EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-110 LHCb-PAPER-2021-010 31 July 2021

Measurement of prompt charged-particle production

in $p$ $p$ collisions at ${\sqrt{s}=13\text{\,Te\kern-2.07413ptV}}$

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

The differential cross-section of prompt inclusive production of long-lived
charged particles in proton-proton collisions is measured using a data sample
recorded by the LHCb experiment at a centre-of-mass energy of
${\sqrt{s}=13\text{\,Te\kern-1.00006ptV}}$. The data sample, collected with an
unbiased trigger, corresponds to an integrated luminosity of
$5.4\text{\,nb}^{-1}$. The differential cross-section is measured as a
function of transverse momentum and pseudorapidity in the ranges
${p_{\mathrm{T}}\in[0.08,10)\text{\,Ge\kern-1.00006ptV\\!/}c}$ and
${\eta\in[2.0,4.8)}$ and is determined separately for positively and
negatively charged particles. The results are compared with predictions from
various hadronic-interaction models.

Submitted to JHEP

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

##  1 Introduction

Hadron production in inelastic high-energy proton-proton ($p$ $p$) collisions
is dominated by soft processes of quantum chromodynamics (QCD). Most of the
hadron production cannot be calculated from first principles in perturbative
QCD due to the small average momentum transfer. Instead, predictions are based
on phenomenological models. The determination of their parameters relies on
input from experiments. Monte Carlo event generators, in which these models
are implemented, are used at the Large Hadron Collider (LHC) to simulate the
final-state particles originating from the soft component of a collision. An
introduction to soft-QCD theories is presented in Refs. [1, 2, 3, 4, 5].

In the field of cosmic-ray research, generators are employed to simulate
interactions of ultra-relativistic nuclei with the atmosphere of the Earth,
which induce extensive particle cascades, referred to as air showers. Although
often used to predict interactions in a phase space that is not covered by the
input from experiments, the generators are remarkably successful at describing
many features of air showers. However, a long-standing excess is observed in
the number of muons produced in high-energy air showers compared to
simulations, termed the Muon Puzzle [6, 7]. Measurements of the production of
light hadrons in the forward region are needed to further guide and constrain
the models [8, 9, 10]. Since the LHCb detector covers the forward
pseudorapidity range, studies performed in its acceptance are of particular
interest for cosmic-ray research.

A suitable proxy for the prompt production of light hadrons is the production
of prompt charged long-lived particles. Precision measurements of prompt
charged-particle production in collisions at the  TeV energy scale are needed
to validate and tune the hadronic-interaction models and to safely extrapolate
them to even higher collision energies that are of interest in astroparticle
physics. This tuning results in a more accurate simulation, which is
essential, e.g., in searches for physics beyond the Standard Model. These
measurements specifically address the question whether the pseudorapidity
distributions of hadrons are narrow or wide [10]. Approaches based on Gribov-
Regge field theory model soft and hard Pomeron interactions. In the approach
used by Sibyll 2.3d [11] and DPMJet III [12, 13], the two regimes are rather
decoupled and the pseudorapidity distribution is narrow, while the approach
used by EPOS-LHC [14] and QGSJet II-04 [15] produces wider distributions.

In this paper, a measurement of the differential cross-section of inclusive
production of prompt long-lived charged particles, i.e. primarily of pions,
kaons and protons, in $p$ $p$ collisions is presented. The data sample was
recorded by the LHCb experiment at a centre-of-mass energy of
${\sqrt{s}=13\text{\,Te\kern-1.00006ptV}}$ in 2015 and corresponds to an
integrated luminosity of $5.4\text{\,nb}^{-1}$. The differential cross-section
is measured as a function of transverse momentum and pseudorapidity in the
ranges ${p_{\mathrm{T}}\in[0.08,10.00)\text{\,Ge\kern-1.00006ptV\\!/}c}$ and
${\eta\in[2.0,4.8)}$ and is determined separately for positively and
negatively charged particles. Both the charge-combined differential cross-
section and the ratio of the differential cross-sections for the two charges
are compared with predictions from four different hadronic-interaction models.

The paper is structured as follows. In Sect. 2, the detector as well as the
data and simulated samples used in this measurement are described. The
analysis strategy is presented in Sect. 3. The efficiencies and the background
contributions are detailed in Sects. 4 and 5, respectively. In Sect. 6, the
results are discussed, and a summary is provided in Sect. 7.

##  2 Detector and data sample

The LHCb detector [16, 17] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of the momentum, $p$,
of charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200$\text{\,Ge\kern-1.00006ptV\\!/}c$. The minimum
distance of a track to a primary $pp$ collision vertex, the impact parameter,
is measured with a resolution of $(15+29/p_{\mathrm{T}})\,\upmu\text{m}$,
where $p_{\mathrm{T}}$ is the component of the momentum transverse to the
beam, in $\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged
hadrons are distinguished using information from two ring-imaging Cherenkov
detectors. Photons, electrons and hadrons are identified by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic and a hadronic calorimeter. Muons are identified by a system
composed of alternating layers of iron and multiwire proportional chambers.

The online event selection for this measurement is performed by an unbiased
trigger. Therefore, no trigger-related systematic uncertainty arises. At the
hardware stage, events are accepted at a fixed rate. The software stage then
restricts the data sample to collisions of leading bunches of the LHC bunch
trains, which avoids background from previous events, while the bunch spacing
of $50\text{\,ns}$ in these low-intensity runs avoids contributions to the
read-out from following events. The analysed data sample contains the events
from two LHC fills, recorded with opposite magnetic-field configurations of
the LHCb dipole magnet. The field configuration that bends positively
(negatively) charged particles in the horizontal plane towards the centre of
the LHC ring is referred to as upwards (downwards). The fill recorded with the
magnetic field pointing upwards comprises ${226\times 10^{6}}$ events and
corresponds to an integrated luminosity of $3.0\text{\,nb}^{-1}$, while the
fill recorded with the magnetic field pointing downwards comprises ${134\times
10^{6}}$ events and corresponds to an integrated luminosity of
$2.4\text{\,nb}^{-1}$. The average numbers of collisions in a bunch crossing
are $0.9$ and $0.7$ for these two fills, respectively. The results are
obtained from the combined data sample, but as a cross-check, the analysis is
also performed separately for each fill. To measure the background from
interactions of the beams with residual gas in the beam pipe, beam-gas
collisions are used, where only one of the two beams traverses the detector.
Such collisions were also collected for each fill.

Simulation is required to model the effects of the imposed selection
requirements and to study the background contributions. In the simulation,
$pp$ collisions are generated using Pythia [18, *Sjostrand:2006za] with a
specific LHCb configuration [20]. Decays of unstable particles are described
by EvtGen [21], in which final-state radiation is generated using Photos [22].
The interaction of the generated particles with the detector, and its
response, are implemented using the Geant4 toolkit [23, *Agostinelli:2002hh]
as described in Ref. [25]. For each of the two magnetic-field configurations,
a trigger-unbiased sample containing $10^{7}$ events was simulated.

##  3 Analysis strategy

Based on a particle count, $n$, in a pseudorapidity interval with a width of
$\Delta\eta$ and a transverse-momentum interval with a width of $\Delta
p_{\mathrm{T}}$ that is obtained from a data set corresponding to an
integrated luminosity of $\mathcal{L}$, the differential cross-section is
determined as

$\frac{\mathrm{d}^{2}\sigma}{\mathrm{d}\eta\,\mathrm{d}p_{\mathrm{T}}}\equiv\frac{n}{\mathcal{L}\,\Delta\eta\,\Delta
p_{\mathrm{T}}}\,.$ (1)

It is computed in finite intervals. The signal in this analysis is the number
of prompt long-lived charged particles produced in beam-beam collisions. A
particle is classified as a long-lived particle if its lifetime is greater
than $30\text{\,ps}$, and prompt if it is produced directly in the primary
interaction or if none of its ancestor particles is long-lived [26]. Long-
lived charged particles are electrons, muons, pions, kaons and protons as well
as ${\mathchar 28934\relax}{}^{+}$, ${\mathchar 28934\relax}{}^{-}$,
${\mathchar 28932\relax}^{-}$ and ${\mathchar 28938\relax}^{-}$ baryons and
their antiparticles.

Tracks that traverse the entire tracking system are selected as candidates for
prompt long-lived charged particles. Among these tracks, some are fakes. One
type of fake tracks does not correspond to any real particle. Their
contribution is reduced by imposing a requirement on the fake-track
probability, provided by a neural-network-based algorithm [27], but the
remaining contribution is still non-negligible. The second type of fake tracks
occurs when two or more tracks are reconstructed for one real particle. Their
contribution is suppressed below the level of $0.1\,\%$ in all kinematic
intervals by the reconstruction software, and is negligible in this analysis.
Non-prompt tracks passing the selection are another source of background.
These tracks originate from interactions of particles with the detector
material, interactions of the beams with residual gas or from decays of long-
lived particles.

Consequently, the number of candidate tracks, $n_{\mathrm{cand}}$, is related
to the number of signal particles, $n$, according to

$n_{\mathrm{cand}}={\varepsilon}\,n+\sum_{i}n_{i}\,,$ (2)

where $\varepsilon$ denotes the total efficiency, i.e. the product of the
geometric acceptance of the detector, the track-reconstruction efficiency and
the selection efficiency, and the sum includes the numbers of background
tracks, $n_{i}$, from source $i$. The values of $\varepsilon$ and $n_{i}$ are
taken from simulation. To correct for imperfect modelling, control
measurements are performed, and the simulation is adjusted. For this purpose,
observables, $\mathcal{P}_{i}$, that are proportional to $n_{i}$ are chosen as
proxies. The proxies for different sources of background are described in
Sect. 5. The ratio of the background counts in data and simulation is assumed
to be equal to the ratio of the proxies in data and simulation,

$\frac{n_{i}}{n_{i,\,\mathrm{sim}}}=\frac{\mathcal{P}_{i}}{\mathcal{P}_{i,\,\mathrm{sim}}}\equiv
R_{i}\,,$ (3)

which allows the background count in data to be estimated as
${n_{i}=R_{i}\,n_{i,\,\mathrm{sim}}}$.

The background induced by beam-gas interactions, which are not simulated, is
determined from the number of candidate tracks, $n_{\mathrm{gas}}$, produced
in the recorded beam-gas events. Both the configuration where the beam travels
from the vertex detector towards the muon system and the opposite
configuration are included. The contributions from these configurations are
scaled to the corresponding number of recorded beam-beam events.

In summary, the number of signal particles in Eq. (1) can be expressed as

$n=\frac{1}{R_{\varepsilon}\,{\varepsilon}_{\mathrm{sim}}}\left(n_{\mathrm{cand}}-\sum_{i}R_{i}\,n_{i,\,\mathrm{sim}}-n_{\mathrm{gas}}\right),$
(4)

where $R_{\varepsilon}$ is a correction to the total efficiency in simulation.

Due to the slow variation of the differential cross-section in $\eta$, only
six intervals in $\eta$ are used with ${\Delta\eta=0.5}$. The width of the
last interval, ${\eta\in[4.5,4.8)}$, is reduced to match the acceptance of the
tracking system. Since the differential cross-section has a power-law shape in
$p_{\mathrm{T}}$, 50 logarithmic intervals are used in the range
${p_{\mathrm{T}}\in[0.01,10.00)\text{\,Ge\kern-1.00006ptV\\!/}c}$ with
${\Delta\\!\log_{10}(p_{\mathrm{T}}/(\\!\text{\,Ge\kern-1.00006ptV\\!/}c))=0.06}$.
The limit of the kinematic acceptance, i.e. the minimum momentum of
approximately $2\text{\,Ge\kern-1.00006ptV\\!/}c$ for a particle to reach the
tracking stations downstream of the magnet, introduces a lower limit on
$p_{\mathrm{T}}$ depending on $\eta$. In this analysis, a tighter requirement
${p>5\text{\,Ge\kern-1.00006ptV\\!/}c}$ is used, since a correction of the
efficiency, which is described in Sect. 4, is based on the two control
measurements presented in Refs. [28, 29], which both applied this requirement.

The track-reconstruction efficiency depends on the detector occupancy. To
ensure that the simulation reproduces the occupancy observed in data, weights
are assigned to the simulated events. The number of tracks that traverse the
entire tracking system is used as a proxy for the occupancy. Simulated events
are weighted by the ratio of the distributions of the number of these tracks
in data and simulation according to the occupancy of the event. Each of the
two simulated samples is weighted to reproduce the occupancy of the LHC fill
with the same magnetic-field configuration. As a cross-check, the chosen proxy
for the occupancy is compared to an alternative proxy, the number of hits in
the scintillating-pad detector, which is not affected by possible artefacts of
the track reconstruction. A linear relation is observed between the number of
tracks that traverse the entire tracking system and the number of hits in the
scintillating-pad detector, confirming this choice of the proxy for the
detector occupancy.

The ROOT [30] and LHCb [31, 32] software frameworks are used for the initial
data preparation, while the analysis is written in the Python language with
standard scientific packages [33, 34, 35, 36, 37, 38] and high-energy-physics-
specific packages [39, 40, 41, 42] from the Scikit-HEP project [43].

##  4 Efficiencies

The total efficiency to observe prompt long-lived charged particles depends on
the geometric acceptance of the detector, the track-reconstruction efficiency
and the particle loss due to decays or interactions with the detector
material. This loss depends on the particle composition and the amount of
traversed material. The detector acceptance and the reconstruction efficiency
are taken from simulation, and validated against data [28]. For the two other
types of efficiencies, corrections are applied in each kinematic interval,
which are described in the following.

First, the track-reconstruction efficiency is corrected. This is based on
results of a separate control measurement [28], in which muon tracks from
${{J\mskip-3.0mu/\mskip-2.0mu\psi}}\\!\rightarrow{\mu^{+}\mu^{-}}$ decays were
studied to determine ratios of the track-reconstruction efficiencies in data
and simulation in intervals of $\eta$ and $p$. A linear transformation matrix
is built to map the results of the efficiency ratios in the control
measurement, which was performed in different kinematic intervals, onto the
intervals of this measurement. Non-uniform track density is accounted for in
this transformation. The obtained efficiency ratios are identical for both
particle charges and are used as the first component of the correction to the
efficiency in simulation. The uncertainty of this component is between $1\,\%$
and $5\,\%$ over the kinematic range.

Second, the simulated particle composition is corrected by splitting the
charged particles into four classes per charge; charged pions, charged kaons,
protons, and a category for all other prompt long-lived charged particles; and
then adjusting the relative yield of each class. As this composition has not
yet been measured in $p$ $p$ collisions at
${\sqrt{s}=13\text{\,Te\kern-1.00006ptV}}$, measurements of ratios of prompt
hadron production in $p$ $p$ collisions at
${\sqrt{s}=0.9\text{\,Te\kern-1.00006ptV}}$ and $7\text{\,Te\kern-1.00006ptV}$
that were performed by the LHCb collaboration [29] are extrapolated to
$13\text{\,Te\kern-1.00006ptV}$. The extrapolations of the
${\overline{p}}/{p}$, ${({{K}^{+}}+{{K}^{-}})/({{\pi}^{+}}+{{\pi}^{-}})}$ and
${({p}+{\overline{p}})/({{\pi}^{+}}+{{\pi}^{-}})}$ ratios are defined as
linear functions of $\ln\sqrt{s}$. The largest deviations of up to $40\,\%$
are observed between the extrapolated and simulated
${({p}+{\overline{p}})/({{\pi}^{+}}+{{\pi}^{-}})}$ ratios.

Then, double ratios of the extrapolated hadron ratios and the corresponding
ratios of the particle counts in simulation are formed. For each $\eta$
interval and each particle charge, corrections to the counts of charged pions,
charged kaons, protons and other prompt long-lived charged particles in
simulation are defined as functions linear in $\ln p_{\mathrm{T}}$. To
determine the corrected particle counts for the last three of these particle
classes, double ratios of the hadron ratios obtained from the corrected
particle counts and the hadron ratios obtained from the original particle
counts in simulation are fitted to the double ratios from the extrapolations.
The double ratios that are fitted have only a small variability within the
$\eta$ and $p_{\mathrm{T}}$ intervals of the control measurement, over which
the particle counts are integrated, reflecting that no strong dependence on
these variables is observed. The corrected count of charged pions is computed
from the condition that the composition correction cannot change the total
number of particles. The reference hadron ratios do not cover the intervals
${\eta\in[2.0,2.5)}$ and ${\eta\in[4.5,4.8)}$. In these intervals, the values
from the corresponding adjacent $\eta$ interval are used. As the corrected
particle counts cannot completely be determined from the available data,
Gaussian penalty terms are introduced as a regularisation to suppress
deviations above $5\,\%$ of the corrected counts from their initial values.

Figure 1: Efficiencies for different particle species in intervals of $\eta$
and as a function of $p_{\mathrm{T}}$ for the simulated sample generated with
the magnetic field pointing upwards. The product of the efficiency and the
particle charge in units of the elementary charge is shown to separate values
for oppositely charged particles. The light-grey areas indicate the limit of
the kinematic acceptance.

For each charge, the composition-corrected efficiency in simulation is
computed by summing the products of the efficiencies for the four particle
classes and their corrected fractions. The efficiencies,
${\varepsilon}_{\mathrm{sim}}$, are shown in Fig. 1. The efficiency for the
fourth class of other prompt long-lived charged particles is the lowest,
because this class contains ${\mathchar 28934\relax}{}^{+}$, ${\mathchar
28934\relax}{}^{-}$, ${\mathchar 28932\relax}^{-}$ and ${\mathchar
28938\relax}^{-}$ baryons and their antiparticles, which have the shortest
lifetimes. The correction is not charge symmetric due to different hadronic-
interaction cross-sections of each particle and its antiparticle, inducing
different efficiencies. The systematic uncertainty of this correction
dominates over its statistical uncertainty. Half of the correction is assigned
as a systematic uncertainty as a conservative estimate, which is at most
$2.5\,\%$.

Material interactions contribute to the uncertainty of the corrected
efficiency as the simulated amount of material has an uncertainty of $10\,\%$,
which is described in Ref. [28]. Here, the interaction losses of charged pions
and charged kaons are estimated to be $14\,\%$ and $11\,\%$, respectively. For
protons, the loss can be estimated from the difference between the efficiency
for protons in simulation and that for muons. Since protons do not decay, any
loss relative to muons, for which interactions are negligible, is caused by
material interactions. The loss is found to be between $20\,\%$ and $30\,\%$
across the full kinematic range. It is generally larger at low
$p_{\mathrm{T}}$ and for antiprotons across the full kinematic range. These
losses and their uncertainty are proportional to the amount of material. In
the computation of the corresponding uncertainty of the efficiency, the
uncertainties of the individual efficiencies for pions, kaons and protons
contribute according to their corrected fractions. This results in an
uncertainty of approximately $1\,\%$. The contribution from other prompt long-
lived charged particles is neglected as their loss is dominated by decays and
not by material interactions.

Figure 2: Efficiency corrections, $R_{\varepsilon}$, for positively and
negatively charged particles in intervals of $\eta$ and as a function of
$p_{\mathrm{T}}$ for the simulated sample generated with the magnetic field
pointing upwards. The bands indicate the systematic uncertainty. The light-
grey areas represent the limit of the kinematic acceptance. The gap between
this limit and the correction is due to the tighter requirement of
${p>5\text{\,Ge\kern-1.00006ptV\\!/}c}$ applied to the control measurements on
which this correction is based.

The combined correction is shown in Fig. 2 and reduces the original efficiency
in simulation by up to $5\,\%$ for negatively charged particles. This
reduction arises primarily from the increase in the fraction of other prompt
long-lived charged particles, which have a lower efficiency.

The systematic uncertainty of the corrected efficiency is the sum of the
contributions from the ratios of track-reconstruction efficiencies, the
particle-composition correction, material interactions and the statistical
uncertainty of the simulated samples. This uncertainty ranges between
$0.06\,\%$ and $2\,\%$, depending on the kinematic interval, while the total
uncertainty ranges from $0.9\,\%$ to $5.1\,\%$.

##  5 Background contributions

Figure 3: Origins of the candidate tracks in intervals of $\eta$ and as a
function of $p_{\mathrm{T}}$ for the simulated sample generated with the
magnetic field pointing upwards. The prompt category refers to the signal
tracks, while the other categories correspond to non-prompt tracks originating
from the listed parent particles and include both decays and material
interactions. Fake tracks are indicated by the white areas above the stacked
histograms. The light-grey areas represent the limit of the kinematic
acceptance.

The origins of the candidate tracks in simulation are shown in Fig. 3. Prompt
long-lived charged particles constitute more than $85\,\%$ of the candidate
tracks around ${p_{\mathrm{T}}=1\text{\,Ge\kern-1.00006ptV\\!/}c}$, but
towards lower or higher values of $p_{\mathrm{T}}$, the background
contributions increase. These background contributions are quantified using
simulation and adjusted with correction factors from proxies obtained from
data and simulation. The background contributions that are sufficiently large
to require a correction are: fake tracks, tracks originating from material
interactions of charged pions and from photon conversions, and tracks produced
in decays of strange hadrons. In the following subsections, the proxies
constructed for these sources of background are presented. The remaining
sources, which are not adjusted, are combined and an uncertainty of $50\,\%$
is assumed for their contribution. The uncertainty of the differential cross-
section resulting from this assumption is negligible, as the contribution from
the remaining sources of background is small.

###  5.1 Fake tracks

The largest background at the limits of the analysed $p_{\mathrm{T}}$ range is
from fake tracks. These are characterised by having a low quality of the track
fit and missing hits in instrumented detector parts. This information is
combined with further variables from the tracking system to estimate a fake-
track probability, $P_{\mathrm{fake}}$. The imposed selection requirement,
${P_{\mathrm{fake}}<0.3}$, rejects between $40\,\%$ and $80\,\%$ of the fake
tracks and retains $99\,\%$ of the real tracks.

Figure 4: Distributions of $P_{\mathrm{fake}}$ in a kinematic interval (left)
at low $p_{\mathrm{T}}$ and (right) at high $p_{\mathrm{T}}$ for the LHC fill
recorded with the magnetic field pointing upwards and the simulated sample
with the same magnetic-field configuration. The statistical uncertainty of the
data is indicated by error bars, but they are not visible on these scales. The
purity of the proxy is shown in the lower subplots, where light-grey boxes
represent the $P_{\mathrm{fake}}$ interval selected to determine the proxy.
Vertical lines indicate the threshold ${P_{\mathrm{fake}}<0.3}$ for candidate
tracks.

For each kinematic interval and each particle charge, data and simulation are
divided into ten equal-width intervals in the $P_{\mathrm{fake}}$ variable.
Distributions in two different kinematic intervals are given as examples in
Fig. 4. In simulation, a pure sample of fake tracks is present at high
$P_{\mathrm{fake}}$ values. Generally, good agreement is found in the shapes
of the $P_{\mathrm{fake}}$ distributions between data and simulation, but in
simulation, fewer fake tracks are observed. Consequently, a correction is used
to adjust the simulated contribution from fake tracks.

The number of tracks in the first interval of the $P_{\mathrm{fake}}$
distribution above 0.3, where the fake-track purity is greater than 80 %, is
chosen as a proxy for fake tracks. This choice balances two sources of
systematic uncertainty. A $P_{\mathrm{fake}}$ interval with a high fake-track
purity is required in order to select a proxy that is insensitive to possible
differences in the number of signal tracks between data and simulation, which
would favour the interval with the highest purity. However, selecting an
interval close to the $P_{\mathrm{fake}}$ region of interest,
${P_{\mathrm{fake}}<0.3}$, minimises the impact of shape differences in the
$P_{\mathrm{fake}}$ distributions between data and simulation.

The uncertainty of the fake-track proxy is the quadratic sum of statistical
and systematic contributions. The statistical uncertainty is propagated from
the track counts in data and simulation. The systematic uncertainty is
estimated by computing an alternative proxy. For this, the integral of the
track counts in the selected $P_{\mathrm{fake}}$ interval and all the
intervals above is used. The alternative proxy is more affected by shape
differences and is therefore an upper limit on the systematic error. This type
of systematic variation is modelled with a uniform distribution of deviations
of which the upper limit corresponds to the alternative proxy, while the
centre is the value of the default proxy. The uncertainty of the proxy is then
given by the standard deviation of this distribution.

Figure 5: Ratio of the proxies for fake tracks in data and simulation in
intervals of $\eta$ and as a function of $p_{\mathrm{T}}$ for the LHC fill
recorded with the magnetic field pointing upwards and the simulated sample
with the same magnetic-field configuration. The mean of the proxy ratios for
positively and negatively charged particles is shown. The error bars indicate
the statistical uncertainty, and the boxes indicate the systematic
uncertainty. The light-grey areas represent the limit of the kinematic
acceptance.

The mean of the resulting proxy ratios between the two particle charges is
shown in Fig. 5. At low $\eta$, values of the proxy ratio of up to $2.8$ are
observed, but in those kinematic intervals in which the background from fake
tracks is large, the ratio is between $1.2$ and $1.4$. In general, the ratio
is smooth as a function of $p_{\mathrm{T}}$. Discontinuities in the range
${\eta\in[2.5,3.5)}$ are caused by changes of the $P_{\mathrm{fake}}$ interval
chosen to determine the proxy.

###  5.2 Material interactions

Non-prompt tracks produced in material interactions constitute the second-
largest source of background. As only tracks that traverse the entire tracking
system are used, these are interactions occurring inside the vertex detector.
Electrons originating from photon conversions, which populate mainly the
kinematic intervals at high $\eta$ and low $p_{\mathrm{T}}$, contribute up to
$20\,\%$ to the candidate tracks, while charged particles stemming from
hadronic material interactions of charged pions contribute less than $5\,\%$.

The number of tracks originating from charged-pion material interactions is
proportional to the product of the total particle flux, consisting primarily
of charged pions, and the amount of traversed material. The number of tracks
included in vertices comprising three tracks is chosen as a proxy for this
product. The threshold of three tracks is used because hadronic interactions
frequently produce three or more charged particles, while decays into three or
more charged particles are rare in the analysed data sample. This approach is
similar to that presented in Ref. [44]. Instead of defining a separate proxy
for photon conversions, their simulated yield is scaled with the proxy for
charged-pion material interactions. This is motivated by the observation that
most photons originate from decays of neutral pions, which are produced in a
fixed ratio to charged pions due to isospin symmetry. Furthermore, the
conversion probability of photons and the interaction probability of charged
pions are both proportional to the amount of material.

In each event, all unique combinations of three candidate tracks are formed.
Their point of closest approach is computed with a vertex fit minimising the
sum of the squared distances of the tracks. This point is the candidate vertex
of an interaction. To reduce combinatorial background, where three tracks are
randomly associated with a common vertex, a lower limit is imposed on the
distance of the vertex from the $z$ axis, which points from the radial centre
of the vertex detector along the beam axis towards the muon system and has its
origin close to the average primary vertex. This discards the region in which
no material is present.

The purity of the obtained sample of vertices is further increased by applying
requirements that are optimised using simulation. First, a simultaneous
optimisation of a lower limit on the $z$ coordinate of the vertex and an upper
limit on the sum of the squared distances of the tracks to their associated
vertex, $d$, is performed without subdividing the sample in $\eta$ and
$p_{\mathrm{T}}$. The $z$ requirement suppresses combinatorial background by
selecting vertices downstream of the region in which most of the primary
vertices are reconstructed. The upper limit on $d$ rejects random combinations
by requiring that the tracks are compatible with originating from a single
point. Second, an optimisation of a lower limit on the mass of the three-track
combination is performed separately for each kinematic interval. As the
species of the produced particles are not known, a zero-mass hypothesis is
assigned to each track. Wider $p_{\mathrm{T}}$ intervals are used in this
study to reduce fluctuations in the proxy ratio to be determined, created by
successively merging groups of three adjacent $p_{\mathrm{T}}$ intervals. The
mass requirement further suppresses the combinatorial background. For both
optimisations, the figure of merit ${S/\sqrt{S+B}}$ is used, where $S$ denotes
the number of tracks that represent the signal for this proxy, and $B$ is the
number of background tracks. The requirements chosen are those that maximise
the value of the figure of merit. This results in a lower limit on $z$ of
$290\text{\,mm}$ and an upper limit on $d$ of $0.1\text{\,mm}^{2}$.

After the application of all optimised requirements, the contribution from
charged pions is approximately equal in size to that from other particles,
e.g. kaons or protons. For each kinematic interval and each particle charge,
the number of tracks that are included in selected vertices is used as the
proxy. In the first two $\eta$ intervals and around
${p_{\mathrm{T}}=0.5\text{\,Ge\kern-1.00006ptV\\!/}c}$, the highest values of
the purity of charged-pion interactions are obtained, which range from
$40\,\%$ to $45\,\%$. Towards higher values of $\eta$ and lower or higher
values of $p_{\mathrm{T}}$, the purity decreases.

The proxy ratio is independent of the purity for kinematic intervals with
purities above $30\,\%$. Therefore, the value of the proxy ratio,
$R_{\mathrm{mat}}$, is only used if the purity in the kinematic interval under
consideration is greater than the threshold value of $30\,\%$. Moreover, an
upper limit of $30\,\%$ is imposed on the statistical uncertainty of the
purity to reject intervals that contain only a small number of tracks. As a
substitute for the values of the proxy ratio in the intervals below the purity
threshold, the median of the values of the proxy ratio in the intervals above
the threshold is computed. The uncertainty of this median value is estimated
assuming a uniform distribution covering the observed range of
$R_{\mathrm{mat}}$.

Figure 6: Ratio of the proxies for material interactions in data and
simulation and purity of the proxy in intervals of $\eta$ and as a function of
$p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing
upwards and the simulated sample with the same magnetic-field configuration.
The quantities are shown separately for positively and negatively charged
particles. The error bars indicate the statistical uncertainty, and the boxes
indicate the systematic uncertainty. The points are slightly displaced
horizontally within the $p_{\mathrm{T}}$ intervals to increase the visibility.
The dashed grey lines represent the purity threshold. The larger points
indicate the median value computed for the intervals below the threshold. The
light-grey areas represent the limit of the kinematic acceptance.

The systematic uncertainty of the proxy for material interactions is
determined by loosening and tightening the optimised $z$ and $d$ requirements
and computing alternative proxy ratios, $R_{\mathrm{mat}}^{\prime}$. The mass
requirement is not varied, as a good agreement is found in the shapes of the
distributions between data and simulation in all kinematic intervals.
Deviations in some of the alternative proxies cannot be explained by
statistical fluctuations and are therefore considered as a systematic
uncertainty. The deviation of an alternative is considered significant if the
condition

$(R_{\mathrm{mat}}^{\prime}-R_{\mathrm{mat}})^{2}>\left|\sigma^{2}(R_{\mathrm{mat}}^{\prime})-\sigma^{2}(R_{\mathrm{mat}})\right|$
(5)

is fulfilled, where $\sigma^{2}$ denotes the variance, which is a consequence
of using the same data set to determine the default proxy ratio and the
alternatives. Following Ref. [45], the systematic uncertainty is taken as the
standard deviation of the variations that differ significantly and the initial
ratio is replaced with the mean of the significant variations. This procedure
is applied to the values of the proxy ratio in the kinematic intervals above
the purity threshold and to the median value computed for the other intervals.
The values and the resulting uncertainties of the proxy ratio are shown in
Fig. 6.

###  5.3 Strange-hadron decays

Up to $7\,\%$ of the candidate tracks are non-prompt tracks produced in decays
of strange hadrons inside the vertex detector. Approximately $80\,\%$ of these
tracks originate from
${{K}^{0}_{\mathrm{S}}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$, ${\mathchar
28931\relax}\\!\rightarrow{p}{{\pi}^{-}}$ and ${\kern
1.79993pt\overline{\kern-1.79993pt\mathchar
28931\relax}}\\!\rightarrow{\overline{p}}{{\pi}^{+}}$ decays. The number of
${K}^{0}_{\mathrm{S}}$ mesons and $\mathchar 28931\relax$ and $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ baryons, of which
both decay products create a candidate track, is chosen as a proxy for this
background.

Candidate decays are obtained by forming pairs of oppositely charged candidate
tracks. A small set of loose requirements is used to maintain high selection
efficiency for strange decays. The distance of closest approach of the two
tracks is required to be less than $1\text{\,mm}$ and the distance along the
$z$ axis of their point of closest approach from the average primary vertex is
required to be greater than $150\text{\,mm}$. For ${K}^{0}_{\mathrm{S}}$
candidates, the mass is computed by assigning the pion-mass hypothesis to both
tracks, while for $\mathchar 28931\relax$ and $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ candidates, the
proton- and pion-mass hypotheses are assigned to the tracks.

Figure 7: Mass distributions of (left) ${K}^{0}_{\mathrm{S}}$ and (right)
$\mathchar 28931\relax$ candidates in one kinematic interval for (top) the LHC
fill recorded with the magnetic field pointing upwards and (bottom) the
simulated sample with the same magnetic-field configuration. Solid lines
indicate the total fit and dotted lines the background. In the case of
simulation, the signal and background contributions are shown for
illustration, but this information is not used in the analysis.

The distributions of ${K}^{0}_{\mathrm{S}}$ and $\mathchar 28931\relax$
candidates in one kinematic interval are shown as examples in Fig. 7.
Extended-maximum-likelihood fits [46] to the mass distributions of the
${K}^{0}_{\mathrm{S}}$, $\mathchar 28931\relax$ and $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ candidates in data
and simulation are performed separately for each $(\eta,p_{\mathrm{T}})$
interval of their kinematic distributions. As in case of the proxy for
material interactions, wider $p_{\mathrm{T}}$ intervals are used in this
study, obtained by merging groups of three adjacent $p_{\mathrm{T}}$
intervals. In the fits, the ${K}^{0}_{\mathrm{S}}$, $\mathchar 28931\relax$ or
$\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ signal is
modelled with a nonstandardised Student’s t-distribution with free location
and width parameters. The background, which is only combinatorial, is modelled
with a third-degree Bernstein polynomial. The yields in each interval of the
mass distributions are modelled with Poisson distributions for the unweighted
histograms in data and with scaled Poisson distributions [47] for the
occupancy-weighted histograms in simulation.

Figure 8: Ratio of the proxies for strange-hadron decays in data and
simulation in intervals of $\eta$ and as a function of $p_{\mathrm{T}}$ for
the LHC fill recorded with the magnetic field pointing upwards and the
simulated sample with the same magnetic-field configuration. The
$\mathit{{V^{0}}}$ model lines indicate the interpolated
${K}^{0}_{\mathrm{S}}$, $\mathchar 28931\relax$ and $\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}$ yield ratios, with
support points indicated by black dots. The lines labelled as products
represent the proxy ratio of the decay products, with the bands representing
the propagated systematic uncertainty. The light-grey areas indicate the limit
of the kinematic acceptance.

The ratios of the signal yields in data and simulation are only computed in
those kinematic intervals where a signal peak is present with a significance
of at least three standard deviations. The ratios of the signal yields are
shown in Fig. 8. In all $\eta$ intervals and for all three strange-hadron
species, a pattern is observed in the yield ratios as a function of
$p_{\mathrm{T}}$. This is interpreted as a general difference in the amount of
produced strange quarks between data and simulation, since it is the same for
a meson and a baryon. The pattern is modelled with a monotone cubic spline
[48]. A least-squares fit of the model to the yield ratios is performed, in
which a Gaussian penalty term is added in order to restrict the value of the
spline at the upper limit of the $p_{\mathrm{T}}$ range, where no data points
are present.

The fitted model is then used to determine the proxy ratio of the strange
hadrons, $R_{\mathrm{parent}}$, over the full kinematic range. However, the
background for prompt long-lived charged particles is caused by the decay
products of these hadrons. The proxy ratio of the products,
$R_{\mathrm{strange}}$, in the $(\eta,p_{\mathrm{T}})$ intervals of their
kinematic distributions is computed as

$R_{\mathrm{strange},\,k\ell}=\frac{\sum_{{h},\,ij}n_{{h},\,ijk\ell}\,R_{\mathrm{parent},\,j}}{\sum_{{h},\,ij}n_{{h},\,ijk\ell}}\,,$
(6)

where: ${h}$ is ${{K}^{0}_{\mathrm{S}}},{\mathchar 28931\relax},{\kern
1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}$; $i$ and $j$
iterate through the $\eta$ and $p_{\mathrm{T}}$ intervals of the kinematic
distributions of the parent particles, respectively; $k$ and $\ell$ iterate
through the $\eta$ and $p_{\mathrm{T}}$ intervals of the kinematic
distributions of the decay products, respectively; and $n$ is the simulated
yield of the decay products in the corresponding intervals. The ratio
$R_{\mathrm{strange}}$ is closer to unity than the ratio
$R_{\mathrm{parent}}$, as the broad kinematic distributions of the decay
products dilute deviations. The statistical uncertainty of the fitted model is
negligible compared to the systematic uncertainty suggested by the deviations
of the yield ratios from the model. A systematic uncertainty of $\pm 15\,\%$
is assigned to the proxy ratio to cover these deviations.

##  6 Results

The differential cross-section of prompt inclusive production of long-lived
charged particles is determined with Eqs. (1) and (4). The fraction of
candidate tracks originating from beam-gas interactions is found to be $1\,\%$
for the LHC fill recorded with the magnetic field pointing downwards,
independent of the kinematic interval. For the fill recorded with the magnetic
field pointing upwards, the fraction is below the level of $0.1\,\%$.

The detector resolution distorts the measured kinematic distributions, by
inducing migration between different $(\eta,p_{\mathrm{T}})$ intervals. This
distortion is between 1 % and 2 %, depending on the kinematic interval. The
total efficiency, $\varepsilon$, in this analysis implicitly takes these
migration effects into account. It is calculated from simulation as the ratio
of the number of candidate tracks that can be associated with signal particles
and the respective number of signal particles, where the candidates are sorted
into intervals using the reconstructed momenta, while the signal particles are
sorted into intervals using the generated momenta. Deviations between the
shapes of the kinematic distributions of charged particles in data and
simulation can introduce a bias in this approach, but the bias in this case is
estimated to be at the order of $0.01\,\%$ and therefore negligible.

The statistical uncertainty of the data sample is subdominant in the full
kinematic range, reaching 1.5 % at high $p_{\mathrm{T}}$. Non-Poissonian
statistical fluctuations of the candidate counts in kinematic intervals are
taken into account. Each event contributes entries to a number of kinematic
intervals, introducing statistical correlations of up to 0.4 between
intervals, and variances that are up to 50 % larger than the Poisson
expectation. The covariance matrix of these statistical fluctuations is
estimated by dividing the full sample into 100 equivalent subsets, computing
the covariance of the subsets and extrapolating the result back to the full
data set.

Figure 9: Leading sources of relative uncertainties of the number of prompt
long-lived charged particles in intervals of $\eta$ and as a function of
$p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing
upwards. The total uncertainty, represented by the grey envelopes, excludes
the uncertainty of the integrated luminosity of $2.0\,\%$. The light-grey
areas indicate the limit of the kinematic acceptance.

The uncertainty on the differential cross-section is computed from the
uncertainties of the individual terms in Eqs. (1) and (4) using full error
propagation of the respective covariance matrices. The contributions to the
uncertainty of the number of prompt long-lived charged particles are shown in
Fig. 9. The correction of the track-reconstruction efficiency is the largest
contribution in most intervals. In the range ${\eta\in[2.0,4.0)}$ and at high
$p_{\mathrm{T}}$, the uncertainty of the proxy for fake tracks dominates,
while in the range ${\eta\in[4.0,4.8)}$ and at low $p_{\mathrm{T}}$, the
uncertainty of the proxy for material interactions contributes most.

The final results are obtained by computing the average of the differential
cross-sections separately calculated for each LHC fill, after confirming that
the two separate results are consistent with each other. As a further cross-
check, data from six other fills, recorded at the same centre-of-mass energy
and with the same trigger as the default data sample, are compared and found
to be consistent with the main result.

The calculation of the covariance matrix of the combined result takes into
account that the fills have correlated and uncorrelated uncertainties.
Uncorrelated are the statistical uncertainties and the systematic
uncertainties of the proxy for fake tracks and of the proxy for material
interactions in the kinematic intervals above the purity threshold. Correlated
uncertainties are all other systematic uncertainties and the uncertainty of
the integrated luminosity. The covariance matrix of the final result is
computed assuming that the uncertainties that are fully correlated within a
fill are also fully correlated between the two fills.

Table 1: Statistical and systematic uncertainties affecting the measured differential cross-section. Source | Relative uncertainty in %
---|---
Statistical uncertainty of the data sample | 0.0– | 1.5
Total efficiency | 0.9– | 5.1
Beam-gas interactions | 0.0– | 1.7
Fake tracks | 0.1– | 9.5
Material interactions | 0.0– | 12
Strange-hadron decays | 0.0– | 1.5
Other background contributions | 0.1– | 1.1
Integrated luminosity |  2.0
Total uncertainty | 2.3– | 15

The minimum and maximum values over all kinematic intervals for the
uncertainties from each source that contribute to the final result are listed
in Table 1. The total uncertainty of the differential cross-section is between
$2.3\,\%$ and $15\,\%$, which includes the fully correlated systematic
uncertainty of $2.0\,\%$ from the integrated luminosity. The correlations are
nonzero and positive between kinematic intervals and the two particle charges,
since the systematic uncertainties dominate. The correlation matrix of the
final differential cross-section is shown in Appendix B.

Figure 10: Differential cross-section of inclusive production of prompt long-lived charged particles in intervals of pseudorapidity, $\eta$, and as a function of transverse momentum, $p_{\mathrm{T}}$. The error bars indicate the total uncertainty. The ratios of the model predictions and this measurement are shown in the lower subplots. The lines labelled as Pythia 8.1 LHCb correspond to the weighted simulated samples of this analysis. Figure 11: Ratios of the differential cross-sections of inclusive production of prompt long-lived positively and negatively charged particles as a function of transverse momentum and pseudorapidity for the data and the models shown in Fig. 10. Table 2: Inelastic cross-sections used in the models of which the predictions are compared with this measurement and values from recent measurements at the LHC. Model or experiment | Inelastic cross-section in  mb
---|---
Pythia 8.3 [18, *Sjostrand:2006za] | $78.05$
EPOS-LHC [14] | $78.98$
QGSJet II-04 [15] | $80.17$
Sibyll 2.3d [11] | $79.86$
ATLAS [49] | $78.1\pm 2.9$
LHCb [50] | $75.4\pm 5.4$
TOTEM [51] | $79.5\pm 1.8$

The measured differential cross-section of prompt inclusive production of
long-lived charged particles is shown in Fig. 10. The values for positively
and negatively charged particles are listed in Appendix A. In the figure, the
measurement is compared with the predictions from the hadronic-interaction
models Pythia 8.3 [18, *Sjostrand:2006za] with the default Monash tune [52],
EPOS-LHC [14], QGSJet II-04 [15] and Sibyll 2.3d [11]. The latter three models
are accessed through the CRMC package [53]. Also shown, but not comparable to
the other models, is the occupancy-weighted LHCb tune of Pythia 8.1 that was
used as the simulated sample in this analysis. The comparably good agreement
of this simulation is based on the occupancy weighting, which removes
deviations in the magnitude and leaves only deviations in the shape, while for
the remaining models, deviations in the magnitude can occur. The calculation
of the differential cross-section,

$\frac{\mathrm{d}^{2}\sigma}{\mathrm{d}\eta\,\mathrm{d}p_{\mathrm{T}}}\equiv\frac{\sigma_{\mathrm{inel}}}{N_{\mathrm{inel}}}\,\frac{n}{\Delta\eta\,\Delta
p_{\mathrm{T}}}\,,$ (7)

is based on: the inelastic cross-section, $\sigma_{\mathrm{inel}}$, that is
implemented in each model; the number of generated inelastic events,
$N_{\mathrm{inel}}$; and the number of prompt long-lived charged particles,
$n$, in each kinematic interval. The inelastic cross-sections of the models
and recent measurements are listed in Table 2.

The deviations of the predictions from the measured values are between
$-26\,\%$ and $+170\,\%$. The models mostly overestimate the differential
cross-section. These deviations are caused by differences in the kinematic
distributions compared to the data as the implemented values of the inelastic
cross-section are compatible with the performed measurements. The occupancy-
weighted LHCb tune of Pythia 8.1, which is the weighted simulated sample used
in this analysis, shows deviations between $-17\,\%$ and $+32\,\%$.

The ratio of the differential cross-sections for positively and negatively
charged particles is shown in Fig. 11. The positively correlated components of
the uncertainties cancel in the computation of the ratio. At high $\eta$ and
high $p_{\mathrm{T}}$, the production of positively charged particles
increases as the initial state has a charge of $+2$, which transfers to the
final state in the forward region. This effect is predicted by the models to a
varying extent. The best description of the ratio is provided by Pythia 8.3.

##  7 Summary

An unbiased measurement of the differential cross-section of prompt inclusive
production of long-lived charged particles in $p$ $p$ collisions at
${\sqrt{s}=13\text{\,Te\kern-1.00006ptV}}$ is presented. The data sample was
recorded by the LHCb experiment and corresponds to an integrated luminosity of
$5.4\text{\,nb}^{-1}$. The differential cross-section is measured as a
function of transverse momentum and pseudorapidity in the ranges
${p_{\mathrm{T}}\in[0.08,10.00)\text{\,Ge\kern-1.00006ptV\\!/}c}$ and
${\eta\in[2.0,4.8)}$ and is determined separately for positively and
negatively charged particles. An uncertainty between $2.3\,\%$ and $15\,\%$ is
achieved. A comparison of the measured charge-combined differential cross-
section with predictions from recent hadronic-interaction models shows that
these models mostly overestimate the differential cross-section. The overall
smallest deviations are observed for EPOS-LHC, while the ratio of the
differential cross-sections for positively and negatively charged particles
are best predicted by Pythia 8.3. The precision achieved in this measurement
is essential for an improved simulation of the underlying event in collisions
at the LHC and of interactions in the atmosphere of the Earth that cause air
showers.

## 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).

## Appendices

##  Appendix A Differential cross-sections

The measured values of the differential cross-sections of prompt inclusive
production of long-lived positively and negatively charged particles are
listed in Table LABEL:tab:differential_cross_sections. The numerical values
and the correlation matrix are provided in machine-readable form at [link].

Table 3: Differential cross-sections of prompt inclusive production of long-lived positively and negatively charged particles as a function of transverse momentum and pseudorapidity. $\eta$ | $\log_{10}(p_{\mathrm{T}}/(\\!\text{\,Ge\kern-1.00006ptV\\!/}c))$ | $(\mathrm{d}^{2}\sigma/(\mathrm{d}\eta\,\mathrm{d}p_{\mathrm{T}}))/(\\!\text{\,mb}/(\\!\text{\,Ge\kern-1.00006ptV\\!/}c))$
---|---|---
|  | $q=-1$ | $q=+1$
$[2.0,2.5)$ | $[-0.14,-0.08)$ | $90\pm 5$ | $89\pm 5$
$[2.0,2.5)$ | $[-0.08,-0.02)$ | $68\pm 4$ | $68\pm 4$
$[2.0,2.5)$ | $[-0.02,0.04)$ | $50.6\pm 2.8$ | $49.7\pm 2.7$
$[2.0,2.5)$ | $[0.04,0.10)$ | $36.2\pm 2.0$ | $35.7\pm 2.0$
$[2.0,2.5)$ | $[0.10,0.16)$ | $25.2\pm 1.4$ | $24.9\pm 1.4$
$[2.0,2.5)$ | $[0.16,0.22)$ | $16.9\pm 0.9$ | $16.8\pm 0.9$
$[2.0,2.5)$ | $[0.22,0.28)$ | $11.0\pm 0.5$ | $11.0\pm 0.5$
$[2.0,2.5)$ | $[0.28,0.34)$ | $6.96\pm 0.24$ | $6.94\pm 0.24$
$[2.0,2.5)$ | $[0.34,0.40)$ | $4.23\pm 0.12$ | $4.23\pm 0.11$
$[2.0,2.5)$ | $[0.40,0.46)$ | $2.49\pm 0.06$ | $2.48\pm 0.06$
$[2.0,2.5)$ | $[0.46,0.52)$ | $1.40\pm 0.04$ | $1.40\pm 0.04$
$[2.0,2.5)$ | $[0.52,0.58)$ | $0.763\pm 0.019$ | $0.766\pm 0.019$
$[2.0,2.5)$ | $[0.58,0.64)$ | $0.405\pm 0.010$ | $0.406\pm 0.010$
$[2.0,2.5)$ | $[0.64,0.70)$ | $0.209\pm 0.005$ | $0.212\pm 0.005$
$[2.0,2.5)$ | $[0.70,0.76)$ | $0.1079\pm 0.0026$ | $0.1069\pm 0.0026$
$[2.0,2.5)$ | $[0.76,0.82)$ | $0.0550\pm 0.0014$ | $0.0546\pm 0.0014$
$[2.0,2.5)$ | $[0.82,0.88)$ | $(28.2\pm 0.8)\cdot 10^{-3}$ | $(28.0\pm 0.8)\cdot 10^{-3}$
$[2.0,2.5)$ | $[0.88,0.94)$ | $(14.3\pm 0.5)\cdot 10^{-3}$ | $(14.7\pm 0.5)\cdot 10^{-3}$
$[2.0,2.5)$ | $[0.94,1.00)$ | $(7.37\pm 0.28)\cdot 10^{-3}$ | $(7.39\pm 0.28)\cdot 10^{-3}$
$[2.5,3.0)$ | $[-0.32,-0.26)$ | $177\pm 10$ | $175\pm 10$
$[2.5,3.0)$ | $[-0.26,-0.20)$ | $144\pm 8$ | $144\pm 8$
$[2.5,3.0)$ | $[-0.20,-0.14)$ | $115\pm 6$ | $114\pm 6$
$[2.5,3.0)$ | $[-0.14,-0.08)$ | $89\pm 5$ | $88\pm 5$
$[2.5,3.0)$ | $[-0.08,-0.02)$ | $67\pm 4$ | $67\pm 4$
$[2.5,3.0)$ | $[-0.02,0.04)$ | $49.1\pm 2.6$ | $48.8\pm 2.6$
$[2.5,3.0)$ | $[0.04,0.10)$ | $35.1\pm 1.4$ | $34.9\pm 1.4$
$[2.5,3.0)$ | $[0.10,0.16)$ | $24.3\pm 0.8$ | $24.2\pm 0.8$
$[2.5,3.0)$ | $[0.16,0.22)$ | $16.2\pm 0.4$ | $16.2\pm 0.4$
$[2.5,3.0)$ | $[0.22,0.28)$ | $10.40\pm 0.27$ | $10.39\pm 0.27$
$[2.5,3.0)$ | $[0.28,0.34)$ | $6.47\pm 0.16$ | $6.47\pm 0.16$
$[2.5,3.0)$ | $[0.34,0.40)$ | $3.87\pm 0.09$ | $3.86\pm 0.09$
$[2.5,3.0)$ | $[0.40,0.46)$ | $2.21\pm 0.05$ | $2.22\pm 0.05$
$[2.5,3.0)$ | $[0.46,0.52)$ | $1.236\pm 0.028$ | $1.242\pm 0.028$
$[2.5,3.0)$ | $[0.52,0.58)$ | $0.680\pm 0.016$ | $0.681\pm 0.016$
$[2.5,3.0)$ | $[0.58,0.64)$ | $0.358\pm 0.009$ | $0.360\pm 0.009$
$[2.5,3.0)$ | $[0.64,0.70)$ | $0.186\pm 0.004$ | $0.189\pm 0.005$
$[2.5,3.0)$ | $[0.70,0.76)$ | $0.0943\pm 0.0026$ | $0.0967\pm 0.0033$
$[2.5,3.0)$ | $[0.76,0.82)$ | $0.0481\pm 0.0013$ | $0.0487\pm 0.0015$
$[2.5,3.0)$ | $[0.82,0.88)$ | $(24.3\pm 1.0)\cdot 10^{-3}$ | $0.0251\pm 0.0012$
$[2.5,3.0)$ | $[0.88,0.94)$ | $(12.3\pm 0.5)\cdot 10^{-3}$ | $(12.6\pm 0.5)\cdot 10^{-3}$
$[2.5,3.0)$ | $[0.94,1.00)$ | $(6.04\pm 0.34)\cdot 10^{-3}$ | $(6.5\pm 0.4)\cdot 10^{-3}$
$[3.0,3.5)$ | $[-0.56,-0.50)$ | $300\pm 17$ | $299\pm 17$
$[3.0,3.5)$ | $[-0.50,-0.44)$ | $268\pm 15$ | $268\pm 15$
$[3.0,3.5)$ | $[-0.44,-0.38)$ | $235\pm 13$ | $234\pm 13$
$[3.0,3.5)$ | $[-0.38,-0.32)$ | $202\pm 10$ | $202\pm 10$
$[3.0,3.5)$ | $[-0.32,-0.26)$ | $168\pm 7$ | $168\pm 7$
$[3.0,3.5)$ | $[-0.26,-0.20)$ | $137\pm 6$ | $137\pm 6$
$[3.0,3.5)$ | $[-0.20,-0.14)$ | $109\pm 4$ | $109\pm 4$
$[3.0,3.5)$ | $[-0.14,-0.08)$ | $84.6\pm 3.0$ | $84.6\pm 3.0$
$[3.0,3.5)$ | $[-0.08,-0.02)$ | $63.7\pm 2.0$ | $63.7\pm 2.0$
$[3.0,3.5)$ | $[-0.02,0.04)$ | $46.5\pm 1.4$ | $46.5\pm 1.4$
$[3.0,3.5)$ | $[0.04,0.10)$ | $32.8\pm 1.0$ | $32.8\pm 1.0$
$[3.0,3.5)$ | $[0.10,0.16)$ | $22.2\pm 0.6$ | $22.2\pm 0.6$
$[3.0,3.5)$ | $[0.16,0.22)$ | $14.45\pm 0.35$ | $14.6\pm 0.4$
$[3.0,3.5)$ | $[0.22,0.28)$ | $9.30\pm 0.23$ | $9.29\pm 0.23$
$[3.0,3.5)$ | $[0.28,0.34)$ | $5.71\pm 0.14$ | $5.71\pm 0.14$
$[3.0,3.5)$ | $[0.34,0.40)$ | $3.39\pm 0.08$ | $3.40\pm 0.08$
$[3.0,3.5)$ | $[0.40,0.46)$ | $1.98\pm 0.05$ | $1.98\pm 0.05$
$[3.0,3.5)$ | $[0.46,0.52)$ | $1.103\pm 0.029$ | $1.102\pm 0.027$
$[3.0,3.5)$ | $[0.52,0.58)$ | $0.597\pm 0.018$ | $0.606\pm 0.016$
$[3.0,3.5)$ | $[0.58,0.64)$ | $0.314\pm 0.010$ | $0.314\pm 0.008$
$[3.0,3.5)$ | $[0.64,0.70)$ | $0.163\pm 0.006$ | $0.163\pm 0.005$
$[3.0,3.5)$ | $[0.70,0.76)$ | $0.0830\pm 0.0035$ | $0.0821\pm 0.0029$
$[3.0,3.5)$ | $[0.76,0.82)$ | $0.0414\pm 0.0017$ | $0.0422\pm 0.0017$
$[3.0,3.5)$ | $[0.82,0.88)$ | $0.0207\pm 0.0011$ | $0.0214\pm 0.0011$
$[3.0,3.5)$ | $[0.88,0.94)$ | $(10.1\pm 0.7)\cdot 10^{-3}$ | $(10.6\pm 0.6)\cdot 10^{-3}$
$[3.0,3.5)$ | $[0.94,1.00)$ | $(5.2\pm 0.5)\cdot 10^{-3}$ | $(5.1\pm 0.4)\cdot 10^{-3}$
$[3.5,4.0)$ | $[-0.74,-0.68)$ | $334\pm 20$ | $335\pm 20$
$[3.5,4.0)$ | $[-0.68,-0.62)$ | $324\pm 19$ | $324\pm 19$
$[3.5,4.0)$ | $[-0.62,-0.56)$ | $307\pm 18$ | $306\pm 18$
$[3.5,4.0)$ | $[-0.56,-0.50)$ | $281\pm 16$ | $280\pm 16$
$[3.5,4.0)$ | $[-0.50,-0.44)$ | $252\pm 14$ | $251\pm 14$
$[3.5,4.0)$ | $[-0.44,-0.38)$ | $221\pm 11$ | $221\pm 11$
$[3.5,4.0)$ | $[-0.38,-0.32)$ | $191\pm 8$ | $191\pm 8$
$[3.5,4.0)$ | $[-0.32,-0.26)$ | $160\pm 6$ | $161\pm 6$
$[3.5,4.0)$ | $[-0.26,-0.20)$ | $131\pm 5$ | $131\pm 5$
$[3.5,4.0)$ | $[-0.20,-0.14)$ | $103\pm 4$ | $103\pm 4$
$[3.5,4.0)$ | $[-0.14,-0.08)$ | $78.5\pm 2.8$ | $79.3\pm 2.8$
$[3.5,4.0)$ | $[-0.08,-0.02)$ | $58.1\pm 1.8$ | $58.6\pm 1.8$
$[3.5,4.0)$ | $[-0.02,0.04)$ | $41.7\pm 1.1$ | $42.1\pm 1.2$
$[3.5,4.0)$ | $[0.04,0.10)$ | $29.0\pm 0.8$ | $29.2\pm 0.8$
$[3.5,4.0)$ | $[0.10,0.16)$ | $19.5\pm 0.5$ | $19.8\pm 0.5$
$[3.5,4.0)$ | $[0.16,0.22)$ | $12.80\pm 0.33$ | $12.96\pm 0.34$
$[3.5,4.0)$ | $[0.22,0.28)$ | $8.15\pm 0.20$ | $8.23\pm 0.21$
$[3.5,4.0)$ | $[0.28,0.34)$ | $5.02\pm 0.13$ | $5.06\pm 0.12$
$[3.5,4.0)$ | $[0.34,0.40)$ | $2.96\pm 0.08$ | $2.99\pm 0.07$
$[3.5,4.0)$ | $[0.40,0.46)$ | $1.70\pm 0.05$ | $1.72\pm 0.05$
$[3.5,4.0)$ | $[0.46,0.52)$ | $0.938\pm 0.029$ | $0.945\pm 0.026$
$[3.5,4.0)$ | $[0.52,0.58)$ | $0.498\pm 0.016$ | $0.510\pm 0.015$
$[3.5,4.0)$ | $[0.58,0.64)$ | $0.258\pm 0.009$ | $0.262\pm 0.008$
$[3.5,4.0)$ | $[0.64,0.70)$ | $0.132\pm 0.005$ | $0.134\pm 0.005$
$[3.5,4.0)$ | $[0.70,0.76)$ | $0.0647\pm 0.0030$ | $0.0675\pm 0.0030$
$[3.5,4.0)$ | $[0.76,0.82)$ | $0.0319\pm 0.0017$ | $0.0337\pm 0.0018$
$[3.5,4.0)$ | $[0.82,0.88)$ | $0.0159\pm 0.0011$ | $0.0168\pm 0.0010$
$[3.5,4.0)$ | $[0.88,0.94)$ | $(8.0\pm 0.7)\cdot 10^{-3}$ | $(8.1\pm 0.6)\cdot 10^{-3}$
$[4.0,4.5)$ | $[-0.98,-0.92)$ | $264\pm 28$ | $260\pm 28$
$[4.0,4.5)$ | $[-0.92,-0.86)$ | $285\pm 26$ | $281\pm 25$
$[4.0,4.5)$ | $[-0.86,-0.80)$ | $300\pm 23$ | $297\pm 23$
$[4.0,4.5)$ | $[-0.80,-0.74)$ | $306\pm 22$ | $305\pm 21$
$[4.0,4.5)$ | $[-0.74,-0.68)$ | $308\pm 19$ | $306\pm 19$
$[4.0,4.5)$ | $[-0.68,-0.62)$ | $301\pm 17$ | $298\pm 17$
$[4.0,4.5)$ | $[-0.62,-0.56)$ | $286\pm 14$ | $284\pm 14$
$[4.0,4.5)$ | $[-0.56,-0.50)$ | $265\pm 10$ | $266\pm 10$
$[4.0,4.5)$ | $[-0.50,-0.44)$ | $241\pm 8$ | $241\pm 8$
$[4.0,4.5)$ | $[-0.44,-0.38)$ | $213\pm 8$ | $213\pm 8$
$[4.0,4.5)$ | $[-0.38,-0.32)$ | $180\pm 6$ | $180\pm 6$
$[4.0,4.5)$ | $[-0.32,-0.26)$ | $150\pm 5$ | $150\pm 5$
$[4.0,4.5)$ | $[-0.26,-0.20)$ | $120.2\pm 3.3$ | $121.0\pm 3.3$
$[4.0,4.5)$ | $[-0.20,-0.14)$ | $93.5\pm 2.4$ | $94.1\pm 2.4$
$[4.0,4.5)$ | $[-0.14,-0.08)$ | $70.5\pm 1.8$ | $71.0\pm 1.8$
$[4.0,4.5)$ | $[-0.08,-0.02)$ | $51.9\pm 1.3$ | $52.4\pm 1.3$
$[4.0,4.5)$ | $[-0.02,0.04)$ | $37.2\pm 0.9$ | $37.6\pm 0.9$
$[4.0,4.5)$ | $[0.04,0.10)$ | $25.7\pm 0.6$ | $26.0\pm 0.6$
$[4.0,4.5)$ | $[0.10,0.16)$ | $17.3\pm 0.4$ | $17.5\pm 0.4$
$[4.0,4.5)$ | $[0.16,0.22)$ | $11.25\pm 0.29$ | $11.37\pm 0.28$
$[4.0,4.5)$ | $[0.22,0.28)$ | $7.03\pm 0.18$ | $7.13\pm 0.18$
$[4.0,4.5)$ | $[0.28,0.34)$ | $4.26\pm 0.12$ | $4.30\pm 0.11$
$[4.0,4.5)$ | $[0.34,0.40)$ | $2.47\pm 0.07$ | $2.49\pm 0.06$
$[4.0,4.5)$ | $[0.40,0.46)$ | $1.36\pm 0.04$ | $1.40\pm 0.04$
$[4.0,4.5)$ | $[0.46,0.52)$ | $0.741\pm 0.025$ | $0.748\pm 0.021$
$[4.0,4.5)$ | $[0.52,0.58)$ | $0.386\pm 0.015$ | $0.390\pm 0.014$
$[4.0,4.5)$ | $[0.58,0.64)$ | $0.195\pm 0.008$ | $0.200\pm 0.007$
$[4.0,4.5)$ | $[0.64,0.70)$ | $0.096\pm 0.004$ | $0.103\pm 0.004$
$[4.0,4.5)$ | $[0.70,0.76)$ | $0.0478\pm 0.0022$ | $0.0523\pm 0.0024$
$[4.0,4.5)$ | $[0.76,0.82)$ | $0.0235\pm 0.0011$ | $0.0253\pm 0.0013$
$[4.0,4.5)$ | $[0.82,0.88)$ | $(11.3\pm 0.6)\cdot 10^{-3}$ | $(13.0\pm 0.7)\cdot 10^{-3}$
$[4.5,4.8)$ | $[-1.10,-1.04)$ | $199\pm 28$ | $195\pm 27$
$[4.5,4.8)$ | $[-1.04,-0.98)$ | $228\pm 25$ | $224\pm 24$
$[4.5,4.8)$ | $[-0.98,-0.92)$ | $251\pm 23$ | $249\pm 22$
$[4.5,4.8)$ | $[-0.92,-0.86)$ | $272\pm 21$ | $270\pm 20$
$[4.5,4.8)$ | $[-0.86,-0.80)$ | $289\pm 20$ | $284\pm 19$
$[4.5,4.8)$ | $[-0.80,-0.74)$ | $299\pm 18$ | $298\pm 17$
$[4.5,4.8)$ | $[-0.74,-0.68)$ | $304\pm 13$ | $303\pm 13$
$[4.5,4.8)$ | $[-0.68,-0.62)$ | $300\pm 12$ | $299\pm 12$
$[4.5,4.8)$ | $[-0.62,-0.56)$ | $282\pm 11$ | $282\pm 11$
$[4.5,4.8)$ | $[-0.56,-0.50)$ | $258\pm 10$ | $258\pm 10$
$[4.5,4.8)$ | $[-0.50,-0.44)$ | $233\pm 8$ | $233\pm 8$
$[4.5,4.8)$ | $[-0.44,-0.38)$ | $203\pm 6$ | $204\pm 6$
$[4.5,4.8)$ | $[-0.38,-0.32)$ | $171\pm 4$ | $172\pm 4$
$[4.5,4.8)$ | $[-0.32,-0.26)$ | $142\pm 4$ | $143\pm 4$
$[4.5,4.8)$ | $[-0.26,-0.20)$ | $114.8\pm 2.9$ | $115.9\pm 2.9$
$[4.5,4.8)$ | $[-0.20,-0.14)$ | $89.3\pm 2.2$ | $90.4\pm 2.2$
$[4.5,4.8)$ | $[-0.14,-0.08)$ | $67.7\pm 1.6$ | $68.4\pm 1.6$
$[4.5,4.8)$ | $[-0.08,-0.02)$ | $49.6\pm 1.2$ | $50.5\pm 1.2$
$[4.5,4.8)$ | $[-0.02,0.04)$ | $35.0\pm 0.8$ | $35.7\pm 0.8$
$[4.5,4.8)$ | $[0.04,0.10)$ | $24.0\pm 0.6$ | $24.4\pm 0.6$
$[4.5,4.8)$ | $[0.10,0.16)$ | $15.8\pm 0.4$ | $16.1\pm 0.4$
$[4.5,4.8)$ | $[0.16,0.22)$ | $10.08\pm 0.25$ | $10.34\pm 0.25$
$[4.5,4.8)$ | $[0.22,0.28)$ | $6.22\pm 0.16$ | $6.35\pm 0.15$
$[4.5,4.8)$ | $[0.28,0.34)$ | $3.66\pm 0.12$ | $3.72\pm 0.11$
$[4.5,4.8)$ | $[0.34,0.40)$ | $2.05\pm 0.08$ | $2.12\pm 0.07$
$[4.5,4.8)$ | $[0.40,0.46)$ | $1.14\pm 0.04$ | $1.18\pm 0.04$
$[4.5,4.8)$ | $[0.46,0.52)$ | $0.596\pm 0.023$ | $0.631\pm 0.022$
$[4.5,4.8)$ | $[0.52,0.58)$ | $0.314\pm 0.013$ | $0.328\pm 0.012$
$[4.5,4.8)$ | $[0.58,0.64)$ | $0.152\pm 0.006$ | $0.169\pm 0.006$
$[4.5,4.8)$ | $[0.64,0.70)$ | $0.075\pm 0.004$ | $0.0854\pm 0.0033$

##  Appendix B Correlation matrix of differential cross-section

Figure 12: Correlation matrix for the uncertainties of the differential cross-
section of prompt inclusive production of long-lived charged particles. The
four large quadrants correspond to the correlations between negatively and
positively charged particles. The 36 cells within each quadrant correspond to
the $\eta$ intervals. In each cell, the correlations of the $p_{\mathrm{T}}$
intervals are shown from low to high $p_{\mathrm{T}}$ in logarithmic
intervals.

The correlation matrix of the measured differential cross-section is shown in
Fig. 12. The correlations are positive since the systematic uncertainties
dominate and most of the systematic uncertainties are positively correlated
between kinematic intervals and the two particle charges. The positive
correlations between neighbouring $p_{\mathrm{T}}$ intervals are particularly
large due to the correction of the tracking efficiency, which affects
neighbouring intervals in the same way. The numerical values of the
correlation matrix are provided in machine-readable form at [link].

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LHCb collaboration

R. Aaij32, C. Abellán Beteta50, T. Ackernley60, B. Adeva46, M. Adinolfi54, H.
Afsharnia9, C.A. Aidala86, S. Aiola25, Z. Ajaltouni9, S. Akar65, L. Alasfar16,
J. Albrecht15, F. Alessio48, M. Alexander59, A. Alfonso Albero45, Z.
Aliouche62, G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, Y. Amhis11, L.
An48, L. Anderlini22, A. Andreianov38, M. Andreotti21, F. Archilli17, A.
Artamonov44, M. Artuso68, K. Arzymatov42, E. Aslanides10, M. Atzeni50, B.
Audurier12, S. Bachmann17, M. Bachmayer49, J.J. Back56, P. Baladron
Rodriguez46, V. Balagura12, W. Baldini21, J. Baptista Leite1, R.J. Barlow62,
S. Barsuk11, W. Barter61, M. Bartolini24, F. Baryshnikov83, J.M. Basels14, G.
Bassi29, B. Batsukh68, A. Battig15, A. Bay49, M. Becker15, F. Bedeschi29, I.
Bediaga1, A. Beiter68, V. Belavin42, S. Belin27, V. Bellee49, K. Belous44, I.
Belov40, I. Belyaev41, G. Bencivenni23, E. Ben-Haim13, A. Berezhnoy40, R.
Bernet50, D. Berninghoff17, H.C. Bernstein68, C. Bertella48, A. Bertolin28, C.
Betancourt50, F. Betti48, Ia. Bezshyiko50, S. Bhasin54, J. Bhom35, L. Bian73,
M.S. Bieker15, S. Bifani53, P. Billoir13, M. Birch61, F.C.R. Bishop55, A.
Bitadze62, A. Bizzeti22,k, M. Bjørn63, M.P. Blago48, T. Blake56, F. Blanc49,
S. Blusk68, D. Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T.
Boettcher65, A. Boldyrev82, A. Bondar43, N. Bondar38,48, S. Borghi62, M.
Borisyak42, M. Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60, A.
Boyer48, C. Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, M.
Brodski48, J. Brodzicka35, A. Brossa Gonzalo56, D. Brundu27, A. Buonaura50, C.
Burr48, A. Bursche72, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
Byczynski48, S. Cadeddu27, H. Cai73, R. Calabrese21,f, L. Calefice15,13, L.
Calero Diaz23, S. Cali23, R. Calladine53, M. Calvi26,j, M. Calvo Gomez85, P.
Camargo Magalhaes54, P. Campana23, A.F. Campoverde Quezada6, S. Capelli26,j,
L. Capriotti20,d, A. Carbone20,d, G. Carboni31, R. Cardinale24, A. Cardini27,
I. Carli4, P. Carniti26,j, L. Carus14, K. Carvalho Akiba32, A. Casais Vidal46,
G. Casse60, M. Cattaneo48, G. Cavallero48, S. Celani49, J. Cerasoli10, A.J.
Chadwick60, M.G. Chapman54, M. Charles13, Ph. Charpentier48, G.
Chatzikonstantinidis53, C.A. Chavez Barajas60, M. Chefdeville8, C. Chen3, S.
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Cobbledick62, V. Coco48, J.A.B. Coelho11, J. Cogan10, E. Cogneras9, L.
Cojocariu37, P. Collins48, T. Colombo48, L. Congedo19,c, A. Contu27, N.
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Dadabaev83, E. Dall’Occo15, J. Dalseno46, C. D’Ambrosio48, A. Danilina41, P.
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Capua62, M. De Cian49, J.M. De Miranda1, L. De Paula2, M. De Serio19,c, D. De
Simone50, P. De Simone23, J.A. de Vries80, C.T. Dean67, D. Decamp8, L. Del
Buono13, B. Delaney55, H.-P. Dembinski15, A. Dendek34, V. Denysenko50, D.
Derkach82, O. Deschamps9, F. Desse11, F. Dettori27,e, B. Dey77, A. Di Cicco23,
P. Di Nezza23, S. Didenko83, L. Dieste Maronas46, H. Dijkstra48, V.
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Dovbnya51, A.G. Downes8, K. Dreimanis60, M.W. Dudek35, L. Dufour48, V. Duk78,
P. Durante48, J.M. Durham67, D. Dutta62, A. Dziurda35, A. Dzyuba38, S. Easo57,
U. Egede69, V. Egorychev41, S. Eidelman43,v, S. Eisenhardt58, S. Ek-In49, L.
Eklund59,w, S. Ely68, A. Ene37, E. Epple67, S. Escher14, J. Eschle50, S.
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D. Fazzini26,j, M. Féo48, A. Fernandez Prieto46, J.M. Fernandez-tenllado
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Sevilla66, M. Frank48, E. Franzoso21, G. Frau17, C. Frei48, D.A. Friday59, J.
Fu25, Q. Fuehring15, W. Funk48, E. Gabriel32, T. Gaintseva42, A. Gallas
Torreira46, D. Galli20,d, S. Gambetta58,48, Y. Gan3, M. Gandelman2, P.
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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, P. Griffith21,f, L.
Grillo62, S. Gromov83, B.R. Gruberg Cazon63, C. Gu3, M. Guarise21, 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, 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, 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, S.
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O. Leroy10, T. Lesiak35, B. Leverington17, H. Li72, L. Li63, P. Li17, S. Li7,
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R. Litvinov27, G. Liu72, H. Liu6, S. Liu4, A. Loi27, J. Lomba Castro46, I.
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M. Lucio Martinez32, V. Lukashenko32,52, Y. Luo3, A. Lupato62, E. Luppi21,f,
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E. Millard56, M. Milovanovic48, M.-N. Minard8, A. Minotti21, L. Minzoni21,f,
S.E. Mitchell58, B. Mitreska62, D.S. Mitzel48, A. Mödden 15, R.A. Mohammed63,
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Nandakumar57, T. Nanut49, I. Nasteva2, M. Needham58, I. Neri21, N. Neri25,i,
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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.
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Zunica62.

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
86University 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
tAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
uP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
vNovosibirsk State University, Novosibirsk, Russia
wDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden
xHanoi University of Science, Hanoi, Vietnam