the EvtGen package [51] interfaced with the Photos final state radiation
generator [74]. No requirement is placed on the maximum number of jets in the
event. The results in Ref. [29] were produced using the CT14 NNLO PDF set [81]
for the matrix element, and the corresponding LO PDF set for the parton
shower. Using the kinematics of the initiating partons, these results were
then weighted in this analysis to produce predictions from more recent PDF
sets.

The associated systematic uncertainty for these predictions consists of PDF,
scale, and strong-coupling uncertainty. Varying the charm mass leads to
negligible changes in the
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
predictions. Full correlations were considered when evaluating these
uncertainties. The PDF uncertainty is determined using the technique of Monte
Carlo PDF replicas [75], while the scale uncertainty is determined from the
envelope obtained by independently varying both the factorization and
renormalization scales by up to a factor of two. The strong coupling
uncertainty is evaluated by varying $\alpha_{s}$ within experimental
uncertainty. Both the scale and strong-coupling uncertainties largely cancel
in the ratio, leaving the PDF as the dominant source of uncertainty.

These theory predictions are validated by comparing to the
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
results from the CMS collaboration at central $y({Z})$ [41], where there is
minimal sensitivity to IC. The CMS collaboration measured
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$ to
be $(10.2\pm 0.9)\%$. Reference [41] also provides NLO SM predictions,
$(11.1\pm 0.3)\%$ and $(9.0\pm 0.9)\%$, obtained using the aMC@NLO generator
interfaced with the Pythia 8 parton shower using FxFx matching and the fixed-
order MCFM generator [76, 77], respectively. Repeating the procedure used to
obtain the theory predictions presented in this Letter, but in the CMS
fiducial region, gives $(9.6\pm 1.0)\%$, $(9.5\pm 1.0)\%$, and $(9.7\pm
1.0)\%$ for the PDF4LHC15 no IC, NNPDF 3.0 IC allowed, and CT14 with BHPS
PDFs, respectively. Therefore, the approach used here produces predictions
that are consistent both with the CMS measurement and with the theory
predictions provided in Ref. [41].

Finally, in Fig. 5 the CT14 with BHPS results are from the PDF set labeled as
BHPS3 in Ref. [38], which is provided for the value $\langle x\rangle_{\rm
IC}=1\%$.

### Additional Numerical Results

Numerical results are provided in Table 3. The statistical uncertainties are
uncorrelated between $y({Z})$ intervals, whereas the systematic uncertainties
are approximately completely correlated. Since many of the systematic
uncertainties are correlated between $y({Z})$ intervals, numerical results are
also provided for the ratios of
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
values between pairs of intervals in Table S1.

Table S1:  Numerical results for the ratios $r^{c}_{j}(i/k)\equiv\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}[y({Z})_{i}]/\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}[y({Z})_{k}]$, where the first uncertainty is statistical and the second is systematic for each result. The labels low, mid, and high refer to $y({Z})$ ranges of 2.00–2.75, 2.75–3.50 and 3.50–4.50, respectively. Ratio | Value
---|---
$r^{c}_{j}({\rm mid}/{\rm low})$ | $0.59\pm 0.07\pm 0.04$
$r^{c}_{j}({\rm high}/{\rm low})$ | $0.70\pm 0.09\pm 0.05$
$r^{c}_{j}({\rm high}/{\rm mid})$ | $1.19\pm 0.16\pm 0.05$

### Additional Figures

Figure S1: Dimuon invariant mass distribution for the ${Z}j$ sample.

Figure S2: Probability density functions for the DV features used in the
$c$-tagging fits for $c$, $b$, and light-parton jets: (left) the corrected
mass and (right) the track multiplicity.  Figure S3:  The detector-response
matrix for inclusive ${Z}j$ events. The shading represents the interval-to-
interval migration probabilities ranging from (white) 0 to (black) 1.
Numerical labels are only shown for values greater than 1%. Jets with true
(reconstructed) $p_{\mathrm{T}}(j)$ in the 20–100 GeV region but for which the
reconstructed (true) $p_{\mathrm{T}}(j)$ is either below 15 GeV or above 100
GeV are included in the unfolding but not shown graphically.

Figure S4: Momentum fraction distributions of the (left) $c$ quark and (right)
gluon for the process $gc\rightarrow Zc$ in the predominant scenario where the
$c$ quark is the leading (higher-$x$) parton. Distributions are shown
separately for the three $y(Z)$ intervals used in the analysis, with each
distribution normalized to have an integral of unity. These distributions are
obtained using the theory calculations described in detail here in the
Supplemental Material.

Figure S5: Measured
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
distribution (gray bands) for three intervals of forward $Z$ rapidity,
compared to NLO SM predictions [29] using various PDF sets. The predictions
are offset in each interval to improve visibility. The left plot shows that
the three PDF sets [81, 79, 78] on which the PDF4LHC15 [42] set is formed from
all provide consistent predictions for
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$. The
right plot shows that the ABM16 [82], JR14 [83], and HERAPDF 2.0 [84] PDF sets
also provide qualitatively similar predictions, though the JR14 and HERAPDF
2.0 predictions are shifted to lower
$\mathcal{R}^{c}\kern-3.99994pt{\raisebox{-1.99997pt}{$\scriptstyle j$}}$
values.

LHCb collaboration

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Luzzi48, S. Filippov39, R.A. Fini19, M. Fiorini21,f, M. Firlej34, K.M.
Fischer63, D.S. Fitzgerald87, C. Fitzpatrick62, T. Fiutowski34, A. Fkiaras48,
F. Fleuret12, M. Fontana13, F. Fontanelli24,h, R. Forty48, D. Foulds-Holt55,
V. Franco Lima60, M. Franco Sevilla66, M. Frank48, E. Franzoso21, G. Frau17,
C. Frei48, D.A. Friday59, J. Fu6, Q. Fuehring15, E. Gabriel32, G. Galati19,c,
A. Gallas Torreira46, D. Galli20,d, S. Gambetta58,48, Y. Gan3, M. Gandelman2,
P. Gandini25, Y. Gao5, M. Garau27, L.M. Garcia Martin56, P. Garcia Moreno45,
J. García Pardiñas26,j, B. Garcia Plana46, F.A. Garcia Rosales12, L.
Garrido45, C. Gaspar48, R.E. Geertsema32, D. Gerick17, L.L. Gerken15, E.
Gersabeck62, M. Gersabeck62, T. Gershon56, D. Gerstel10, L. Giambastiani28, V.
Gibson55, H.K. Giemza36, A.L. Gilman63, M. Giovannetti23,p, A. Gioventù46, P.
Gironella Gironell45, L. Giubega37, C. Giugliano21,f,48, K. Gizdov58, E.L.
Gkougkousis48, V.V. Gligorov13, C. Göbel70, E. Golobardes85, D. Golubkov41, A.
Golutvin61,83, A. Gomes1,a, S. Gomez Fernandez45, F. Goncalves Abrantes63, M.
Goncerz35, G. Gong3, P. Gorbounov41, I.V. Gorelov40, C. Gotti26, E.
Govorkova48, J.P. Grabowski17, T. Grammatico13, L.A. Granado Cardoso48, E.
Graugés45, E. Graverini49, G. Graziani22, A. Grecu37, L.M. Greeven32, N.A.
Grieser4, L. Grillo62, S. Gromov83, B.R. Gruberg Cazon63, C. Gu3, M.
Guarise21, M. Guittiere11, P. A. Günther17, E. Gushchin39, A. Guth14, Y.
Guz44, T. Gys48, T. Hadavizadeh69, G. Haefeli49, C. Haen48, J. Haimberger48,
T. Halewood-leagas60, P.M. Hamilton66, J.P. Hammerich60, Q. Han7, X. Han17,
T.H. Hancock63, E.B. Hansen62, S. Hansmann-Menzemer17, N. Harnew63, T.
Harrison60, C. Hasse48, M. Hatch48, J. He6,b, M. Hecker61, K. Heijhoff32, K.
Heinicke15, A.M. Hennequin48, K. Hennessy60, L. Henry48, J. Heuel14, A.
Hicheur2, D. Hill49, M. Hilton62, S.E. Hollitt15, R. Hou7, Y. Hou8, J. Hu17,
J. Hu72, W. Hu7, X. Hu3, W. Huang6, X. Huang73, W. Hulsbergen32, R.J.
Hunter56, M. Hushchyn82, D. Hutchcroft60, D. Hynds32, P. Ibis15, M. Idzik34,
D. Ilin38, P. Ilten65, A. Inglessi38, A. Ishteev83, K. Ivshin38, R.
Jacobsson48, H. Jage14, S. Jakobsen48, E. Jans32, B.K. Jashal47, A.
Jawahery66, V. Jevtic15, F. Jiang3, M. John63, D. Johnson48, C.R. Jones55,
T.P. Jones56, B. Jost48, N. Jurik48, S.H. Kalavan Kadavath34, S. Kandybei51,
Y. Kang3, M. Karacson48, M. Karpov82, F. Keizer48, D.M. Keller68, M. Kenzie56,
T. Ketel33, B. Khanji15, A. Kharisova84, S. Kholodenko44, T. Kirn14, V.S.
Kirsebom49, O. Kitouni64, S. Klaver32, N. Kleijne29, K. Klimaszewski36, M.R.
Kmiec36, S. Koliiev52, A. Kondybayeva83, A. Konoplyannikov41, P. Kopciewicz34,
R. Kopecna17, P. Koppenburg32, M. Korolev40, I. Kostiuk32,52, O. Kot52, S.
Kotriakhova21,38, P. Kravchenko38, L. Kravchuk39, R.D. Krawczyk48, M. Kreps56,
F. Kress61, S. Kretzschmar14, P. Krokovny43,u, W. Krupa34, W. Krzemien36, M.
Kucharczyk35, V. Kudryavtsev43,u, H.S. Kuindersma32,33, G.J. Kunde67, T.
Kvaratskheliya41, D. Lacarrere48, G. Lafferty62, A. Lai27, A. Lampis27, D.
Lancierini50, J.J. Lane62, R. Lane54, G. Lanfranchi23, C. Langenbruch14, J.
Langer15, O. Lantwin83, T. Latham56, F. Lazzari29,q, R. Le Gac10, S.H. Lee87,
R. Lefèvre9, A. Leflat40, S. Legotin83, O. Leroy10, T. Lesiak35, B.
Leverington17, H. Li72, P. Li17, S. Li7, Y. Li4, Y. Li4, Z. Li68, X. Liang68,
T. Lin61, R. Lindner48, V. Lisovskyi15, R. Litvinov27, G. Liu72, H. Liu6, Q.
Liu6, S. Liu4, A. Lobo Salvia45, A. Loi27, J. Lomba Castro46, I. Longstaff59,
J.H. Lopes2, S. Lopez Solino46, G.H. Lovell55, Y. Lu4, C. Lucarelli22, D.
Lucchesi28,l, S. Luchuk39, M. Lucio Martinez32, V. Lukashenko32,52, Y. Luo3,
A. Lupato62, E. Luppi21,f, O. Lupton56, A. Lusiani29,m, X. Lyu6, L. Ma4, R.
Ma6, S. Maccolini20,d, F. Machefert11, F. Maciuc37, V. Macko49, P.
Mackowiak15, S. Maddrell-Mander54, O. Madejczyk34, L.R. Madhan Mohan54, O.
Maev38, A. Maevskiy82, D. Maisuzenko38, M.W. Majewski34, J.J. Malczewski35, S.
Malde63, B. Malecki48, A. Malinin81, T. Maltsev43,u, H. Malygina17, G.
Manca27,e, G. Mancinelli10, D. Manuzzi20,d, D. Marangotto25,i, J. Maratas9,s,
J.F. Marchand8, U. Marconi20, S. Mariani22,g, C. Marin Benito48, M.
Marinangeli49, J. Marks17, A.M. Marshall54, P.J. Marshall60, G. Martelli78, G.
Martellotti30, L. Martinazzoli48,j, M. Martinelli26,j, D. Martinez Santos46,
F. Martinez Vidal47, A. Massafferri1, M. Materok14, R. Matev48, A. Mathad50,
V. Matiunin41, C. Matteuzzi26, K.R. Mattioli87, A. Mauri32, E. Maurice12, J.
Mauricio45, M. Mazurek48, M. McCann61, L. Mcconnell18, T.H. Mcgrath62, N.T.
Mchugh59, A. McNab62, R. McNulty18, J.V. Mead60, B. Meadows65, G. Meier15, N.
Meinert76, D. Melnychuk36, S. Meloni26,j, M. Merk32,80, A. Merli25,i, L. Meyer
Garcia2, M. Mikhasenko48, D.A. Milanes74, E. Millard56, M. Milovanovic48,
M.-N. Minard8, A. Minotti26,j, L. Minzoni21,f, S.E. Mitchell58, B. Mitreska62,
D.S. Mitzel15, A. Mödden 15, R.A. Mohammed63, R.D. Moise61, S. Mokhnenko82, T.
Mombächer46, I.A. Monroy74, S. Monteil9, M. Morandin28, G. Morello23, M.J.
Morello29,m, J. Moron34, A.B. Morris75, A.G. Morris56, R. Mountain68, H. Mu3,
F. Muheim58,48, M. Mulder48, D. Müller48, K. Müller50, C.H. Murphy63, D.
Murray62, P. Muzzetto27,48, P. Naik54, T. Nakada49, R. Nandakumar57, T.
Nanut49, I. Nasteva2, M. Needham58, I. Neri21, N. Neri25,i, S. Neubert75, N.
Neufeld48, R. Newcombe61, E.M. Niel11, S. Nieswand14, N. Nikitin40, N.S.
Nolte64, C. Normand8, C. Nunez87, A. Oblakowska-Mucha34, V. Obraztsov44, T.
Oeser14, D.P. O’Hanlon54, S. Okamura21, R. Oldeman27,e, F. Oliva58, M.E.
Olivares68, C.J.G. Onderwater79, R.H. O’Neil58, J.M. Otalora Goicochea2, T.
Ovsiannikova41, P. Owen50, A. Oyanguren47, K.O. Padeken75, B. Pagare56, P.R.
Pais48, T. Pajero63, A. Palano19, M. Palutan23, Y. Pan62, G. Panshin84, A.
Papanestis57, M. Pappagallo19,c, L.L. Pappalardo21,f, C. Pappenheimer65, W.
Parker66, C. Parkes62, B. Passalacqua21, G. Passaleva22, A. Pastore19, M.
Patel61, C. Patrignani20,d, C.J. Pawley80, A. Pearce48, A. Pellegrino32, M.
Pepe Altarelli48, S. Perazzini20, D. Pereima41, A. Pereiro Castro46, P.
Perret9, M. Petric59,48, K. Petridis54, A. Petrolini24,h, A. Petrov81, S.
Petrucci58, M. Petruzzo25, T.T.H. Pham68, A. Philippov42, L. Pica29,m, M.
Piccini78, B. Pietrzyk8, G. Pietrzyk49, M. Pili63, D. Pinci30, F. Pisani48, M.
Pizzichemi26,48,j, Resmi P.K10, V. Placinta37, J. Plews53, M. Plo Casasus46,
F. Polci13, M. Poli Lener23, M. Poliakova68, A. Poluektov10, N. Polukhina83,t,
I. Polyakov68, E. Polycarpo2, S. Ponce48, D. Popov6,48, S. Popov42, S.
Poslavskii44, K. Prasanth35, L. Promberger48, C. Prouve46, V. Pugatch52, V.
Puill11, H. Pullen63, G. Punzi29,n, H. Qi3, W. Qian6, J. Qin6, N. Qin3, R.
Quagliani49, B. Quintana8, N.V. Raab18, R.I. Rabadan Trejo6, B. Rachwal34,
J.H. Rademacker54, M. Rama29, M. Ramos Pernas56, M.S. Rangel2, F.
Ratnikov42,82, G. Raven33, M. Reboud8, F. Redi49, F. Reiss62, C. Remon
Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S. Ricciardi57, K. Rinnert60,
P. Robbe11, G. Robertson58, A.B. Rodrigues49, E. Rodrigues60, J.A. Rodriguez
Lopez74, E.R.R. Rodriguez Rodriguez46, A. Rollings63, P. Roloff48, V.
Romanovskiy44, M. Romero Lamas46, A. Romero Vidal46, J.D. Roth87, M.
Rotondo23, M.S. Rudolph68, T. Ruf48, R.A. Ruiz Fernandez46, J. Ruiz Vidal47,
A. Ryzhikov82, J. Ryzka34, J.J. Saborido Silva46, N. Sagidova38, N. Sahoo56,
B. Saitta27,e, M. Salomoni48, C. Sanchez Gras32, R. Santacesaria30, C.
Santamarina Rios46, M. Santimaria23, E. Santovetti31,p, D. Saranin83, G.
Sarpis14, M. Sarpis75, A. Sarti30, C. Satriano30,o, A. Satta31, M. Saur15, D.
Savrina41,40, H. Sazak9, L.G. Scantlebury Smead63, A. Scarabotto13, S.
Schael14, S. Scherl60, M. Schiller59, H. Schindler48, M. Schmelling16, B.
Schmidt48, S. Schmitt14, O. Schneider49, A. Schopper48, M. Schubiger32, S.
Schulte49, M.H. Schune11, R. Schwemmer48, B. Sciascia23,48, S. Sellam46, A.
Semennikov41, M. Senghi Soares33, A. Sergi24,h, N. Serra50, L. Sestini28, A.
Seuthe15, Y. Shang5, D.M. Shangase87, M. Shapkin44, I. Shchemerov83, L.
Shchutska49, T. Shears60, L. Shekhtman43,u, Z. Shen5, V. Shevchenko81, E.B.
Shields26,j, Y. Shimizu11, E. Shmanin83, J.D. Shupperd68, B.G. Siddi21, R.
Silva Coutinho50, G. Simi28, S. Simone19,c, N. Skidmore62, T. Skwarnicki68,
M.W. Slater53, I. Slazyk21,f, J.C. Smallwood63, J.G. Smeaton55, A. Smetkina41,
E. Smith50, M. Smith61, A. Snoch32, M. Soares20, L. Soares Lavra9, M.D.
Sokoloff65, F.J.P. Soler59, A. Solovev38, I. Solovyev38, F.L. Souza De
Almeida2, B. Souza De Paula2, B. Spaan15, E. Spadaro Norella25,i, P.
Spradlin59, F. Stagni48, M. Stahl65, S. Stahl48, S. Stanislaus63, O.
Steinkamp50,83, O. Stenyakin44, H. Stevens15, S. Stone68, M. Straticiuc37, D.
Strekalina83, F. Suljik63, J. Sun27, L. Sun73, Y. Sun66, P. Svihra62, P.N.
Swallow53, K. Swientek34, A. Szabelski36, T. Szumlak34, M. Szymanski48, S.
Taneja62, A.R. Tanner54, M.D. Tat63, A. Terentev83, F. Teubert48, E. Thomas48,
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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
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. 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
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong
Joint Laboratory of Quantum Matter, Institute of Quantum Matter, South China
Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77Eotvos Lorand University, Budapest, Hungary, associated to 48
78INFN Sezione di Perugia, Perugia, Italy, associated to 21
79Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
80Universiteit Maastricht, Maastricht, Netherlands, associated to 32
81National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
82National Research University Higher School of Economics, Moscow, Russia,
associated to 42
83National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
84National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
85DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
86Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden,
associated to 59
87University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Genova, Genova, Italy
iUniversità degli Studi di Milano, Milano, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Modena e Reggio Emilia, Modena, Italy
lUniversità di Padova, Padova, Italy
mScuola Normale Superiore, Pisa, Italy
nUniversità di Pisa, Pisa, Italy
oUniversità della Basilicata, Potenza, Italy
pUniversità di Roma Tor Vergata, Roma, Italy
qUniversità di Siena, Siena, Italy
rUniversità di Urbino, Urbino, Italy
sMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
tP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
uNovosibirsk State University, Novosibirsk, Russia
†Deceased