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Eur. Phys. J. C (2014) 74:3014

DOI 10.1140/epjc/s10052-014-3014-0

Regular Article - Experimental Physics

Measurement of jet multiplicity distributions in tt production

in pp collisions at

√

s = 7TeV

The CMS Collaboration

∗

CERN, 1211 Geneva 23, Switzerland

Received: 11 April 2014 / Accepted: 30 July 2014 / Published online: 20 August 2014

Abstract The normalised differential top quark-antiquark

production cross section is measured as a function of the jet

multiplicity in proton-proton collisions at a centre-of-mass

energy of 7 TeV at the LHC with the CMS detector. The mea-

surement is performed in both the dilepton and lepton+jets

decay channels using data corresponding to an integrated

luminosity of 5.0 fb

−1

. Using a procedure to associate jets to

decay products of the top quarks, the differential cross sec-

tion of the t

t production is determined as a function of the

additional jet multiplicity in the lepton+jets channel. Fur-

thermore, the fraction of events with no additional jets is

measured in the dilepton channel, as a function of the thresh-

old on the jet transverse momentum. The measurements are

compared with predictions from perturbative quantum chro-

modynamics and no signiﬁcant deviations are observed.

1 Introduction

Precise measurements of the top quark-antiquark (t

t) produc-

tion cross section and top-quark properties performed at the

CERN Large Hadron Collider (LHC) provide crucial infor-

mation for testing the predictions of perturbative quantum

chromodynamics ( QCD) at large energy scales and in pro-

cesses with multiparticle ﬁnal states.

About half of the t

t events are expected to be accompanied

by additional hard jets that do not originate from the decay of

the t

t pair (tt +jets). In this paper, these jets will be referred to

as additional jets. These processes typically arise from either

initial- or ﬁnal-state QCD r adiation, providing an essential

handle to test the validity and completeness of higher-order

QCD calculations of processes leading to multijet events.

Calculations at next-to-leading order (NLO) are available for

t production in association with one [1]ortwo[2] additional

jets. The correct description of t

t +jets production is impor-

tant to the overall LHC physics program since it constitutes

an important background to processes with multijet ﬁnal

∗

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

states, such as associated Higgs-boson production with a tt

pair, with the Higgs boson decaying into a b

b pair, or ﬁnal

states predicted in supersymmetric theories. Anomalous pro-

duction of additional jets accompanying a t

t pair could be a

sign of new physics beyond the standard model [3].

This paper presents studies of the t

t production with addi-

tional jets in the ﬁnal state using data collected in proton-

proton (pp) collisions with centre-of-mass energy

√

s =

7 TeV with the Compact Muon Solenoid (CMS) detector [4].

The analysis uses data recorded in 2011, corresponding to a

total integrated luminosity of 5.0 ± 0.1fb

−1

. For the ﬁrst

time, the t

t cross section is measured differentially as a func-

tion of jet multiplicity and characterised both in terms of

the total number of jets in the event, as well as the num-

ber of additional jets with respect to the leading-order hard-

interaction ﬁnal state. Kinematic properties of the additional

jets are also investigated. The results are corrected for detec-

tor effects and compared at particle level with theoretical

predictions obtained using different Monte Carlo (MC) event

generators.

The differential cross sections as a function of jet multi-

plicity are measured in both the dilepton (ee, µµ, and eµ) and

+jets ( =eorµ) channels. For the dilepton channel, data

containing two oppositely charged leptons and at least two

jets in the ﬁnal state are used, while for the +jets channel,

data containing a single isolated l epton and at least three jets

are used. Following the analysis strategy applied to the mea-

surement of other t

t differential cross sections [5], the results

are normalised to the i nclusive cross section measured in

situ, eliminating systematic uncertainties related to the nor-

malisation. Lastly, the fraction of events that do not contain

additional jets (gap fraction), ﬁrst measured by ATLAS [6],

is determined in the dilepton channel as a function of the

threshold on the transverse momentum (p

) of the leading

additional jet and of the s calar sum of the p

of all additional

jets.

The measurements are performed in the visible phase

space, deﬁned as the kinematic region in which all selected

ﬁnal-state objects are produced within the detector accep-

123

3014 Page 2 of 29 Eur. Phys. J. C (2014) 74:3014

tance. This avoids additional model uncertainties due to the

extrapolation of the measurements into experimentally inac-

cessible regions of phase space.

The paper is structured as follows. A brief description of

the CMS detector is provided in Sect. 2. Section 3 gives a

description of the event simulation, followed by details of

the object reconstruction and event selection in Sect. 4.A

discussion of the sources of systematic uncertainties is given

in Sect. 5. The measurement of the differential cross section

is presented as a function of the jet multiplicity in Sect. 6 and

as a function of the additional jet multiplicity in Sect. 7.The

study of the additional jet gap fraction is described in Sect. 8.

Finally, a summary is given in Sect. 9.

2 The CMS detector

The central feature of the CMS apparatus is a superconduct-

ing solenoid, 13 m in length and 6 m in diameter, which

provides an axial magnetic ﬁeld of 3.8 T. The bore of the

solenoid is outﬁtted with various particle detection sys-

tems. Charged-particle trajectories are measured with sil-

icon pixel and strip trackers, covering 0 ≤ φ<2π in

azimuth and |η| < 2.5 in pseudorapidity, where η is deﬁned

as η =−ln[tan(θ/2)], with θ being the polar angle of the

trajectory of the particle with respect to the anticlockwise-

beam direction. A lead tungstate crystal electromagnetic

calorimeter (ECAL) and a brass/scintillator hadron calorime-

ter (HCAL) surround the tracking volume. The calorime-

try provides excellent resolution in energy for electrons

and hadrons within |η| < 3.0. Muons are measured up to

|η| < 2.4 using gas-ionisation detectors embedded in the

steel ﬂux return yoke outside the solenoid. The detector is

nearly hermetic, providing accurate measurements of any

imbalance in momentum in the plane transverse to the beam

direction. The two-level trigger system selects most interest-

ing ﬁnal states for further analysis. A detailed description of

the CMS detector can be found in Ref. [4].

3 Event simulation

The reference simulated t

t sample used in the analysis is gen-

erated with the MadGraph (v. 5.1.1.0) matrix element gen-

erator [7], with up to three additional partons. The generated

events are subsequently processed using pythia (v. 6.424) [8]

to add parton showering using the MLM prescription [9]for

removing the overlap in phase space between the matrix ele-

ment and the parton shower approaches. The pythia Z2 tune

is used to describe the underlying event [10]. The top-quark

mass is assumed to be m

= 172.5 GeV. The proton struc-

ture is described by the CTEQ6L1 [11] parton distribution

functions (PDFs).

The MadGraph generator is used to simulate W+jets and

Z/γ

∗

+jets production. Single-top-quark events (s-, t-, and

tW-channels) are s imulated using powheg (r1380) [12 –15 ].

Diboson (WW, WZ, and ZZ) and QCD multijet events are

simulated using pythia.

Additional t

t and W+jets MadGraph samples are gen-

erated using different choices for the common factorisation

and renormalisation scale (μ

= μ

= Q

) and for the jet-

parton matching threshold. These are used to determine the

systematic uncertainties due to model uncertainties and for

comparisons with the measured distributions. The nominal

scale is deﬁned as m



(jet). This is varied between

and Q

/4. For the reference MadGraph sample, a jet-

parton matching threshold of 20 GeV is chosen, while for

the up and down variations, thresholds of 40 and 10 GeV are

used, respectively.

In addition to MadGraph, samples of t

t events are

generated with powheg and mc@nlo (v. 3.41) [16]. The

CTEQ6M [11] PDF set is used in both cases. Both powheg

and mc@nlo match calculations to full NLO accuracy with

parton shower MC generators. For powheg, pythia is cho-

sen for hadronisation and parton shower simulation, with the

same Z2 tune utilised for other samples. For mc@nlo, her-

wig (v. 6.520) [17] with the default tune is used.

For comparison with the measured distributions, the event

yields in the simulated samples are normalised to an inte-

grated luminosity of 5.0 fb

−1

according to their theoretical

cross sections. These are taken from next-to-next-to-leading-

order (NNLO) (W+jets and Z/γ

∗

+jets), NLO plus next-to-

next-to-leading-log(NNLL) (single-top-quark s-[18], t-[19]

and tW-channels [20]), NLO (diboson [21]), and leading-

order (LO) (QCD multijet [8]) calculations. For the sim-

ulated t

t sample, the full NNLO+NNLL calculation, per-

formed with the Top++ 2.0 program [22], is used. The PDF

and α

uncertainties are estimated using the PDF4LHC pre-

scription [23,24] with the MSTW2008nnlo68cl [25], CT10

NNLO [26,27], and NNPDF2.3 5f FFN [28] PDF sets, and

added in quadrature to the scale uncertainty to obtain a t

production cross section of 177.3

+10.1

−10.8

pb (for a top-quark

mass value of 172.5 GeV).

All generated samples are passed through a full detector

simulation using Geant4 [29], and the number of additional

pp collisions (pileup) is matched to the real distribution as

inferred from data.

4 Event reconstruction and selection

The event selection is based on the reconstruction of the t

decay products. The top quark decays almost exclusively into

a W boson and a b quark. Only the subsequent decays of one

or both W bosons to a charged lepton and a neutrino are

considered here. Candidate events are required to contain

123

Eur. Phys. J. C (2014) 74:3014 Page 3 of 29 3014

the corresponding reconstructed objects: isolated leptons and

jets. The requirement of the presence of jets associated with

b quarks or antiquarks (b jets) is used to increase the purity

of the selected sample. The selection has been optimised

independently in each channel to maximise the signal content

and background rejection.

4.1 Lepton, jet, and missing transverse energy

reconstruction

Events are reconstructed using a particle-ﬂow (PF) tech-

nique [30,31], in which signals from all CMS sub-detectors

are combined to identify and reconstruct the individual par-

ticle candidates produced in the pp collision. The recon-

structed particles include muons, electrons, photons, charged

hadrons, and neutral hadrons. Charged particles are required

to originate from the primary collision vertex, deﬁned as

the vertex with the highest sum of transverse momenta of

all reconstructed tracks associated to it. Therefore, charged

hadron candidates from pileup events, i.e. originating from

a vertex other than the one of the hard interaction, are

removed before jet clustering on an event-by-event basis.

Subsequently, the remaining neutral-hadron pileup com-

ponent is subtracted at the level of jet energy correction

[32].

Electron candidates are reconstructed from a combina-

tion of their track and energy deposition in the ECAL [33].

In the dilepton channel, they are required to have a trans-

verse momentum p

> 20 GeV, while in the +jets channel

they are required to have p

> 30 GeV. In both cases they

are required to be reconstructed within |η| < 2.4, and elec-

trons from identiﬁed photon conversions are rejected. As an

additional quality criterion, a relative isolation variable I

rel

is computed. This is deﬁned as the sum of the p

of all neu-

tral and charged reconstructed PF candidates inside a cone

around the lepton (excluding the lepton itself) inthe η-φ plane

with radius R ≡



(η)

+ (φ)

< 0.3, divided by the

of the lepton. In the dilepton (e+jets) channel, electrons

are selected as isolated if I

rel

< 0.12 (0.10).

Muon candidates are reconstructed from tracks that can

be matched between the silicon tracker and the muon sys-

tem [34]. They are required to have a transverse momentum

> 20 GeV within the pseudorapidity interval |η| < 2.4in

the dilepton channel, and to have p

> 30 GeV and |η| < 2.1

in the +jets channel. Isolated muon candidates are selected

by demanding a relative isolation of I

rel

< 0.20 (0.125) in

the dilepton (μ+jets) channel.

Jets are reconstructed by clustering the particle-ﬂow can-

didates [35] using the anti-k

algorithm with a distance

parameter of 0.5[36,37]. An offset correction is applied

to take into account the extra energy clustered in jets due

to pileup, using the FastJet algorithm [38] based on aver-

age pileup energy density in the event. The raw jet energies

are corrected to establish a relative uniform response of the

calorimeter in η and a calibrated absolute response in p

.Jet

energy corrections are derived from the simulation, and are

conﬁrmed with in situ measurements with the energy balance

of dijet and photon+jet events [35]. Jets are selected within

|η| < 2.4 and with p

> 30 (35) GeV in the dilepton (+jets)

channel.

Jets originating from b quarks or antiquarks are identiﬁed

with the Combined Secondary Vertex algorithm [39], which

provides a b-tagging discriminant by combining secondary

vertices and track-based lifetime information. The chosen

working point used in the dilepton channel corresponds to

an efﬁciency for tagging a b jet of about 80–85 %, while

the probability to misidentify light-ﬂavour or gluon jets as

b jets (mistag rate) is around 10 %. In the +jets channel, a

tighter requirement is applied, corresponding to a b-tagging

efﬁciency of about 65–70 % with a mistag r ate of 1%. The

probability to misidentifyacjetasbjetisabout 40 % and

20% for the working points used in the dilepton and +jets

channels respectively [39].

The missing transverse energy (E

miss

) is deﬁned as the

magnitude of the sum of the momenta of all reconstructed

PF candidates in the plane transverse to the beams.

4.2 Event selection

Dilepton events are collected using combinations of triggers

which require two leptons fulﬁlling p

and isolation criteria.

During reconstruction, events are selected if they contain at

least two isolated leptons (electrons or muons) of opposite

charge and at least two jets, of which at least one is identiﬁed

as a b jet. Events with a lepton pair invariant mass smaller

than 12 GeV are removed in order to suppress events from

heavy-ﬂavour resonance decays. In the ee and µµ channels,

the dilepton invariant mass is required to be outside a Z-boson

mass window of 91 ± 15 GeV (Z-boson veto), and E

miss

required to be larger than 30 GeV.

A kinematic reconstruction method [5] is used to deter-

mine the kinematic properties of the t

t pair and to identify

the two b jets originating from the decay of the top quark

and antiquark. In the kinematic reconstruction the follow-

ing constraints are imposed: the E

miss

originated entirely

from the two neutrinos; the reconstructed W-boson invari-

ant mass of 80.4 GeV [40] and the equality of the recon-

structed top quark and antiquark masses. The remaining

ambiguities are resolved by prioritising those event solutions

with two or one b-tagged jets over solutions using untagged

jets. Finally, among the physical solutions, the solutions are

ranked according to how the neutrino energies match with a

simulated neutrino energy spectrum and the highest ranked

one is chosen. The kinematic reconstruction yields no valid

solution for about 11% of the events. These are excluded

123

3014 Page 4 of 29 Eur. Phys. J. C (2014) 74:3014

from further analysis. A possible bias due to rejected solu-

tions has been studied and found to be negligible.

In the e+jets channel, events are triggered by an isolated

electron with p

> 25 GeV and at least three jets with p

30 GeV. Events in the μ+jets channel are triggered by the

presence of an isolated muon with p

> 24 GeV fulﬁlling

η requirements. Only triggered events that have exactly one

high-p

isolated lepton are retained in the analysis. In the

e+jets channel, events are rejected if any additional electron

is found with p

> 20 GeV, |η| < 2.5, and relative isolation

rel

< 0.20. In the μ+jets channel, events are rejected if

any electron candidate with p

> 15 GeV, |η| < 2.5 and

rel

< 0.20 is reconstructed. In both +jets channels events

with additional muons with p

> 10 GeV, |η| < 2.5, and

relative isolation I

rel

< 0.20 are rejected. The presence of

at least three reconstructed jets is required. At least two of

them are required to be b-tagged.

Only t

t events from the decay channel under study are con-

sidered as signal. All other t

t events are considered as back-

ground, including those containing leptons from τ decays,

which are the dominant contribution to this background.

4.3 Background estimation

After t he full event selection is applied, the dominant back-

ground in the eμ channel comes from other t

t decay modes,

estimated using simulation. In the ee and µµ channels, it

arises from Z/γ

∗

+jets production. The normalisation of this

background contribution is derived from data using the events

rejected by the Z-boson veto, scaled by the ratio of events

failing and passing this selection estimated in simulation

out/in

)[41]. The number of Z/γ

∗

+jets → ee/µµ events

near the Z-boson peak, N

Z/γ

∗

, is given by the number of

all events failing the Z-boson veto, N

, after subtracting the

contamination from non-Z/γ

∗

+jets processes. This contribu-

tion is extracted from eμ events passing the same selection,

eµ

, and corrected for the differences between the electron

and muon identiﬁcation efﬁciencies using a correction factor

k.TheZ/γ

∗

+jets contribution is thus given by

out

= R

out/in

Z/γ

∗

= R

out/in

− 0.5kN

eµ

) (1)

The factor k is estimated from k

= N

eµ

µµ

)

for the Z/γ

∗

→ e

−

(µ

−

)+jets contribution, respec-

tively. Here N

µµ

) i s the number of ee (µµ) events in

the Z-boson region, without the requirement on E

miss

.The

remaining backgrounds, including single-top-quark, W+jets,

diboson, and QCD multijet events are estimated from simu-

lation.

In the +jets channel, the main background contributions

arise from W+jets and QCD multijet events, which are greatly

suppressed by the b-tagging requirement. A procedure based

on control samples in data is used to extract the QCD multijet

background. The leptons in QCD multijet events are expected

to be less isolated than leptons from other processes. Thus,

inverting the selection on t he lepton relative isolation pro-

vides a relatively pure sample of QCD multijet events in

data. Events passing the standard event selection but with an

rel

between 0.3 and 1.0, and with at least one b-tagged jet are

selected. The sample is divided in two: the sideband region

(one b jet) and the signal region (≥2 b jets). The shape of the

QCD multijet background is taken from the signal region,and

the normalisation is determined from the sideband region. In

the sideband region, the E

miss

distribution of the QCD mul-

tijet model, other sources of background (determined from

simulation), and the t

t signal are ﬁtted to data. The resulting

scaling of QCD multijet background is applied to the QCD

multijet shape from the signal region.

Since the initial state of LHC collision is enriched in up

quarks with respect to down quarks, more W bosons are

produced with positive charge than negative charge. In lep-

tonic W-boson decays, this translates into a lepton charge

asymmetry A. Therefore, a difference between the num-

ber of events with a positively charged lepton and those

with a negatively charged lepton (±) is observed. In data,

this quantity (±

data

) is proportional to the number of

W+jets events when assuming that only the charge asym-

metry from W-boson production is signiﬁcant. The charge

asymmetry has been measured by CMS [42] and found

to be well described by the simulation, thus the simulated

value can be used to extract the number of W+jets events

from data: N

data

W+jets

=  ±

data

/A. The correction factor on

the W+jets normalisation, calculated before any b-tagging

requirement, is between 0.81 and 0.92 depending on the W

decay channel and the jet selection. Subsequently, b-tagging

is applied to obtain the number of W+jets events in the signal

region.

In addition, a heavy-ﬂavour correction must be applied on

the W+jets sample to account for the differences observed

between data and simulation [43]. Using t he matching

between selected jets and generated partons, simulated events

are classiﬁed as containing at least one b jet (W+bX), at least

one c jet and no b jets (W+cX), or containing neither b jets

nor c jets (W+light quarks). The rate of W+bX events is mul-

tiplied by 2 ±1 and the rate of W+cX events is multiplied by

+1.0

−0.5

. No correction is applied to W+light-jets events. These

correction factors are calculated in [43] in a phase space

which is close to the one used in the analysis. The uncer-

tainties in the correction factors are taken i nto account as

systematic uncertainties. The total number of W+jets events

is modiﬁed to conserve this number when applying the heavy-

ﬂavour corrections. The remaining backgrounds, originating

from single-top-quark, diboson, and Z/γ

∗

+jets processes,

are small and their contributions are estimated using simula-

tion.

123

Eur. Phys. J. C (2014) 74:3014 Page 5 of 29 3014

Events

-1

Data

Signaltt

Othertt

Single t

W+Jets

μμ ee/→*γZ /

ττ→*γZ /

Diboson

QCD Multijet

Dilepton Combined

= 7 TeVs

-1

CMS, L = 5.0 fb

jets

234

8≥

Data/MC

0.5

1.5

Jets / 10 GeV

10×

Data

Signaltt

Othertt

Single t

W+Jets

μμ ee/→*γZ /

ττ→*γZ /

Diboson

QCD Multijet

Dilepton Combined

= 7 TeVs

-1

CMS, L = 5.0 fb

GeV

50 100 150 200 250

Data/MC

0.5

1.5

Events

Data

Signaltt

Othertt

Single t

W+Jets

*+JetsγZ/

Diboson

QCD Multijet

Lepton+Jets Combined

= 7 TeVs

-1

CMS, L = 5.0 fb

jets

8≥

Data/MC

0.5

1.5

Jets / 10 GeV

10×

Data

Signaltt

Othertt

Single t

W+Jets

*+JetsγZ/

Diboson

QCD Multijet

Lepton+Jets Combined

= 7 TeVs

-1

CMS, L = 5.0 fb

[GeV]

50 100 150 200 250

Data/MC

0.5

1.5

Fig. 1 Number of reconstructed jets (left)andjetp

spectrum (right)

after event selection in the dilepton channel for jets with p

> 30 GeV

(top), and in the +jets channel for jets with p

> 35 GeV (bottom). The

hatched band represents the combined effectof all sources of systematic

uncertainty

The multiplicity and the p

distributions of the selected

reconstructed jets are shown for the dilepton and +jets chan-

nels in Fig. 1. Good agreement for the jet multiplicity is

observed between data and simulation for up to 5 (6) jets in

the dilepton (+jets) channels. For higher jet multiplicities,

the simulation predicts slightly more events than observed in

data. The modelling of the jet p

spectrum in data is shifted

towards smaller values, covered by the systematic uncertain-

ties. The uncertainty from all systematic sources, which are

described in Sect. 5, is determined by estimating t heir effect

on both the normalisation and the shape. The size of these

global uncertainties does not reﬂect those in the ﬁnal mea-

surements, since they are normalised and, therefore, only

affected by shape uncertainties.

5 Systematic uncertainties

Systematic uncertainties in the measurement arise from

detector effects, background modelling, and theoretical

assumptions. Each systematic uncertainty is investigatedsep-

arately and estimated for each bin of the measurement by

varying the corresponding efﬁciency, resolution, or scale

within its uncertainty. For each variation, the measured nor-

123

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使用ATLAS探测器测量在pp = s = 13 TeV的pp碰撞中衰减到全强最终状态的高激发夸克的tt微分截面

使用eLAS事件，在b =标记的pp碰撞中，使用ATLAS探测器在pp碰撞中使用e-事件测量tt的生产横截面

在s = 13 $$ \ sqrt {s} = 13 $$ TeV的pp碰撞中，在dilepton通道中测量归一化微分tt¯$$ \ mathrm {t} \ overline {\ mathrm {t}} $$横截面

在s = 13TeV的pp碰撞中，使用dilepton最终态测量与b喷射和包含喷射有关的tt横截面及其比率。

在s = 7TeV的pp碰撞中differential（1S），ϒ（2S）和ϒ（3S）微分截面的测量

在s = 7 TeV的pp碰撞中快中速D介子生产的测量

在s = 13TeV的pp碰撞中具有至少一个光子且缺少横向动量的事件中搜索量规介导的超对称性

在与ATLAS的s = 13 TeV pp碰撞中具有四个或更多轻子的事件中搜索超对称性

在s = 8 TeV的pp碰撞中Drell-Yan轻子对的前后不对称性

在s = 13TeV的pp碰撞中测量夸克生产截面

最新资源

在s = 8 TeV的pp碰撞中，截面比σtt′bb′/ σtt′jj的测量