EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2016-232 LHCb-PAPER-2016-038 October 25, 2016

Measurement of forward ${t}{\overline{t}}$, ${W}\\!+\\!{{b}{\overline{b}}}$
and ${W}\\!+\\!{{c}{\overline{c}}}$ production in $pp$ collisions at
$\sqrt{s}=8$ TeV

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

The production of ${t}{\overline{t}}$, ${W}\\!+\\!{{b}{\overline{b}}}$ and
${W}\\!+\\!{{c}{\overline{c}}}$ is studied in the forward region of proton-
proton collisions collected at a centre-of-mass energy of 8 TeV by the LHCb
experiment, corresponding to an integrated luminosity of 1.98 $\pm$ 0.02
$\mbox{\,fb}^{-1}$. The $W$ bosons are reconstructed in the decays
$W\rightarrow{\ell}\nu$, where $\ell$ denotes muon or electron, while the $b$
and $c$ quarks are reconstructed as jets. All measured cross-sections are in
agreement with next-to-leading-order Standard Model predictions.

Published in Phys. Lett. B767 (2017) 110

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

##  1 Introduction

The production of ${t}{\overline{t}}$ pairs from proton-proton ($pp$)
collisions in the forward region is of considerable interest, as it may be
sensitive to physics beyond the Standard Model (SM) [1]. Furthermore, forward
${t}{\overline{t}}$ events can be used to constrain the gluon parton
distribution function (PDF) at large momentum fraction [2]. The
${t}{\overline{t}}$ cross-section has been measured at ATLAS and CMS using
several final states and at various centre-of-mass energies [3, 4, 5]. LHCb
has also measured top quark production in the forward region in the
$W\\!+\\!b$ final state [6].

Measurements of the production cross-sections of
${W}\\!+\\!{{b}{\overline{b}}}$ and ${W}\\!+\\!{{c}{\overline{c}}}$ in the
forward region provide experimental tests of perturbative quantum
chromodynamics (pQCD) [7, 8, 9], in a complementary phase space region to
ATLAS and CMS. Previous studies of the ${W}\\!+\\!{{b}{\overline{b}}}$ final
state have been performed by ATLAS [10] and CMS [11, 12] at centre-of-mass
energies $\sqrt{s}=7\mathrm{\,Te\kern-1.00006ptV}$ and
$8\mathrm{\,Te\kern-1.00006ptV}$. LHCb has previously performed measurements
of the production cross-sections of a $W$ boson with at least one observed $b$
or $c$ jet [13] at $7$ and $8\mathrm{\,Te\kern-1.00006ptV}$, and a $Z$ boson
with at least one $b$ jet at $7\mathrm{\,Te\kern-1.00006ptV}$ [14].

This Letter reports a study of events containing one isolated lepton (muon or
electron) and two heavy-flavour tagged jets to measure the production cross-
sections of ${t}{\overline{t}}$, ${W^{+}}\\!+\\!{{b}{\overline{b}}}$,
${W^{-}}\\!+\\!{{b}{\overline{b}}}$, ${W^{+}}\\!+\\!{{c}{\overline{c}}}$ and
${W^{-}}\\!+\\!{{c}{\overline{c}}}$. The study of
${W}\\!+\\!{{c}{\overline{c}}}$ is the first of its kind. Measurements are
performed using a data sample corresponding to an integrated luminosity of
$1.98\pm 0.02\mbox{\,fb}^{-1}$ of $pp$ collisions recorded at
$8\mathrm{\,Te\kern-1.00006ptV}$ during 2012 by the LHCb experiment.

##  2 The LHCb detector and samples

The LHCb detector [15, 16] is a single-arm forward spectrometer fully
instrumented in 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 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$\mathrm{\,Ge\kern-1.00006ptV}$.111In this Letter natural units
where $c$ = 1 are used. 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_{\rm T}$}){\,\upmu\rm m}$, where $p_{\rm T}$ is the component
of the momentum transverse to the beam, in $\mathrm{\,Ge\kern-1.00006ptV}$.
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 (SPD) and
preshower (PRS) 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.

The ${W}\rightarrow\mu\nu$ candidates are required to satisfy the hardware
trigger requirement for muons, of having hits in the muon system corresponding
to a high transverse momentum particle, and to satisfy the software trigger
requirement of $\mbox{$p_{\rm T}$}(\mu)>10\mathrm{\,Ge\kern-1.00006ptV}$. The
${W}\rightarrow e\nu$ candidates are required to satisfy the hardware trigger
requirement for electrons of having an electromagnetic cluster of high
transverse energy associated with signals in the PRS and SPD detectors, and
the software trigger, which selects events with an electron with
$\mbox{$p_{\rm T}$}(e)>15\mathrm{\,Ge\kern-1.00006ptV}$. A global event cut
(GEC) on the number of hits in the SPD is applied in order to prevent high-
multiplicity events from dominating the processing time of the reconstruction
code.

Simulated event samples of ${W}\\!+\\!\rm{jets}$, ${Z}\\!+\\!\rm{jets}$,
${t}{\overline{t}}$, single-top and diboson (${W}\\!{Z}$,${Z}\\!{Z}$)
production are generated using Pythia 8 [17, *Sjostrand:2006za] with a
specific LHCb configuration [19]. Event samples of
${W}\\!+\\!{{b}{\overline{b}}}$, ${W}\\!+\\!{{c}{\overline{c}}}$,
${Z}\\!+\\!{{b}{\overline{b}}}$ and ${Z}\\!+\\!{{c}{\overline{c}}}$ production
are generated with Alpgen [20], which includes tree-level contributions with
up to four additional emissions of final state partons with respect to the
leading-order diagram. Pythia 8 is used to perform the hadronisation for these
samples. The cross-sections of the simulated processes are calculated at next-
to-leading-order (NLO) including spin correlation effects with MCFM [21] using
the CT10 PDF set [22]. Decays of hadronic particles are described by EvtGen
[23], in which final-state radiation is generated using Photos [24]. The
interaction of the generated particles with the detector, and its response,
are implemented using the Geant4 toolkit [25, *Agostinelli:2002hh] as
described in Ref. [27]. Since neither showering nor hadronisation are included
in MCFM, an overall correction is calculated to compare the measurements with
the predicted cross-section at particle-level. This is done by generating
${W}\\!+\\!{{b}{\overline{b}}}$, ${W}\\!+\\!{{c}{\overline{c}}}$ and
${t}{\overline{t}}$ events with Pythia 8 with the CT10 PDF set [22] where the
same acceptance requirements are applied. The particle-level lepton momentum
used here is the momentum after final-state radiation as implemented in Pythia
8.

##  3 Event selection

Events are selected by requiring the presence of either a high-$p_{\rm T}$
muon or electron and two heavy-flavour tagged jets. The same fiducial
definition for lepton and jets used in previous studies [6, 13, 28] is
applied. The lepton must have $\mbox{$p_{\rm
T}$({$\ell$})}>20\mathrm{\,Ge\kern-1.00006ptV}$ and
$2.0<\eta({\ell})<\eta_{\rm{max}}({\ell})$, where $\eta_{\rm{max}}({\ell})$ is
$4.50$ for a muon candidate, corresponding to the muon identification system
acceptance, and is $4.25$ for an electron candidate, corresponding to the
electromagnetic calorimeter acceptance. The jets are required to have
$\mbox{$p_{\rm T}({\rm j})$}>12.5\mathrm{\,Ge\kern-1.00006ptV}$ and
$2.2<\mbox{$\eta({\rm j})$}<4.2$. Due to the limited sample size to validate
the heavy-flavour tagging algorithm for higher $p_{\rm T}$ jets [29], only
jets with $\mbox{$p_{\rm T}({\rm j})$}<100\mathrm{\,Ge\kern-1.00006ptV}$ are
considered. The lepton is required to be isolated from both jets using
$\Delta\text{\it R}({\ell},\mathrm{j})>0.5$, where $\Delta\text{\it
R}=\sqrt{\Delta\eta^{2}+\Delta\phi^{2}}$ is the distance between them in
$\eta$-$\phi$ space and $\phi$ is the azimuthal angle. This requirement serves
to remove the background formed by leptons coming from the same parton as the
jets. The jets are also required to have $\Delta\text{\it
R}({\mathrm{j}_{1}},{\mathrm{j}_{2}})>0.5$, where $\mathrm{j}_{1}$
($\mathrm{j}_{2}$) is the highest (second highest) $p_{\rm T}$ jet of the
pair. Events with $\mbox{$p^{\rm miss}_{\rm
T}$}<15\mathrm{\,Ge\kern-1.00006ptV}$, where $p^{\rm miss}_{\rm T}$ is the
transverse component of
$(\vec{p}({{\ell}})+\vec{p}({\mathrm{j}_{1}})+\vec{p}({{\mathrm{j}_{2}}}))$,
are removed to reduce the contamination from events not containing a $W$
boson. If more than one (${\ell}+{\mathrm{j}_{1}}+{\mathrm{j}_{2}}$) candidate
is found in the event, the candidate with highest $p^{\rm miss}_{\rm T}$ is
selected.

Jets are reconstructed using a particle flow algorithm [30] and clustered
using the $\text{anti-}k_{\mathrm{T}}$ algorithm [31] with distance parameter
$R=0.5$ as implemented in the FastJet software package [32]. As in Ref. [30],
the jet energy is corrected to the particle level, excluding neutrinos, and
the same jet quality requirements are applied. Jets are heavy-flavour tagged,
i.e. as originating from a $b$ or $c$ quark, by the presence of a secondary
vertex (SV) with $\Delta\text{\it R}<0.5$ between the jet axis and the
direction of flight of the heavy-flavour hadron candidate, defined by the
vector from the PV to the SV position.

The SV-tagger algorithm, described in detail in Ref. [29], uses two boosted
decision trees (BDTs) [33, 34]: one that separates heavy-flavour from light-
parton jets ($\mathrm{BDT}({bc|udsg})$) and one that separates $b$ jets from
$c$ jets ($\mathrm{BDT}({b|c})$). Both jets used in the analysis are required
to have $\mathrm{BDT}({bc|udsg})>0.2$, which gives a heavy-flavour tagging
efficiency of about $50\%$ ($20\%$) for $b$ ($c$) jets and a misidentification
probability of about $0.1\%$ for light jets.

In order to suppress the ${Z}\\!+\\!\rm{jets}$ background, events with an
additional oppositely charged high-$p_{\rm T}$ lepton that fulfills the lepton
requirements described above are vetoed. Backgrounds from misidentified
leptons or semileptonic decays of heavy-flavour hadrons are suppressed by two
requirements applied to the lepton: $\rm IP({\ell})$ must be less than
$0.04\rm\,mm$ and $\mbox{$p_{\rm T}$({$\ell$})}/\mbox{$p_{\rm T}({{\rm
j}_{\ell}})$}>0.8$, where ${{\rm j}_{\ell}}$ is defined as a reconstructed jet
with relaxed quality criteria that contains the lepton.

##  4 Backgrounds

In both the electron and muon channels, the background processes include
${Z}\\!+\\!{{b}{\overline{b}}}$ and ${Z}\\!+\\!{{c}{\overline{c}}}$ production
with $Z\rightarrow\mu\mu$ or $Z\rightarrow ee$, where one of the final state
leptons is not reconstructed. $Z(\rightarrow\tau\tau)+{{b}{\overline{b}}}$
production is also considered, where at least one $\tau$ decays to an electron
or a muon. A small contribution of $Z\rightarrow\tau\tau$ produced in
association with one $b$ or $c$ jet is also included. Other processes of $Z$
production associated to jets are negligible. Background contributions from
$W(\rightarrow\ell{\nu})$+jets where the event does not contain two $b$ jets,
and $W(\rightarrow\tau{{\nu}_{\tau}})+{{b}{\overline{b}}}$ where $\tau$ decays
to an electron or muon are also included. Single-top,
$W(\rightarrow\ell{\nu})Z(\rightarrow{{b}{\overline{b}}})$ and
$Z(\rightarrow\ell\ell)Z(\rightarrow{{b}{\overline{b}}})$ production are
considered as background processes. The expected yields of the background
processes described above are obtained from NLO cross-sections. Weight factors
are applied to compensate for residual differences between data and simulation
for GEC, trigger and heavy-flavour tagging efficiencies. Further details about
these factors and their uncertainties are given in Sec. 5.4.

The QCD multi-jet background, which includes lepton misidentification and
semileptonic decays of a beauty or charm hadron, is estimated by using events
which fail the $\mbox{$p_{\rm T}$({$\ell$})}/\mbox{$p_{\rm T}({{\rm
j}_{\ell}})$}>0.8$ requirement. The QCD multi-jet background normalisation is
adjusted in order to describe the event yield at $\rm IP({\ell})>0.04\rm\,mm$,
after subtracting the non-QCD backgrounds obtained from simulation.

##  5 Signal yield determination

###  5.1 Overview

The data sample is split into four subsamples, according to the flavour and
charge of the lepton ($\mu^{\pm}$ and $e^{\pm}$). A simultaneous fit to the
distributions of four variables is performed to determine the
${t}{\overline{t}}$, ${W^{+}}\\!+\\!{{b}{\overline{b}}}$,
${W^{-}}\\!+\\!{{b}{\overline{b}}}$, ${W^{+}}\\!+\\!{{c}{\overline{c}}}$, and
${W^{-}}\\!+\\!{{c}{\overline{c}}}$ yields in each sample. The four variables
used in the fit are the invariant mass of the two jets ($m_{\rm jj}$), the
response of a multivariate classifier trained to distinguish between
${t}{\overline{t}}$ and ${W}\\!+\\!{{b}{\overline{b}}}$ events and the
multivariate discriminant classifier for each jet, $\mathrm{j}_{1}$
$\mathrm{BDT}({b|c})$ and $\mathrm{j}_{2}$ $\mathrm{BDT}({b|c})$, trained to
discriminate between $b$ and $c$ jets. The expected background components are
obtained from simulation, with the exception of the QCD multijet background.
The fitted signal yields are converted into cross-sections using simulation
and data-driven efficiencies and the measurement of the integrated luminosity
[35]. The systematic uncertainties are included as nuisance parameters in the
fit and propagated to the final result.

###  5.2 Fit variables

While ${W}\\!+\\!{{b}{\overline{b}}}$ and ${W}\\!+\\!{{c}{\overline{c}}}$
processes can be disentangled using the $\mathrm{BDT}({b|c})$ variables for
both jets, the separation between ${t}{\overline{t}}$ and
${W}\\!+\\!{{b}{\overline{b}}}$ or ${W}\\!+\\!{{c}{\overline{c}}}$ is obtained
by using the $m_{\rm jj}$ variable and a multivariate discriminant, uGB,
constructed such that its response is minimally correlated with $m_{\rm jj}$
[36]. The variables $m_{\rm jj}$, $\mathrm{j}_{1}$ $\mathrm{BDT}({b|c})$ and
$\mathrm{j}_{2}$ $\mathrm{BDT}({b|c})$ are found to be uncorrelated. The uGB
response is trained in simulation using 11 kinematic variables of the lepton
and jets: $p_{\rm T}$($\ell$), $\eta({\ell})$, $\mbox{$p_{\rm
T}$}({{\mathrm{j}_{1}}})$, $\mbox{$p_{\rm T}$}({{\mathrm{j}_{2}}})$,
$m({\mathrm{j}_{1}})$, $m({\mathrm{j}_{2}})$, $p_{\rm T}({\rm jj})$,
$\Delta\text{\it R}({\mathrm{j}_{1}},{\mathrm{j}_{2}})$, $\Delta\text{\it
R}({\rm jj},{\mathrm{j}_{1}})$, $\Delta\text{\it R}({\rm
jj},{\mathrm{j}_{2}})$ and $\cos(\theta_{{\rm jj}}({{\ell}}))$, where
$\theta_{{\rm jj}}({\ell})$ is the lepton scattering angle in the dijet rest
frame and ${\rm jj}$ represents the dijet system. The muon and electron decay
channels are trained separately. Figure 1 shows the correlation between the
uGB and the $m_{\rm jj}$ variables. In the fit all variables are treated as
uncorrelated; the effect of the observed small correlations is taken into
account in the systematic uncertainties of the results.

  * Figure 1: Average of uGB response in different intervals of $m_{\rm jj}$ for ${W}\\!+\\!{{b}{\overline{b}}}$ (black) and ${t}{\overline{t}}$ (green). The vertical error bars represent the standard error of the uGB mean in each interval.

###  5.3 Signal determination

A binned maximum likelihood fit is performed to determine the yields of
${{t}{\overline{t}}}$, ${{W^{+}}\\!+\\!{{b}{\overline{b}}}}$,
${{W^{-}}\\!+\\!{{b}{\overline{b}}}}$, ${{W^{+}}\\!+\\!{{c}{\overline{c}}}}$
and ${{W^{-}}\\!+\\!{{c}{\overline{c}}}}$. The simulated background yields are
normalised to NLO predictions and they are allowed to vary in the fit within
their uncertainties. The QCD multijet background is normalised from a data-
driven method as explained in Section 4. The fit is performed assuming the
four variables ($m_{\rm jj}$, uGB, $\mathrm{j}_{1}$ $\mathrm{BDT}({b|c})$ and
$\mathrm{j}_{2}$ $\mathrm{BDT}({b|c})$) to be uncorrelated.

The free parameters in the fit are the normalisation factors with respect to
the SM predicted yields $K(i)$, where
$i={{t}{\overline{t}}},{{W^{+}}\\!+\\!{{b}{\overline{b}}}},{{W^{-}}\\!+\\!{{b}{\overline{b}}}},{{W^{+}}\\!+\\!{{c}{\overline{c}}}},{{W^{-}}\\!+\\!{{c}{\overline{c}}}}$.
The $K({{t}{\overline{t}}})$ parameter is fitted using all four samples, while
the others are fitted in each corresponding sample. The projections of the fit
in each of the four samples are shown in Figs. 2-5, while the fit results are
given in Table 1.

Figure 2: Projections of the simultaneous 4D-fit results for the $\mu^{+}$
sample: a) the dijet mass; b) the uGB response; the $\mathrm{BDT}({b|c})$ of
the c) leading and d) sub-leading jets.

Figure 3: Projections of the simultaneous 4D-fit results for the $\mu^{-}$
sample: a) the dijet mass; b) the uGB response; the $\mathrm{BDT}({b|c})$ of
the c) leading and d) sub-leading jets.

Figure 4: Projections of the simultaneous 4D-fit results for the $e^{+}$
sample: a) the dijet mass; b) the uGB response; the $\mathrm{BDT}({b|c})$ of
the c) leading and d) sub-leading jets.

Figure 5: Projections of the simultaneous 4D-fit results for the $e^{-}$ sample: a) the dijet mass; b) the uGB response; the $\mathrm{BDT}({b|c})$ of the c) leading and d) sub-leading jets.  Table 1: Simultaneous 4D-fit results for each of the four signal categories ($e$ and $\mu$, negative and positive). The normalisation factor $K$ and the fitted yields per sample are shown. The uncertainties quoted are statistical only. Signal | $K$ |  $\mu$ sample yields |  $e$ sample yields
---|---|---|---
${W^{+}}\\!+\\!{{b}{\overline{b}}}$ | $1.49^{+0.23}_{-0.22}$ | $45.5^{+6.9}_{-6.4}$ | $20.5^{+3.1}_{-2.9}$
${W^{-}}\\!+\\!{{b}{\overline{b}}}$ | $1.67^{+0.33}_{-0.30}$ | $28.7^{+5.6}_{-4.9}$ | $12.1^{+2.3}_{-2.1}$
${W^{+}}\\!+\\!{{c}{\overline{c}}}$ | $1.92^{+0.68}_{-0.58}$ | $12.8^{+4.5}_{-3.9}$ | $5.7^{+2.0}_{-1.7}$
${W^{-}}\\!+\\!{{c}{\overline{c}}}$ | $1.58^{+0.87}_{-0.73}$ | $5.7^{+3.1}_{-2.6}$ | $2.5^{+1.4}_{-1.2}$
${t}{\overline{t}}$ | $1.17^{+0.35}_{-0.31}$ |  $8.7^{+2.6}_{-2.3}$ ($\mu^{+}$) |  $3.7^{+1.1}_{-1.0}$ ($e^{+}$)
$8.3^{+2.5}_{-2.2}$ ($\mu^{-}$) |  $4.0^{+1.2}_{-1.1}$ ($e^{-}$)

###  5.4 Systematic uncertainties

Systematic effects can impact the results in two ways: by affecting signal and
background yields, or by altering template shapes used in the fits. The
efficiency of the GEC is measured in a ${Z}\\!+\\!\rm{jet}$ sample selected
with a looser trigger requirement [28] and a $2\%$ uncertainty is assigned to
account for the final-state dependence of the GEC efficiency observed in
simulation. The systematic uncertainty on the integrated luminosity is
$1.16\%$ [35].

The lepton reconstruction and trigger efficiencies are studied using data-
driven methods in $Z\rightarrow\ell^{+}\ell^{-}$ [37, 38]. Those studies show
that data and simulation agree within 1.0–$5.0\%$ depending on $\eta(\ell)$
and $\mbox{$p_{\rm T}$}(\ell)$, which is taken as systematic uncertainty. The
uncertainty of the lepton kinematic efficiency, which includes the effect of
final-state radiation, is neglected. The method described in Ref. [29] is used
to assess the systematic uncertainty due to the errors of the heavy-flavour
tagging efficiency weight-factor described in Sec. 4, which amounts to
5–$10\%$ depending on $p_{\rm T}({\rm j})$.

The systematic uncertainty of the jet energy calibration includes possible
biases due to flavour dependence ($2\%$), tracks not associated to a real
particle ($1.2\%$), track momentum resolution ($1\%$) and residual differences
between simulation and data due to pile-up and calorimeter response ($1\%$) as
described in Refs. [28, 30]. The jet energy resolution at LHCb is modelled in
simulation to an accuracy of about $10\%$ [30, 13]. The uncertainties related
to the jet reconstruction and quality selection efficiencies are found to be
below $2\%$. The jet-related systematic uncertainties affect both the template
shapes and the expected yields.

The simulated background normalisations are predicted at NLO and they are
affected by uncertainties on the PDF ($\delta_{\rm PDF}$), on the strong
coupling constant $\alpha_{\rm s}$ ($\delta_{\alpha s}$) and on the
renormalisation and factorisation scales ($\delta_{\rm scale}$). The PDF
uncertainty is evaluated following the procedure of Ref. [39]. The influence
of the uncertainty on the strong coupling constant is evaluated by calculating
the cross-sections with PDF sets [22] using values of $\alpha_{\rm s}(M_{Z})$:
0.117, 0.118 and 0.119. The scale uncertainty is evaluated by calculating the
cross-sections varying the renormalisation and factorisation scale by a factor
of two. The total uncertainty is taken as $\sqrt{({\delta^{2}_{\rm
PDF}}+{\delta^{2}_{\alpha s}})}+\delta_{\rm scale}$ as done in Ref. [6] which
translates to relative uncertainties on the signal yields in the range
3–$10\%$. These theoretical uncertainties are also considered in the signal
yields in the experimental acceptance.

The systematic uncertainties in the normalisations due to the limited size of
the simulated samples are between 1 and 7%. The uncertainty on the
normalisation of the QCD multi-jet background, taken from data, is found to
have a negligible effect.

Possible correlation effects between the fitted variables are studied by using
templates generated randomly from the analysis templates with or without
correlations found in simulation. It is found that the correlation and the fit
procedure can affect the final yields by up to $10\%$.

All significant systematic uncertainties are correlated between the four
samples except for the uncertainty due to the finite size of the simulated
samples, which affects each sample and process independently.

##  6 Results and Conclusions

The production cross-sections for ${t}{\overline{t}}$,
$W^{+}+{{b}{\overline{b}}}$, $W^{-}+{{b}{\overline{b}}}$,
$W^{+}+{{c}{\overline{c}}}$ and $W^{-}+{{c}{\overline{c}}}$ are measured for
$pp$ collisions at a centre-of-mass energy of 8
$\mathrm{\,Te\kern-1.00006ptV}$ corresponding to an integrated luminosity of
$1.98\pm 0.02\mbox{\,fb}^{-1}$ of data collected in 2012 by the LHCb
experiment. These production cross-sections are obtained as the product of the
normalisation factors shown in Table 1 and the expected SM cross-sections. The
muons (electrons) coming from the $W$ boson are required to have
$2.0<\eta({\ell})<4.5$ ($2.0<\eta({\ell})<4.25$) and $\mbox{$p_{\rm
T}$({$\ell$})}>20\mathrm{\,Ge\kern-1.00006ptV}$, while the jets are required
to have $2.2<\mbox{$\eta({\rm j})$}<4.2$ and $\mbox{$p_{\rm T}({\rm
j})$}>12.5\mathrm{\,Ge\kern-1.00006ptV}$. In addition, the transverse
component of
$(\vec{p}({{\ell}})+\vec{p}({\mathrm{j}_{1}})+\vec{p}({{\mathrm{j}_{2}}}))$ is
required to be $\mbox{$p^{\rm miss}_{\rm
T}$}>15\mathrm{\,Ge\kern-1.00006ptV}$. The measured and expected cross-
sections are presented in Table 2 and Fig. 6. The significance obtained using
Wilks’ theorem [40] is 4.9$\sigma$ for ${t}{\overline{t}}$, 7.1$\sigma$ for
${W^{+}}\\!+\\!{{b}{\overline{b}}}$, 5.6$\sigma$ for
${W^{-}}\\!+\\!{{b}{\overline{b}}}$, 4.7$\sigma$ for
${W^{+}}\\!+\\!{{c}{\overline{c}}}$ and 2.5$\sigma$ for
${W^{-}}\\!+\\!{{c}{\overline{c}}}$. The correlation matrix of the measured
cross-sections is presented in Table 3. The measured cross-sections are in
agreement with the SM predictions calculated at NLO using MCFM and the CT10
PDF set.

Table 2:  Observed and expected cross-sections in the fiducial region defined in Section 3. The first uncertainty on the expected cross-sections is related to the scale variation and the second is the total. The first uncertainty on the observed cross-sections is statistical and the second is systematic. Process | Expected $[\rm\,pb]$ | Observed $[\rm\,pb]$ |  Significance
---|---|---|---
${W^{+}}\\!+\\!{{b}{\overline{b}}}$ | $0.081$ | ${}^{+0.022}_{-0.013}$ | ${}^{+0.040}_{-0.018}$ | $0.121$ | ${}^{+0.019}_{-0.018}$ | ${}^{+0.029}_{-0.020}$ | $7.1\sigma$
${W^{-}}\\!+\\!{{b}{\overline{b}}}$ | $0.056$ | ${}^{+0.014}_{-0.010}$ | ${}^{+0.018}_{-0.013}$ | $0.093$ | ${}^{+0.018}_{-0.017}$ | ${}^{+0.023}_{-0.016}$ | $5.6\sigma$
${W^{+}}\\!+\\!{{c}{\overline{c}}}$ | $0.123$ | ${}^{+0.034}_{-0.020}$ | ${}^{+0.060}_{-0.027}$ | $0.24$ | ${}^{+0.08}_{-0.07}$ | ${}^{+0.08}_{-0.04}$ | $4.7\sigma$
${W^{-}}\\!+\\!{{c}{\overline{c}}}$ | $0.084$ | ${}^{+0.021}_{-0.015}$ | ${}^{+0.027}_{-0.020}$ | $0.133$ | ${}^{+0.073}_{-0.062}$ | ${}^{+0.050}_{-0.022}$ | $2.5\sigma$
${t}{\overline{t}}$ | $0.045$ | ${}^{+0.008}_{-0.007}$ | ${}^{+0.012}_{-0.010}$ | $0.05$ | ${}^{+0.02}_{-0.01}$ | ${}^{+0.02}_{-0.01}$ | $4.9\sigma$
Table 3:  Correlation matrix for the measured cross sections. The correlations are given in %.  Process |  ${t}{\overline{t}}$ |  ${W^{+}}\\!+\\!{{b}{\overline{b}}}$ |  ${W^{-}}\\!+\\!{{b}{\overline{b}}}$ |  ${W^{+}}\\!+\\!{{c}{\overline{c}}}$ |  ${W^{-}}\\!+\\!{{c}{\overline{c}}}$
---|---|---|---|---|---
${t}{\overline{t}}$ | 100.00 |  |  |  |
${W^{+}}\\!+\\!{{b}{\overline{b}}}$ | 39.02 | 100.00 |  |  |
${W^{-}}\\!+\\!{{b}{\overline{b}}}$ | 35.10 | 58.62 | 100.00 |  |
${W^{+}}\\!+\\!{{c}{\overline{c}}}$ | 31.26 | 30.87 | 37.65 | 100.00 |
${W^{-}}\\!+\\!{{c}{\overline{c}}}$ | 19.06 | 31.97 | 20.16 | 22.99 | 100.00
Figure 6: Graphical representation of Table 2. The outer bars (light yellow)
correspond to the total uncertainties of the measured cross-sections and the
inner bars (dark yellow) correspond to the statistical uncertainties.
Theoretical prediction is represented by the black markers and error bars,
where inner and outer uncertainties represent the scale and the total errors
respectively.

## 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); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOM
and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES
and 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), Conseil Général de Haute-
Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR and Yandex
LLC (Russia), GVA, XuntaGal and GENCAT (Spain), Herchel Smith Fund, The Royal
Society, Royal Commission for the Exhibition of 1851 and the Leverhulme Trust
(United Kingdom).

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LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar6, J. Albrecht10,
F. Alessio40, M. Alexander53, S. Ali43, G. Alkhazov31, P. Alvarez Cartelle55,
A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L. An41, 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, G. Auriemma26, M. Baalouch5, I. Babuschkin56, S. Bachmann12, J.J.
Back50, A. Badalov38, C. Baesso62, S. Baker55, W. Baldini17, R.J. Barlow56, C.
Barschel40, S. Barsuk7, W. Barter40, M. Baszczyk27, V. Batozskaya29, B.
Batsukh61, V. Battista41, A. Bay41, L. Beaucourt4, J. Beddow53, F. Bedeschi24,
I. Bediaga1, L.J. Bel43, V. Bellee41, N. Belloli21,i, K. Belous37, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson43, J. Benton48, A.
Berezhnoy33, R. Bernet42, A. Bertolin23, F. Betti15, M.-O. Bettler40, M. van
Beuzekom43, Ia. Bezshyiko42, S. Bifani47, P. Billoir8, T. Bird56, A.
Birnkraut10, A. Bitadze56, A. Bizzeti18,u, T. Blake50, F. Blanc41, J.
Blouw11,†, S. Blusk61, V. Bocci26, T. Boettcher58, A. Bondar36,w, N.
Bondar31,40, W. Bonivento16, I. Bordyuzhin32, A. Borgheresi21,i, S. Borghi56,
M. Borisyak35, M. Borsato39, F. Bossu7, M. Boubdir9, T.J.V. Bowcock54, E.
Bowen42, C. Bozzi17,40, S. Braun12, M. Britsch12, T. Britton61, J.
Brodzicka56, E. Buchanan48, C. Burr56, A. Bursche2, J. Buytaert40, S.
Cadeddu16, R. Calabrese17,g, M. Calvi21,i, M. Calvo Gomez38,m, A. Camboni38,
P. Campana19, D. Campora Perez40, 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,i, L. Castillo
Garcia41, M. Cattaneo40, Ch. Cauet10, G. Cavallero20, R. Cenci24,t, M.
Charles8, Ph. Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S.
Chen56, S.-F. Cheung57, V. Chobanova39, M. Chrzaszcz42,27, X. Cid Vidal39, G.
Ciezarek43, P.E.L. Clarke52, M. Clemencic40, H.V. Cliff49, J. Closier40, V.
Coco59, J. Cogan6, E. Cogneras5, V. Cogoni16,40,f, L. Cojocariu30, G.
Collazuol23,o, P. Collins40, A. Comerma-Montells12, A. Contu40, A. Cook48, G.
Coombs40, S. Coquereau38, G. Corti40, M. Corvo17,g, C.M. Costa Sobral50, B.
Couturier40, G.A. Cowan52, D.C. Craik52, A. Crocombe50, M. Cruz Torres62, S.
Cunliffe55, R. Currie55, C. D’Ambrosio40, F. Da Cunha Marinho2, E.
Dall’Occo43, J. Dalseno48, P.N.Y. David43, A. Davis59, O. De Aguiar
Francisco2, K. De Bruyn6, 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, M.
Deckenhoff10, L. Del Buono8, M. Demmer10, A. Dendek28, D. Derkach35, O.
Deschamps5, F. Dettori40, B. Dey22, A. Di Canto40, H. Dijkstra40, F. Dordei40,
M. Dorigo41, A. Dosil Suárez39, A. Dovbnya45, K. Dreimanis54, L. Dufour43, G.
Dujany56, K. Dungs40, P. Durante40, R. Dzhelyadin37, A. Dziurda40, A.
Dzyuba31, N. Déléage4, S. Easo51, M. Ebert52, U. Egede55, V. Egorychev32, S.
Eidelman36,w, S. Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53,
Ch. Elsasser42, S. Ely61, S. Esen12, H.M. Evans49, T. Evans57, A. Falabella15,
N. Farley47, S. Farry54, R. Fay54, D. Fazzini21,i, D. Ferguson52, A. Fernandez
Prieto39, F. Ferrari15,40, F. Ferreira Rodrigues1, M. Ferro-Luzzi40, S.
Filippov34, R.A. Fini14, M. Fiore17,g, M. Fiorini17,g, M. Firlej28, C.
Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, K. Fohl40, M. Fontana16,40, F.
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D. Gerick12, E. Gersabeck12, M. Gersabeck56, T. Gershon50, Ph. Ghez4, S.
Gianì41, V. Gibson49, O.G. Girard41, L. Giubega30, K. Gizdov52, V.V.
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E. Graugés38, E. Graverini42, G. Graziani18, A. Grecu30, P. Griffith47, L.
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Head41, A. Heister9, K. Hennessy54, P. Henrard5, L. Henry8, J.A. Hernando
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H. Hopchev41, W. Hulsbergen43, T. Humair55, M. Hushchyn35, N. Hussain57, D.
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Jones49, C. Joram40, B. Jost40, N. Jurik61, S. Kandybei45, W. Kanso6, M.
Karacson40, J.M. Kariuki48, S. Karodia53, M. Kecke12, M. Kelsey61, I.R.
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F. Palombo22,q, M. Palutan19, J. Panman40, A. Papanestis51, M. Pappagallo14,d,
L.L. Pappalardo17,g, W. Parker60, C. Parkes56, G. Passaleva18, A. Pastore14,d,
G.D. Patel54, M. Patel55, C. Patrignani15,e, A. Pearce56,51, A. Pellegrino43,
G. Penso26, M. Pepe Altarelli40, S. Perazzini40, P. Perret5, L. Pescatore47,
K. Petridis48, A. Petrolini20,h, A. Petrov67, M. Petruzzo22,q, E. Picatoste
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S. Playfer52, M. Plo Casasus39, T. Poikela40, F. Polci8, A. Poluektov50,36, I.
Polyakov61, E. Polycarpo2, G.J. Pomery48, A. Popov37, D. Popov11,40, B.
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S. Reichert10, A.C. dos Reis1, C. Remon Alepuz68, V. Renaudin7, S.
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T. Williams47, F.F. Wilson51, J. Wimberley60, J. Wishahi10, W. Wislicki29, M.
Witek27, G. Wormser7, S.A. Wotton49, K. Wraight53, S. Wright49, K. Wyllie40,
Y. Xie64, Z. Xing61, Z. Xu41, Z. Yang3, H. Yin64, J. Yu64, X. Yuan36,w, O.
Yushchenko37, K.A. Zarebski47, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, Y.
Zhang63, A. Zhelezov12, Y. Zheng63, A. Zhokhov32, X. Zhu3, V. Zhukov9, S.
Zucchelli15.

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
4LAPP, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, 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
17Sezione INFN di 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 INFN 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 RAN),
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
39Universidad de Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Ecole 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
64Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
65Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
66Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
67National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
68Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 38
69Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

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, Viet Nam
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
†Deceased