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Eur. Phys. J. C (2017) 77:15

DOI 10.1140/epjc/s10052-016-4504-z

Regular Article - Experimental Physics

Measurements of the tt production cross section in lepton+jets

ﬁnal states in pp collisions at 8 TeV and ratio of 8 to 7 TeV cross

sections

CMS Collaboration

∗

CERN, 1211 Geneva 23, Switzerland

Received: 29 February 2016 / Accepted: 14 November 2016 / Published online: 7 January 2017

Abstract A measurement of the top quark pair produc-

tion (t

t) cross section in proton–proton collisions at the

centre-of-mass energy of 8 TeV is presented using data col-

lected with the CMS detector at the LHC, corresponding to

an integrated luminosity of 19.6 fb

−1

. This analysis is per-

formed in the t

t decay channels with one isolated, high trans-

verse momentum electron or muon and at least four jets,

at least one of which is required to be identiﬁed as origi-

nating from hadronization of a b quark. The calibration of

the jet energy scale and the efﬁciency of b jet identiﬁcation

are determined from data. The measured t

t cross section is

228.5 ± 3.8(stat)± 13.7 (syst) ± 6.0 (lumi) pb. This mea-

surement is compared with an analysis of 7 TeV data, cor-

responding to an integrated luminosity of 5.0 fb

−1

, to deter-

mine the ratio of 8 TeV to 7 TeV cross sections, which is

found to be 1.43 ± 0.04 (stat) ± 0.07 (syst) ± 0.05 (lumi).

The measurements are in agreement with QCD predictions

up to next-to-next-to-leading order.

1 Introduction

Top quarks are abundantly produced at the CERN LHC. The

predicted top quark pair production cross section (σ

)in

proton–proton (pp) collisions, at a centre-of-mass energy of

8 TeV, is 253 pb, with theoretical uncertainties at the level of

5–6%. A precise measurement of σ

is an important test of

perturbative quantum chromodynamics (QCD) at high ener-

gies. Furthermore, precision t

t cross section measurements

can be used to constrain the top quark mass m

and QCD

parameters, such as the strong coupling constant α

[1], or

the parton distribution functions (PDF) of the proton [2].

The t

t production cross section was measured at the LHC

√

s = 7 and 8 TeV [3–18,18–25]. In this paper, a measure-

ment of the t

t production cross section in the ﬁnal state with

one high transverse momentum lepton (muon or electron)



e-mail: cms-publication-committee-chair@cern.ch

and jets is presented using the 2012 data set at

√

s = 8TeV,

collected by the CMS experimentat the LHC and correspond-

ing to an integrated luminosity of 19.6 fb

−1

. To measure the

cross section ratio, where several systematic uncertainties

cancel, the 2011 data set at

√

s = 7 TeV, corresponding to

an integrated luminosity of 5.0 fb

−1

, has been concurrently

analyzed with a similar strategy to the one developed for

the cross section measurement at 8 TeV. The new measure-

ment agrees very well with the previously published CMS

result [8]. The larger statistical uncertainty of the present

measurement with respect to the previous one is due to the

simultaneous determination of the b tagging efﬁciency, as

discussed in Sect. 6. Similarly to the 8 TeV analysis, an addi-

tional signal modelling uncertainty has been considered in

the 7 TeV analysis, as reported in Sect. 6.

In the standard model, top quarks are predominantly pro-

duced in pairs via the strong interaction and decay almost

exclusively into a W boson and a b quark. The event sig-

nature is determined by the subsequent decays of the two

W bosons. This analysis uses lepton+jets decays into muons

or electrons, where one of the W bosons decays into two

quarks and the other to a lepton and a neutrino. Decays of

the W boson into a tau lepton and a neutrino can enter the

selection if the tau lepton decays leptonically. The top quark

decaying into a b quark and a leptonically decaying W boson

is deﬁned in the following as the “leptonic top quark”, while

the other top quark is referred to as “hadronic top quark”. For

the t

t signal two jets result from the hadronization of the b

and

b quarks (b jets), thus b tagging algorithms are employed

for the identiﬁcation of b jets in order to improve the purity

of the t

t candidate sample.

The technique for extracting the t

t cross section consists

of a binned log-likelihood ﬁt of signal and background to

the distribution of a discriminant variable in data showing a

good separation between signal and background: the invari-

ant mass of the b jet related to the leptonic top quark and the

lepton  (M

b

). The mass of the three-jet combination with

123

15 Page 2 of 27 Eur. Phys. J. C (2017) 77 :15

the highest transverse momentum in the event (M

)isusedas

a discriminant in an alternative analysis. The M

b

variable is

related to the leptonic top quark mass, while M

is a measure

for the hadronic top quark mass. Both quantities provide a

good separation between signal and background processes.

The analysis employs calibration techniques to reduce the

experimental uncertainties related to b tagging efﬁciencies

and jet energy scale (JES). The t

t topology is reconstructed

using a jet sorting algorithm in which the b jet most likely

originating from the leptonic top quark is identiﬁed. The

b tagging efﬁciency is then determined from a b-enriched

sample, in the peak region of the M

b

distribution, correcting

for the contamination from non-b jets, following the method

described in Refs. [26,27]. The rate of jets that are wrongly

tagged as originating from a b quark is also measured using

data as described in [28]. Independently, the JES is deter-

mined using the jets associated with the hadronically decay-

ing W boson by correcting the reconstructed mass of the

W boson in the simulation to that determined from the data.

The results of the cross section measurements are given

both for the visible region, i.e. for the phase space corre-

sponding to the event selection, and for the full phase space.

The visible region is deﬁned by requiring the presence in the

simulation of exactly one lepton, one neutrino, and at least

four jets passing the selection criteria, as presented in Sect. 5.

This paper is structured as follows: after a description of

the CMS detector (see Sect. 2), the data and the simulated

samples are discussed in Sect. 3, while Sect. 4 is dedicated

to the event selection. The analysis technique and the impact

of the systematic uncertainties are addressed in Sect. 5 and

in Sect. 6. The results of the cross section measurements

are discussed in Sect. 7. Section 8 describes the alternative

analysis based on M

, followed by a summary in Sect. 9.

2 The CMS detector

The central feature of the CMS apparatus is a superconduct-

ing solenoid, of 6 m internal diameter, providing an axial

magnetic ﬁeld of 3.8 T. Within the solenoidal ﬁeld volume

are a silicon pixel and strip tracker which measure charged

particle trajectories in the pseudorapidity range |η| < 2.5.

Also within the ﬁeld volume, the silicon detectors are sur-

rounded bya lead tungstate crystal electromagneticcalorime-

ter (|η| < 3.0) and a brass and scintillator hadron calorimeter

(|η| < 5.0) that provide high-resolution energy and direction

measurements ofelectrons and hadronic jets. Muons are mea-

sured in gas-ionization detectors embedded in the steel mag-

netic ﬂux-return yoke outside the solenoid. The muon detec-

tion systems provide muon detection in the range |η| < 2.4.

A two-level trigger system selects the pp collision events

for use in physics analysis. A more detailed description of

the CMS detector, together with a deﬁnition of the coordi-

nate system used and the relevant kinematic variables, can

be found elsewhere [29].

3 Data and simulation

The cross section measurement is performed using the 8 TeV

pp collisions recorded by the CMS experiment in 2012, cor-

responding to an integrated luminosity of 19.6 ± 0.5fb

−1

[30], and the 2011 data set at

√

s = 7 TeV, corresponding to

an integrated luminosity of 5.0 ± 0.2fb

−1

[31].

The t

t events are simulated using the Monte Carlo (MC)

event generators MadGraph (version 5.1.1.0) [32,33] and

powheg (v1.0 r1380) [34,35]. In MadGraph the top quark

pairs are generated at leading order with up to three additional

high-p

jets. The powheg generator implements matrix ele-

ments to next-to-leading order (NLO) in perturbative QCD,

with up to one additional jet. The mass of the top quark

is set to 172.5 GeV. The CT10 [36]PDFsetisusedby

powheg and the CTEQ6M [37–39]byMadGraph.The

pythia (v.6.426) [40] and herwig (v.6.520) [41] generators

are used to model the parton showering. The pythia shower

matching is done using the MLM prescription [42,43].

The top quark pair production cross section values are

predicted to be 177.3

+4.6

−6.0

(scale) ± 9.0 (PDF+α

) pb at

7 TeV and 252.9

+6.4

−8.6

(scale) ± 11.7 (PDF+α

) pb at 8 TeV,

as calculated with the Top++ 2.0 program to next-to-next-

to-leading order (NNLO) in perturbative QCD, including

soft-gluon resummation to next-to-next-to-leading logarith-

mic (NNLL) order (Ref. [44] and references therein), and

assuming m

= 172.5 GeV. The ﬁrst uncertainty comes from

the independent variation of the factorization and renormal-

ization scales, while the second one is associated to variations

in the PDF and α

following the PDF4LHC prescription with

the MSTW2008 68% conﬁdence level NNLO, CT10 NNLO,

and NNPDF2.3 5f FFN PDF sets (Refs. [37,38] and refer-

ences therein, and Refs. [36,39]).

The top quark transverse momentum is reweighted in sam-

ples simulated with MadGraph and powheg, when inter-

faced to pythia, in order to better describe the p

distribution

observed in the data. Based on studies of differential distri-

butions [45,46] in the top quark transverse momentum, an

event weight w =

√

is applied, where the weights w

of the two top quarks are given as a function of the generated

top quark p

values: w

= exp(0.199−0.00166 p

/GeV) at

7 TeV, and w

= exp(0.156 − 0.00137 p

/GeV) at 8 TeV.

This reweighting is only applied to the phase space corre-

sponding to the experimental selections in the muon and

electron channels. The agreement between data and samples

generated with powheg interfaced with herwig is found to

be satisfactory, and no reweighting is applied in this case.

The W/Z+jets events, i.e. the associated production of

W/Z vector bosons with jets, with leptonic decays of the

123

Eur. Phys. J. C (2017) 77 :15 Page 3 of 27 15

W/Z bosons, constitute the largest background. These are

also simulated using MadGraph withmatrix elements corre-

sponding to at least one jet and up to four jets. The W/Z+jets

events are generated inclusively with respect to the jet ﬂavour.

Drell–Yan production of charged leptons is generated for

dilepton invariant masses above 50 GeV, as those events con-

stitute the relevant background in the phase space of this anal-

ysis. The contribution from Drell–Yan events with dilepton

invariant masses below 50 GeV is negligible, as veriﬁed with

a sample with a mass range of 10–50 GeV. Single top quark

production is simulated with powheg. The background pro-

cesses are normalized to NLO and NNLO cross section cal-

culations [47–51], with the exception of the QCD multijet

background, for which the normalization is obtained from

data in the M

analysis (see Sect. 8). In the M

b

analysis the

multijet background is reduced to a negligible fraction (see

Sect. 4) and thus not considered further.

Pileup signals, i.e. extra activity due to additional pp inter-

actions in the same bunch crossing, are incorporated by sim-

ulating additional interactions with a multiplicity matching

the one inferred from data. The CMS detector response is

modeled using Geant4 [52]. The simulated events are pro-

cessed by the same reconstruction software as the collision

data.

4 Reconstruction and event selection

This analysis focuses on the selection of t

t lepton+jets decays

in the muon and electron channels, with similar selection

requirements applied for the two channels. Muons, elec-

trons, photons, and neutral and charged hadrons are recon-

structed and identiﬁed by the CMS particle-ﬂow (PF) algo-

rithm [53,54]. The energy of muons is obtained from the cor-

responding track momentum using the combined information

of the silicon tracker and the muon system [55]. The energy

of electrons is determined from a combination of the track

momentum in the tracker, the corresponding cluster energy

in the electromagnetic calorimeter, and the energy sum of

all bremsstrahlung photons associated to the track [56]. The

vertex with the largest p

sum of the tracks associated to it

is chosen as primary vertex.

Candidate t

t events are ﬁrst accepted by dedicated trig-

gers requiring at least one muon or electron. Lepton isolation

requirements are applied to improve the purity of the selected

sample. At the trigger level the relative muon isolation, the

sum of transverse momenta of other particles in a cone of size

R =

√

(φ)

+ (η)

= 0.4 around the direction of the

candidate muon divided by the muon transverse momentum,

is required to be less than 0.2. Similarly, for electrons, the cor-

responding requirement is less than 0.3 in a cone of size 0.3.

Events with a muon in the ﬁnal state are triggered on the pres-

ence of a muon candidate with p

> 24 GeV and |η| < 2.1.

Eventswith an electron candidate with |η| < 2.5 are accepted

by triggers requiring an electron with p

> 27 GeV.

Tighter p

requirements are applied in the ofﬂine selec-

tions. Muons are required to have a good quality [55] track

with p

> 25 GeV and |η| < 2.1. Electrons are identiﬁed

using a combination of the shower shape information and

track-electromagnetic cluster matching [56], and are required

to have p

> 32 GeV and |η| < 2.5, with the exclusion of the

transition region between the barrel and endcap electromag-

netic calorimeter, 1.44 < |η| < 1.57. Electrons identiﬁed

to come from photon conversions [56] are vetoed. Correc-

tion factors for trigger and lepton identiﬁcation efﬁciencies

have been determined with a tag-and-probe method [57]from

data/simulation comparison as a function of the lepton p

and

η, and are applied to the simulation.

Signal events are required to have at least one pp inter-

action vertex, successfully reconstructed from at least four

tracks, within limits on the longitudinal and radial coordi-

nates [58], and exactly one muon, or electron, with an origin

consistent with the reconstructed vertex within limits on the

impact parameters. Since the lepton from the W boson decay

is expected to be isolated from other activity in the event, iso-

lation requirements are applied. A relativeisolation is deﬁned

as I

rel

= (I

charged

+ I

photon

+ I

neutral

)/ p

, where p

is the

transverse momentum of the lepton and I

charged

, I

photon

, and

neutral

are the sums of the transverse energies of the charged

particles, the photons, and the neutral particles not identiﬁed

as photons, in a cone R < 0.4 (0.3) for muons (electrons)

around the lepton direction, excluding the lepton itself. The

relative isolation I

rel

is required to be less than 0.12 for muons

and 0.10 for electrons. Events with more than one lepton can-

didate with relaxed requirements are vetoed in order to reject

Z boson or t

t decays into dileptons.

The missing energy in the transverse plane (E

miss

)is

deﬁned as the magnitude of the projection on the plane per-

pendicular to the beams of the vector sum of the momenta

of all PF candidates. It is required to be larger than 30 GeV

in the muon channel and larger than 40 GeV in the electron

channel, because of the larger multijet background.

Jets are clustered from the charged and neutral particles

reconstructed with the PF algorithm, using the anti-k

jet

algorithm [59] with a radius parameter of 0.5. Particles iden-

tiﬁed as isolated muons or electrons are not used in the jet

clustering. Jet energies are corrected for nonlinearities due

to different responses in the calorimeters and for the dif-

ferences between measured and simulated responses [60].

Furthermore, to account for extra activity within a jet cone

due to pileup, jet energies are corrected [53,54] for charged

hadrons that belong to a vertex other than the primary vertex,

and for the amount of pileup expected in the jet area from

neutral jet constituents.

At least four jets are required with p

> 40 GeV and

|η| < 2.5. An additional global calibration factor of the jet

123

15 Page 4 of 27 Eur. Phys. J. C (2017) 77 :15

200

400

600

800

1000

1200

CMS

1400

Data

signaltt

trehtot

Single t

W/Z+jets

(GeV)

jet1

0 50 100 150 200 250 300 350 400 450 500

Data / MC

Events / 5 GeV

0.6

0.8

1.2

(8 TeV)

-1

19.6 fb

500

1000

1500

2000

CMS

2500

Data

tlangist

trehtot

Single t

W/Z+jets

(GeV)

jet2

0 50 100 150 200 250 300 350 400 450 500

Data / MC

Events / 5 GeV

0.6

0.8

1.2

(8 TeV)

-1

19.6 fb

500

1000

1500

2000

CMS

2500

3000

Data

tlang

treh

Single t

W/Z+jets

0 50 100 150 200 250 300 350 400 450 500

Data / MC

Events / 5 GeV

0.6

0.8

1.2

(8 TeV)

-1

19.6 fb

(GeV)

200

400

600

800

1000

1200

CMS

1400

Data

tlang

treh

Single t

W/Z+jets

0 50 100 150 200 250 300

Data / MC

Events / 3 GeV

0.6

0.8

1.2

(8 TeV)

-1

19.6 fb

(GeV)

jmiss

Fig. 1 Transverse momentum distributions of the ﬁrst- and second-

leading jet (top), the muon and E

miss

distribution (bottom) for all rele-

vant processes in the muon+jets channel with the requirement of at least

one b-tagged jet. The simulation is normalized to the standard model

cross section values and p

-reweighting is applied to the tt contribu-

tion. The multijet background is negligible and not shown. The distribu-

tions are already corrected for the b tagging efﬁciency scale factor. The

hashed area shows the uncertainty in the luminosity measurement and

the b tagging systematic uncertainty. The last bin includes the overﬂow.

The ratio between data and simulation is shown in the lower panels for

bins with non-zero entries.eps

energy scale is obtained by ﬁtting the W boson mass distri-

bution in the data and in the simulation. The scale factor is

determined as the ratio of the W boson mass reconstructed

from non-b-tagged jet pairs in data and in the simulation.

This scale correction is applied in the simulation to all jets

before the selection requirements are implemented. It largely

reduces the systematic uncertainty related to the jet energy

scale, discussed in Sect. 6.

To reduce contamination from background processes, at

least one of the jets has to be identiﬁed as a b jet. The b tagging

algorithm used is the “combined secondary vertex” (CSV)

algorithm at the medium working point [26,27], correspond-

ing to a misidentiﬁcation probability of about 1% for light-

parton jets (mistag rate) and an efﬁciency for b jets in the

range 60–70% depending on the jet p

and pseudorapid-

ity. Figure 1 shows kinematic distributions after applying the

b tagging requirement. Good agreement between data and

simulation is observed.

The M

b

analysis uses control samples in data for the esti-

mation of the b tagging efﬁciency, as described in Refs. [26–

28]. Among the four leading jets, three are assigned to the

hadronically decaying top quark through a χ

sorting algo-

rithm using top quark and W boson mass constraints. The

remaining fourth jet is the b jet candidate assigned to the

123

Eur. Phys. J. C (2017) 77 :15 Page 5 of 27 15

(GeV)

bμ

0 50 100 150 200 250 300 350 400 450 500

Events / 10 GeV

500

CMS

1000

1500

2000

2500

Data

Background

/ndf = 0.92

χFit

(8TeV)

-1

19.6 fb

(GeV)

0 50 100 150 200 250 300 350 400 450 500

Events / 10 GeV

200

400

CMS

600

800

1000

1200

1400

1600

1800

Data

Background

/ndf = 0.73

χFit

(8 TeV)

-1

19.6 fb

Fig. 2 Distributions of the lepton-jet mass in the muon+jets (left) and electron+jets (right) channels, rescaled to the ﬁt results

leptonically decaying top quark. The b tagging algorithm is

only applied to this b jet candidate.

Owing to differences in the triggers and in the centre-of-

mass energies, in the 7 TeV analysis slightly different selec-

tion criteria are applied on the lepton p

and E

miss

.The

muon transverse momentum is required to be larger than

26 GeV, while the electron p

has to be larger than 30 GeV.

No explicit E

miss

requirement is needed in the muon chan-

nel. Events with E

miss

> 30 GeV are selected in the electron

channel.

5 Visible and total cross section measurements

The number of t

t events is determined with a binned

maximum-likelihood ﬁt of distributions (templates), describ-

ing signal and background processes, to the data sample pass-

ing the ﬁnal selection, by ﬁtting M

b

, the invariant mass dis-

tribution of the b jet and the lepton.

The t

t visible (σ

vis

) and total (σ

) production cross sec-

tions are extracted from the number of t

t events observed in

the data using the equations

vis

L ε

,σ

vis

, (1)

where N

is the number of tt events (including both signal

events from the lepton+jets channel considered and events

from other decay channels) extracted from the ﬁt, L is the

integrated luminosity, A is the t

t acceptance, and ε

is the tt

selection efﬁciency within the acceptance requirements out-

lined in the next section. Results are presented for both the

visible and total cross section, in order to separate experi-

mental uncertainties from theoretical assumptions as much

as possible.

One template is used for t

t events (both for the tt signal

events and the other t

t events passing the selection criteria)

and one template for all background processes (W/Z+jets

and single top quark production). The ﬁt is performed in the

range 0–500 GeV. Figure 2 shows the results for the ﬁt to the

data distributions in the muon and electron channels.

5.1 Acceptance

The t

t acceptance A corresponding to the visible phase space

depends on the theoretical model and it is determined at the

generator level by requiring the presence of exactly one lep-

ton, one neutrino, and at least four jets, passing p

and |η|

selection criteria similar to the ones delineated in Sect. 4.

For simplicity a single acceptance deﬁnition, corresponding

to the tightest selection criteria, is used for both channels

at each centre-of-mass energy: exactly one muon, or elec-

tron, with p

> 32 GeV and |η| < 2.1, one neutrino with

> 40 GeV, and at least four jets with p

> 40 GeV and

|η| < 2.5.

The acceptance values include contributions from other t

decay channels, in particular from the dilepton channel, at

the level of about 9%.

The acceptance values are provided in Table 1 for the two

generators used in this analysis, MadGraph and powheg.

The acceptance values are in agreement at the 1–2% level

at 8 TeV and at better than 5% at 7 TeV. This different level

of agreement is due to the fact that the common acceptance

deﬁnition described above corresponds the tightest p

cri-

teria, i.e. to the p

requirements of the electron channel at

√

s = 8 TeV. The reweighted acceptance is determined as

the number of reweighted t

t events in the visible phase space,

123

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在s = 8TeV的pp碰撞中，从顶夸克对到轻子+射流最终状态的衰变中W玻色子螺旋度的测量

在s = 8 TeV处pp碰撞中W + W-截面的测量以及异常量规接头的极限

在pp \碰撞中，在$$ \ sqrt {s} = 13 \，\ text {TeV} $$ s = 13TeV的pp碰撞中，搜索在轻子+射流最终状态下衰减至顶夸克和矢量状顶夸克的重共振。

W s Z玻色子对生产横截面在pp碰撞中的pp碰撞下，使用ATLAS探测器的s = 13 TeV的测量

pp→ZZ生产截面的测量以及在s = 8 TeV的四轻子最终状态下异常三重量规耦合的约束

在s = 7 $$ \ sqrt {s} = 7 $$和13 TeV的pp碰撞中测量B±生产横截面

在s = 1.96 TeV的pp碰撞中，W + b射流和W + c射流差分生产横截面的测量

测量的电渗流与Z玻色子在s = 13 TeV的pp碰撞中的Z玻色子与ATLAS检测器的电弱生产的横截面

以s $$ \ sqrt {s} $$ = 13 TeV的质子-质子碰撞，搜索具有两个tau轻子的最终状态中的顶级对副生产

用ATLAS探测器在s = 13TeV pp碰撞中用tau轻子搜索最终状态下的charginos和中性蛋白直接产生

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在s = 8 $$ \ sqrt {s} =的pp碰撞中，测量tt W $$ t \ overline {t} W $$和tt z $$ t \ overline {t} Z $$生产横截面。带有ATLAS探测器的8 $$ TeV

使用最终状态为的s = 5.02 $$ \ sqrt {s} = 5.02 $$ TeV在pp碰撞中测量包含tt $$ \ mathrm {t} \ overline {\ mathrm {t}} $$横截面至少一个带电的轻子

用ATLAS测量在$$ \ sqrt {s} = 13〜\ text {TeV} $$ s = 13TeV pp碰撞中pp碰撞中的$$ W ^ {\ pm} Z $$ W±Z生产横截面并测量玻色子极化探测器

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