EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-022 LHCb-PAPER-2017-050 3 September 2018

Measurement of forward top pair production in the dilepton channel in $pp$
collisions at $\sqrt{s}=13\mathrm{\,Te\kern-2.07413ptV}$

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

Forward top quark pair production is studied in $pp$ collisions in the $\mu
eb$ final state using a data sample corresponding to an integrated luminosity
of 1.93$\mbox{\,fb}^{-1}$ collected with the LHCb experiment at a centre-of-
mass energy of 13 TeV. The cross-section is measured in a fiducial region
where both leptons have a transverse momentum greater than
20$\mathrm{\,Ge\kern-1.00006ptV}$ and a pseudorapidity between 2.0 and 4.5.
The quadrature sum of the azimuthal separation and the difference in
pseudorapidities, denoted $\Delta R$, between the two leptons must be larger
than 0.1. The $b$-jet axis is required to be separated from both leptons by a
$\Delta R$ of 0.5, and to have a transverse momentum in excess of
20$\mathrm{\,Ge\kern-1.00006ptV}$ and a pseudorapidity between 2.2 and 4.2.
The cross-section is measured to be

$\sigma_{t\bar{t}}=126\pm 19\,(\mathrm{stat})\pm 16\,(\mathrm{syst})\pm
5\,(\mathrm{lumi})\,\,\mathrm{fb}$

where the first uncertainty is statistical, the second is systematic, and the
third is due to the luminosity determination. The measurement is compatible
with the Standard Model prediction.

Published in JHEP 08 (2018) 174

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

##  1 Introduction

The production of top quarks at hadron colliders represents an important test
of the Standard Model of particle physics (SM). The top quark is the heaviest
known fundamental particle and its production and decay properties are
sensitive to a number of scenarios beyond the Standard Model. The unique
forward acceptance of the LHCb detector allows measurements in a phase space
inaccessible to general purpose detectors such as ATLAS and CMS. Top-quark
production in this region receives a higher contribution from quark-antiquark
(${q}{\overline{q}}$) annihilation than in the central region and probes
higher values of Bjorken-$x$, where large uncertainties are present in the
proton parton distribution functions (PDFs). Precise measurements of top quark
production at LHCb can thus be used to constrain PDFs in this region [1]. The
greater contribution from quark-initiated production also results in a larger
expected charge asymmetry [2, 3] in the forward region than in the central
region.

The first observation of top-quark production in the forward region was
performed by the LHCb collaboration using data corresponding to an integrated
luminosity of 3$\mbox{\,fb}^{-1}$ collected between 2010 and 2012 at centre-
of-mass energies of 7 and 8$\mathrm{\,Te\kern-1.00006ptV}$ (Run 1) [4]. The
measurement was performed in the $\mu b$ final state, consisting of a muon and
a $b$-jet, where $b$-jet refers to a jet originating from the fragmentation of
a $b$ quark. A precision of 20% was achieved on the top quark production
cross-section. Measurements in this final state have the greatest statistical
precision but also suffer from a large background due to the production of a
$W$ boson in association with a $b$-jet. Additionally, this final state does
not differentiate between single top quark and top quark pair production. A
measurement of top quark production was also performed by the LHCb
collaboration in the $\mu b\bar{b}$ and $eb\bar{b}$ final states using the
same dataset [5], where the top quark pair (${t}{\overline{t}}$) production
cross-section was measured with a precision of 40%. The measurements are in
agreement with the SM prediction, calculated to a precision of 25% to 30% with
MCFM [6] using the CT10 PDF set [7], and are limited by uncertainties on the
$b$-tagging efficiency and the background composition.

In 2015 and 2016, a data sample corresponding to an integrated luminosity of
1.93$\mbox{\,fb}^{-1}$ was collected by the LHCb experiment at a centre-of-
mass energy of 13$\mathrm{\,Te\kern-1.00006ptV}$. The increased energy leads
to an increase of a factor of ten in the ${t}{\overline{t}}$ production cross-
section within the LHCb acceptance with respect to collisions at a energy of
8$\mathrm{\,Te\kern-1.00006ptV}$ [8]. The larger cross-section allows access
to a number of final states inaccessible in Run 1, including the dilepton
final state, where both top quarks decay to a $W$ boson and a $b$ quark, and
the $W$ bosons decay leptonically to a lepton and a neutrino. This paper
details the first measurement of $t\bar{t}$ production in the $\mu eb$ final
state at LHCb, where the dilepton channel is partially reconstructed by
requiring that a muon, an electron and a $b$-jet are present in the proton-
proton ($pp$) collision, where the leptons are produced by the $W$ boson
decay, either directly or through the decay of a tau lepton. This final state
yields a high purity with respect to other final states; the selection of two
leptons reduces the background from single $W$-boson production and lepton
mis-identification, the choice of different flavour leptons suppresses the
contribution from the production of $Z$ bosons, and the $b$-tagged jet reduces
the contribution from light jets.

The LHCb detector is introduced in Sec. 2, the event selection and purity is
discussed in Sec. 3, the cross-section calculation is presented in Sec. 4, the
results are given in Sec. 5 and the conclusions are drawn in Sec. 6.

##  2 Detector and simulation

The LHCb detector [9, 10] 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 momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200$\mathrm{\,Ge\kern-1.00006ptV}$.111Natural units with
$\hbar=c=1$ are used throughout, so that mass and momentum are measured in
units of energy. The minimum distance of a track to a primary vertex (PV), the
impact parameter (IP), is measured with a resolution of
$(15+29/\mbox{$p_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
$\mathrm{\,Ge\kern-1.00006ptV}$. Photons, electrons and hadrons are identified
by a calorimeter system consisting of scintillating-pad and preshower
detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons
are identified by a system composed of alternating layers of iron and
multiwire proportional chambers. The online event selection is performed by a
trigger, which consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage, which applies a
full event reconstruction. In this paper, the presence of a muon is used to
select candidate events at both stages of the trigger; the hardware stage
selects muons with a transverse momentum $p_{\rm
T}>1.76\mathrm{\,Ge\kern-1.00006ptV}$ and the subsequent software trigger
requires that a muon with
$\mbox{$p_{\mathrm{T}}$}>12\mathrm{\,Ge\kern-1.00006ptV}$ is present.

To estimate the trigger, reconstruction and selection efficiencies, to
determine background contributions, and to compare the selected data sample to
theoretical expectations, simulated $pp$ collisions are generated using
Pythia8 [11, 12]. The interaction of the generated particles with the
detector, and its response, are implemented using the Geant4 toolkit [13] as
described in Ref. [14].

Results are compared to theoretical predictions calculated at next-to-leading-
order (NLO) in perturbative QCD using the POWHEG [15, 16, 17], aMC@NLO [18]
and MCFM [19, 20] generators. The MCFM prediction is provided at fixed order,
while the POWHEG and aMC@NLO predictions are interfaced with Pythia8 to
provide a parton shower. In the case of aMC@NLO, the decay of the top quarks
is performed using MADSPIN [21, 22]. For background studies, samples of single
top quark production in association with a $W$ boson are produced with POWHEG
using both the diagram removal and diagram subtraction schemes [23], and
samples of $WW$ and $WZ$ boson production are produced using aMC@NLO. For
POWHEG and MCFM, the factorisation and normalisation scales are set to the
transverse mass of the final state top quarks, while for aMC@NLO, they are set
to half the sum of the transverse mass of the final state particles. In all
cases, the dynamics of the colliding protons are described by the NNPDF3.0
[24] PDF set, and the mass of the top quark is set to
173$\mathrm{\,Ge\kern-1.00006ptV}$.

##  3 Event selection and purity

Events containing a high-$p_{\mathrm{T}}$ muon and electron of opposite charge
in addition to a high-$p_{\mathrm{T}}$ jet are selected. Muons are identified
as reconstructed tracks that are matched to hits in each of the four muon
stations furthest downstream, while electrons are identified as tracks that
have left large energy deposits in the preshower detector and electromagnetic
calorimeter, in addition to small energy deposits in the hadronic calorimeter.
The muons and electrons are required to have $p_{\mathrm{T}}$ in excess of
20$\mathrm{\,Ge\kern-1.00006ptV}$, a pseudorapidity in the range
$2.0<\eta<4.5$, and to be separated by a distance, $\Delta R$, of greater than
0.1 in ($\eta$,$\phi$) space, where $\phi$ refers to the azimuthal angle. The
reconstructed final state particles used as inputs to the jet building are
prepared using a particle flow algorithm and clustered using the anti-$k_{\rm
T}$ algorithm as implemented in Fastjet [25], with a distance parameter of
0.5. Requirements are placed on the candidate jet in order to reduce the
background formed by particles which are either incorrectly reconstructed or
produced in additional $pp$ interactions in the same event. The jet is
required to have $p_{\mathrm{T}}$ above 20$\mathrm{\,Ge\kern-1.00006ptV}$ and
a pseudorapidity between 2.2 and 4.2. Separation between the jet and each
lepton is ensured by requiring that the $\Delta R$ distance between the jet
and the leptons is greater than 0.5. A dedicated tagging algorithm is used to
select $b$-jets. The tagger proceeds by building two-body secondary vertices
(SVs) using all tracks not associated to any PV in the event, and merging any
vertices sharing a common track. A jet is said to be tagged if the event
contains an SV with a flight direction satisfying $\Delta R<0.5$ with respect
to the jet axis, where the flight direction is taken to be the vector joining
the SV to the primary vertex. More details are given in Ref. [26]. Lepton
isolation criteria is applied by rejecting events where the transverse
component of the vector sum of the momentum of all reconstructed charged
particles within $\Delta R<0.5$ of either lepton is greater than
5$\mathrm{\,Ge\kern-1.00006ptV}$. The leptons are also required to be
consistent with originating from a common primary vertex, satisfying
$\mathrm{IP}<0.04\mathrm{\,mm}$. After applying the full selection, a total of
44 events are retained in the data sample.

In addition to the signal, several physics processes contribute to the
selected data sample, either through the presence of an identical final state,
or through the misidentification of one or more of the final state objects.
The following background processes are considered.

  * •

Lepton misidentification where the muon and electron candidates are produced
through the misidentification of one or two hadrons. A number of processes can
contribute to this background, including QCD multijet production, $W$ and $Z$
production, and $t\bar{t}$ events where only one lepton is produced in the
LHCb acceptance.

  * •

The production of a $Z$ boson in association with a jet contributes either
through the $Z\rightarrow\tau^{+}\tau^{-}$ final state, where the subsequent
tau lepton decays produce a final state with a muon and electron, or through
the $Z\rightarrow\mu^{+}\mu^{-}$ and $Z\rightarrow e^{+}e^{-}$ final states,
where one of the final state leptons is misidentified. The associated jet can
either be a genuine $b$-jet produced in association with the $Z$ boson, or due
to the misidentification of a charm or light jet.

  * •

The production of a single top quark in association with a $W$ boson, known as
$W^{\pm}t$ production, contributes an identical final state.

  * •

Multiboson processes, such as $W^{+}W^{-}$, $W^{\pm}Z$ and $ZZ$ production,
give rise to a high $p_{\mathrm{T}}$ muon and electron in the final state with
an associated jet.

As the background from lepton misidentification produces events containing
leptons with both same- and opposite-sign charges, the number of background
events is determined by first applying the full selection to the data but
requiring that the leptons should have the same charge. The $b$-tagging
requirement is also removed to increase the statistical precision. The number
of events selected in this same-sign control region is then extrapolated using
a factor obtained in an additional background-enriched control sample, where
the identification requirements on the electron candidate are reversed. This
gives an expectation of 3.5$\,\pm\,$1.9 events, where the uncertainty is due
to the combined statistical uncertainties on the selected number of events and
the extrapolation factor, which dominate over any expected systematic effects.

The number of $Z\rightarrow\tau^{+}\tau^{-}$ events is determined by
normalising the number of $Z\rightarrow\tau^{+}\tau^{-}$ events observed in
Pythia8 simulation using the ratio of the number of
$Z\rightarrow\mu^{+}\mu^{-}$ events observed in data and simulation. A total
of 0.32 $\pm$ 0.03 events are expected, where the uncertainty is obtained by
combining the statistical precision of the determination with the uncertainty
on the reconstruction and selection efficiency, determined from comparisons
between data and simulation. The contributions from misidentification of a
lepton in the dimuon and dielectron decay modes of the $Z$ boson are
determined using simulation and found to be negligible.

The $W^{\pm}t$ background is determined using predictions from POWHEG
calculated in the diagram removal scheme. The predicted number of events is
scaled by the efficiency obtained by reweighting the simulated
${t}{\overline{t}}$ sample to match the kinematics of the $W^{\pm}t$ process,
yielding an expectation of 1.8$\,\pm\,$0.5 events. The uncertainty is
determined by combining the theoretical uncertainties, determined as described
in Sec. 5, with the difference in the cross-section as calculated using the
diagram removal and diagram subtraction schemes. An additional systematic
uncertainty is added to account for the differences in the reconstruction and
selection efficiency. The contribution from multiboson processes is determined
from simulations to be negligible.

The total number of expected background events from all sources is
5.6$\,\pm\,$2.0. The total number of selected events is shown as a function of
the muon, electron and jet $\eta$ and $p_{\mathrm{T}}$ distributions in Figs.
1, 2 and 3. The invariant mass of the muon, electron and jet is shown in Fig.
4. The expected signal and background contributions are shown, where the
signal yield is taken to be the total number of selected events minus the
expected background contribution. The lepton misidentification background
shape is obtained from the control samples with the electron identification
requirements reversed, while all other distributions come from simulation. A
reasonable agreement is observed in all distributions.

Figure 1: The muon (left) $\eta$ and (right) $p_{\mathrm{T}}$ distribution in
data compared to the expected contributions. The ${t}{\overline{t}}$ signal
yield is determined to be the number of selected events minus the sum of the
expected backgrounds. The multiboson background is determined to be
negligible.

Figure 2: The electron (left) $\eta$ and (right) $p_{\mathrm{T}}$ distribution
in data compared to the expected contributions. The ${t}{\overline{t}}$ signal
yield is determined to be the number of selected events minus the sum of the
expected backgrounds. The multiboson background is determined to be
negligible.

Figure 3: The $b$-jet (left) $\eta$ and (right) $p_{\mathrm{T}}$ distribution
in data compared to the expected contributions. The ${t}{\overline{t}}$ signal
yield is determined to be the number of selected events minus the sum of the
expected backgrounds. The multiboson background is determined to be
negligible. Figure 4: The combined invariant mass of the muon, electron and
$b$-jet in data compared to the expected contributions. The
${t}{\overline{t}}$ signal yield is determined to be the number of selected
events minus the sum of the expected backgrounds. The multiboson background is
determined to be negligible.

##  4 Cross-section calculation

The cross-section, $\sigma_{{t}{\overline{t}}}$, is measured in the fiducial
region defined by the $p_{\mathrm{T}}$, $\eta$, and $\Delta R$ requirements
placed on the muon, electron and $b$-jet candidates, and is calculated using
the formula

$\sigma_{{t}{\overline{t}}}=\frac{N-N_{\rm
bkg}}{\mathcal{L}\cdot\varepsilon}{\cdot\mathcal{F}_{\rm res}},$ (1)

where $N$ is the total number of candidates selected in data, $N_{\rm bkg}$ is
the sum of the expected background contributions, $\mathcal{F}_{\rm res}$ is a
resolution factor that accounts for migrations in to and out of the fiducial
region, $\varepsilon$ is the efficiency to reconstruct and select the signal
events, and $\mathcal{L}$ is the integrated luminosity of the data sample.

The instantaneous luminosity is measured continuously during the acquisition
of physics data by recording the rates of several selected reference
processes. The cross-section of these processes is measured during a dedicated
data-taking calibration period, using a beam-gas imaging method specific to
the LHCb detector [27, 28], which gives a luminosity calibration with an
uncertainty of 3.9%. The integrated luminosity of the data sample used,
$\mathcal{L}$, is obtained from the accumulated counts of the calibrated rates
and is determined to be $1.93\pm 0.07\mbox{\,fb}^{-1}$.

The event reconstruction and selection efficiency, $\varepsilon$, can be
further divided into eight components

$\varepsilon=\varepsilon^{\rm rec}_{\mu}\cdot\varepsilon^{\rm
id}_{\mu}\cdot\varepsilon^{\rm trg}\cdot\varepsilon^{\rm
rec}_{e}\cdot\varepsilon^{\rm id}_{e}\cdot\varepsilon^{\rm
jet}\cdot\varepsilon^{\rm tag}\cdot\varepsilon^{\rm sel}$ (2)

where the equation is ordered from left to right such that, for each
component, the efficiency is evaluated for candidates passing the stages to
the left. The efficiencies to reconstruct and identify the muon candidate are
given by $\varepsilon^{\rm rec}_{\mu}$ and $\varepsilon^{\rm id}_{\mu}$
respectively, while $\varepsilon^{\rm trg}$ refers to the efficiency to
trigger the event on the muon candidate. The efficiencies to reconstruct and
identify the electron candidate are given by $\varepsilon^{\rm rec}_{e}$ and
$\varepsilon^{\rm id}_{e}$ respectively. The efficiency to reconstruct and tag
the jet are given by $\varepsilon^{\rm jet}$ and $\varepsilon^{\rm tag}$
respectively, and the efficiency of the additional selection requirements is
given by $\varepsilon^{\rm sel}$.

The efficiencies to reconstruct, identify, and trigger the muon candidate are
determined from simulation, where the simulated Pythia8 sample is weighted in
the muon $p_{\mathrm{T}}$ and $\eta$ to match NLO predictions from aMC@NLO.
Additionally, corrections are applied as a function of the muon
$p_{\mathrm{T}}$ and $\eta$ to account for observed differences in the
efficiency between data and simulation. The corrections are obtained using a
tag-and-probe method on $Z\rightarrow\mu^{+}\mu^{-}$ events, where one of the
muons, the tag, is required to have triggered the event and be fully
reconstructed and identified, and a probe is selected that represents the
other muon and acts as an unbiased estimator of the efficiency, using similar
techniques as those used in Ref. [29]. In the case of the reconstruction
efficiency, the probe is a track reconstructed using the muon stations and
information from tracking detectors not used in the primary track
reconstruction algorithms. For the identification efficiency, the probe is a
fully reconstructed particle with no identification requirements applied, and
for the trigger efficiency, it is a fully reconstructed and identified muon.
The uncertainty is determined by combining the statistical uncertainty due to
the size of the simulated sample, the uncertainties on the correction factors,
and the difference between the efficiencies obtained with and without the NLO
weighting.

The efficiencies related to the reconstruction and identification of the
electron are again obtained from Pythia8 simulation, weighted as a function of
the electron $p_{\mathrm{T}}$ and $\eta$ to match NLO predictions from
aMC@NLO. Data-driven studies of these efficiencies are made again using
similar techniques to Ref. [29]. Corrections to the electron identification
efficiency are obtained using a tag-and-probe method on recorded $Z\rightarrow
e^{+}e^{-}$ decays, where the probe is a reconstructed particle with no
identification requirements applied. For the electron reconstruction
efficiency, no corrections are applied to the simulated sample, but a
systematic uncertainty related to the potential mismodelling in simulation is
determined by comparing the ratio of the number of $Z\rightarrow e^{+}e^{-}$
events where either the two electrons are fully reconstructed, or where one of
the electrons is only reconstructed as a deposit in the electromagnetic
calorimeter. The statistical uncertainty due to the limited size of the
simulated sample is combined with the uncertainty on the corrections and the
difference in the efficiency before and after weighting to determine the total
uncertainty.

The jet reconstruction and tagging efficiencies are determined directly from
Pythia8 simulation with NLO weighting in the jet $p_{\mathrm{T}}$ and $\eta$.
A systematic uncertainty on the reconstruction efficiency is determined by
comparing the variation in the yield of $Z\rightarrow\mu^{+}\mu^{-}$ events
containing a jet in data and simulation when the quality requirements on the
jet are varied, and taking the difference as the uncertainty. The jet tagging
efficiency was previously determined to be modelled accurately in simulation
to a level of 10% using data collected in Run 1 [26]. The level of agreement
is evaluated in the data sample used in this paper by comparing the tagging
efficiency of jets containing fully reconstructed
$B^{\pm}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{\pm}$
decays in data and simulation, where the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson is reconstructed through
its decay to a muon pair. The signal yield is determined by a fit to the
invariant mass of the reconstructed $B$ hadron before and after the tagging
requirement is applied. A similar level of agreement between data and
simulation is observed as in the previous studies, and consequently the same
uncertainty is applied.

The selection efficiency refers to the efficiency of the isolation and impact
parameter requirements applied to the leptons. The impact parameter efficiency
is obtained from Pythia8 simulation where the impact parameter distribution is
smeared using factors obtained from a comparison of
$Z\rightarrow\mu^{+}\mu^{-}$ events in data and simulation. The difference
between the efficiency obtained before and after the smearing procedure is
taken as a systematic uncertainty. The efficiency of the isolation requirement
is obtained directly from Pythia8 simulation, with a systematic uncertainty
applied to account for differences in data and simulation. The difference in
the efficiency of the requirement when applied to $Z\rightarrow\mu^{+}\mu^{-}$
events in data and simulation is taken as a systematic uncertainty to account
for differences due to the underlying event and contributions from additional
$pp$ interactions. An additional contribution to the systematic uncertainty,
due to possible mismodelling of the $t\bar{t}$ process, is determined as the
maximum difference in the efficiency in simulated $t\bar{t}$ events with
different jet multiplicities. A summary of the efficiencies and their
uncertainties is given in Table 1.

The largest contribution to $\mathcal{F}_{\rm res}$ arises from the momentum
resolution of the electron due to bremsstrahlung. A scaling factor is applied
to the electron momentum obtained in simulation to better match the
$p_{\mathrm{T}}$ spectrum of electrons in $Z\rightarrow e^{+}e^{-}$ events in
data. As the jet resolution also contributes, the level of agreement between
data and simulation is evaluated by selecting events containing a $Z$ boson
and a jet which are azimuthally opposed. As the ratio of the $p_{\mathrm{T}}$
of the jet and the $Z$ boson in these events is expected to be close to unity,
the width of the distribution gives an estimate of the jet resolution.
Corrections are obtained that are used to smear the reconstructed jet energy
in simulation. The resolution factor is determined from simulation with both
of these corrections applied, and the difference between the computed values
before and after the corrections taken as a systematic uncertainty. The
resolution factor is determined to be 1.207 $\pm$ 0.006.

Table 1: The efficiency to fully reconstruct and identify the candidates. Source | Efficiency
---|---
trigger | 0.811 $\pm$ 0.016
muon reconstruction | 0.930 $\pm$ 0.010
electron reconstruction | 0.916 $\pm$ 0.026
muon identification | 0.978 $\pm$ 0.008
electron identification | 0.918 $\pm$ 0.012
jet reconstruction | 0.975 $\pm$ 0.016
event selection | 0.564 $\pm$ 0.023
jet tagging | 0.556 $\pm$ 0.056
total | 0.190 $\pm$ 0.022

##  5 Results

Using the formula and inputs described in the previous sections, the cross-
section in the fiducial region defined by the $p_{\mathrm{T}}$,
pseudorapidity, and $\Delta R$ requirements placed on the leptons and the
$b$-jet is determined to be

$\sigma_{t\bar{t}}=126\pm 19\,(\mathrm{stat})\pm 16\,(\mathrm{syst})\pm
5\,(\mathrm{lumi})\,\,\mathrm{fb}$

where the first uncertainty is statistical, the second is systematic, and the
third is due to the luminosity determination. This cross-section is compared
to the theoretical predictions obtained from aMC@NLO, POWHEG and MCFM. Three
different sources of uncertainty are considered on the theoretical
predictions: uncertainties due to the description of the PDFs ($\delta_{\rm
PDF}$), the uncertainty due to the choice of renormalisation and factorisation
scales ($\delta_{\rm scale}$), and the uncertainty on the value of the strong
coupling constant used in the calculation ($\delta_{{\alpha_{s}}}$). The
uncertainty due to the choice of the top quark mass is expected to be small
and is not considered further. The total theoretical uncertainty, $\delta_{\rm
theory}$, is determined by combining the individual uncertainties according to
the formula $\delta_{\rm theory}=\sqrt{\delta_{\rm
PDF}^{2}+\delta_{{\alpha_{s}}}^{2}}+\delta_{\rm scale}$ [30]. A comparison of
the measured cross-section with the predictions is shown in Fig. 5. The result
is shown in the case where the fiducial requirements are placed on the final
state muon, electron and $b$-jet, and where the fiducial requirements are
placed on the top quarks, where the top quarks are defined at parton level
after QCD radiation. The latter fiducial region requires that both top quarks
have a rapidity between 2.0 and 5.0. The measured cross-section in the top
quark fiducial region is obtained by extrapolating from the measured fiducial
region using predictions from aMC@NLO, which contributes an additional 1.5%
uncertainty to the measurement uncertainty, evaluated using the same
techniques as for the theoretical predictions described earlier. The cross-
section in the top quark fiducial region is additionally compared to
predictions from MCFM. The measured cross-section in both fiducial regions is
seen to be in agreement with the predictions.

Table 2: Summary of the systematic uncertainties on the measurement of the $t\bar{t}$ cross-section in the fiducial region defined by the requirements placed on the leptons and the $b$-jet, expressed as a percentage of the measured cross-section. An additional uncertainty due to ${t}{\overline{t}}$ modelling is considered when extrapolating to the top quark fiducial region. Source | %
---|---
trigger |  12.0
muon reconstruction |  11.1
electron reconstruction |  12.8
muon identification |  10.8
electron identification |  11.3
jet reconstruction |  11.6
event selection |  14.0
jet tagging | 10.0
background |  15.1
resolution factor |  10.5
total | 12.7

A summary of the systematic uncertainties contributing to the measurement is
given in Table 2. The dominant systematic uncertainty is due to the knowledge
of the jet tagging efficiency.

Figure 5: Graphical comparison of the measured cross-sections with the
predictions from the aMC@NLO, POWHEG and MCFM generators. For the data, the
inner error band represents the statistical uncertainty, and the outer the
total, while for the theoretical predictions, the inner band represents the
scale uncertainty and the outer represents the total. The prediction is shown
(above) for the muon, electron and jet fiducial, and (below) for the top quark
fiducial region.

##  6 Conclusion

The cross-section for top quark pair production in the forward region at LHCb
has been measured using the $\mu eb$ final state, where the presence of a
muon, electron and $b$-jet are used to identify ${t}{\overline{t}}$
candidates. The cross-section is measured in two fiducial regions: where
fiducial requirements are placed on the final state objects, and where
fiducial requirements are placed on the top quarks themselves. The latter
fiducial cross-section is obtained by scaling the former by an extrapolation
factor obtained from aMC@NLO. The measurement precision of 20% is comparable
to prior measurements of top quark production at LHCb in Run 1 and to the
precision of the theoretical predictions. The measurement uncertainty is
dominated by the statistical precision of the data sample and the knowledge of
the $b$-tagging efficiency.

The final state presented here is selected with a high purity with respect to
measurements in other final states. While a number of systematic uncertainties
contributing to the measurement are uncorrelated with measurements in other
final states, future reductions of the uncertainty on the $b$-tagging
efficiency, common to all final states, will be required in order to fully
exploit their complementarity. With the increase in the data-taking
capabilities of the LHCb detector in future upgrades [31, 32], measurements in
the $\mu eb$ final state will no longer be statistically limited, and have the
potential to achieve the highest precision on the measurement of the
${t}{\overline{t}}$ production cross-section at LHCb.

## 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 (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FASO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing
resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany),
INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom),
RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF
(Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities
behind the multiple open-source software packages on which we depend.
Individual groups or members have received support from AvH Foundation
(Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union),
ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France), RFBR, RSF
and Yandex LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund,
the Royal Society, the English-Speaking Union and the Leverhulme Trust (United
Kingdom).

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LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, A. Alfonso Albero38, S. Ali43, G. Alkhazov31, P.
Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L.
An3, L. Anderlini18, G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B.
Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M.
Artuso61, E. Aslanides6, M. Atzeni42, G. Auriemma26, I. Babuschkin56, S.
Bachmann12, J.J. Back50, A. Badalov38,m, C. Baesso62, S. Baker55, V.
Balagura7,b, W. Baldini17, A. Baranov35, R.J. Barlow56, C. Barschel40, S.
Barsuk7, W. Barter56, F. Baryshnikov32, V. Batozskaya29, V. Battista41, A.
Bay41, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61, L.J. Bel43, N.
Beliy63, V. Bellee41, N. Belloli21,i, K. Belous37, I. Belyaev32,40, E. Ben-
Haim8, G. Bencivenni19, S. Benson43, S. Beranek9, A. Berezhnoy33, R. Bernet42,
D. Berninghoff12, E. Bertholet8, A. Bertolin23, C. Betancourt42, F. Betti15,
M.O. Bettler40, M. van Beuzekom43, Ia. Bezshyiko42, S. Bifani47, P. Billoir8,
A. Birnkraut10, A. Bizzeti18,u, M. Bjørn57, T. Blake50, F. Blanc41, S.
Blusk61, V. Bocci26, T. Boettcher58, A. Bondar36,w, N. Bondar31, I.
Bordyuzhin32, S. Borghi56,40, M. Borisyak35, M. Borsato39, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12, J.
Brodzicka27, D. Brundu16, E. Buchanan48, C. Burr56, A. Bursche16,f, J.
Buytaert40, W. Byczynski40, S. Cadeddu16, H. Cai64, R. Calabrese17,g, R.
Calladine47, M. Calvi21,i, M. Calvo Gomez38,m, A. Camboni38,m, P. Campana19,
D.H. Campora Perez40, L. Capriotti56, A. Carbone15,e, G. Carboni25,j, R.
Cardinale20,h, A. Cardini16, P. Carniti21,i, L. Carson52, K. Carvalho Akiba2,
G. Casse54, L. Cassina21, M. Cattaneo40, G. Cavallero20,40,h, R. Cenci24,t, D.
Chamont7, M.G. Chapman48, M. Charles8, Ph. Charpentier40, G.
Chatzikonstantinidis47, M. Chefdeville4, S. Chen16, S.F. Cheung57, S.-G.
Chitic40, V. Chobanova39, M. Chrzaszcz42, A. Chubykin31, P. Ciambrone19, X.
Cid Vidal39, G. Ciezarek40, P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J.
Closier40, V. Coco40, J. Cogan6, E. Cogneras5, V. Cogoni16,f, L. Cojocariu30,
P. Collins40, T. Colombo40, A. Comerma-Montells12, A. Contu16, G. Coombs40, S.
Coquereau38, G. Corti40, M. Corvo17,g, C.M. Costa Sobral50, B. Couturier40,
G.A. Cowan52, D.C. Craik58, A. Crocombe50, M. Cruz Torres1, R. Currie52, C.
D’Ambrosio40, F. Da Cunha Marinho2, C.L. Da Silva73, E. Dall’Occo43, J.
Dalseno48, A. Davis3, O. De Aguiar Francisco40, K. De Bruyn40, S. De Capua56,
M. De Cian12, J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone19,
C.T. Dean53, D. Decamp4, L. Del Buono8, B. Delaney49, H.-P. Dembinski11, M.
Demmer10, A. Dendek28, D. Derkach35, O. Deschamps5, F. Dettori54, B. Dey65, A.
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Dziurda40, A. Dzyuba31, S. Easo51, U. Egede55, V. Egorychev32, S.
Eidelman36,w, S. Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53,
S. Ely61, A. Ene30, S. Esen12, H.M. Evans49, T. Evans57, A. Falabella15, N.
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Kucewicz27,l, M. Kucharczyk27, V. Kudryavtsev36,w, A.K. Kuonen41, T.
Kvaratskheliya32,40, D. Lacarrere40, G. Lafferty56, A. Lai16, G. Lanfranchi19,
C. Langenbruch9, T. Latham50, C. Lazzeroni47, R. Le Gac6, A. Leflat33,40, J.
Lefrançois7, R. Lefèvre5, F. Lemaitre40, E. Lemos Cid39, P. Lenisa17, O.
Leroy6, T. Lesiak27, B. Leverington12, P.-R. Li63, T. Li3, Y. Li7, Z. Li61, X.
Liang61, T. Likhomanenko68, R. Lindner40, F. Lionetto42, V. Lisovskyi7, X.
Liu3, D. Loh50, A. Loi16, I. Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M.
Lucio Martinez39, A. Lupato23, E. Luppi17,g, O. Lupton40, A. Lusiani24, X.
Lyu63, F. Machefert7, F. Maciuc30, V. Macko41, P. Mackowiak10, S. Maddrell-
Mander48, O. Maev31,40, K. Maguire56, D. Maisuzenko31, M.W. Majewski28, S.
Malde57, B. Malecki27, A. Malinin68, T. Maltsev36,w, G. Manca16,f, G.
Mancinelli6, D. Marangotto22,q, J. Maratas5,v, J.F. Marchand4, U. Marconi15,
C. Marin Benito38, M. Marinangeli41, P. Marino41, J. Marks12, G.
Martellotti26, M. Martin6, M. Martinelli41, D. Martinez Santos39, F. Martinez
Vidal71, A. Massafferri1, R. Matev40, A. Mathad50, Z. Mathe40, C. Matteuzzi21,
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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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Sezione INFN di Milano Bicocca, Milano, Italy
22Sezione di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National University of Science and Technology MISIS, Moscow, Russia,
associated to 32
70National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
71Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
72Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43
73Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xNational Research University Higher School of Economics, Moscow, Russia
†Deceased