Measurement of the cross section and angular correlations for associated production of a Z boson

35 Pages·2013·0.71 MB·English

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP/2013-153
2013/12/17
CMS-EWK-11-015
Measurement of the cross section and angular correlations
for associated production of a Z boson with b hadrons in
√
pp collisions at s = 7TeV
3
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The CMS Collaboration

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Abstract
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A study of proton-proton collisions in which two b hadrons are produced in associ-
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ation with a Z boson is reported. The collisions were recorded at a centre-of-mass
2
energy of 7TeV with the CMS detector at the LHC, for an integrated luminosity of
v
9 5.2fb−1. Thebhadronsareidentifiedbymeansofdisplacedsecondaryvertices,with-
4
outtheuseofreconstructedjets,permittingthestudyofb-hadronpairproductionat
3
smallangularseparation. Differentialcrosssectionsarepresentedasafunctionofthe
1
. angularseparationofthebhadronsandtheZboson. Inaddition,inclusivemeasure-
0
1 ments are presented. For both the inclusive and differential studies, different ranges
3 ofZbosonmomentumareconsidered,andeachmeasurementiscomparedtothepre-
1
dictions from different event generators at leading-order and next-to-leading-order
:
v
accuracy.
i
X
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a
PublishedintheJournalofHighEnergyPhysicsasdoi:10.1007/JHEP12(2013)039.
(cid:13)c 2013CERNforthebenefitoftheCMSCollaboration. CC-BY-3.0license
∗SeeAppendixAforthelistofcollaborationmembers

1
1 Introduction
ThemeasurementofZ/γ∗(henceforthdenotedby“Z”)productioninassociationwithbquarks
attheLargeHadronCollider(LHC)isrelevantforvariousexperimentalsearches. Inparticular,
theprocessconstitutesoneofthedominantbackgroundstostandardmodel(SM)Higgsboson
production associated with a Z boson, where the Higgs boson decays subsequently to a bb
pair. The discovery by the ATLAS and Compact Muon Solenoid (CMS) experiments of a neu-
tral boson with a mass of about 125GeV [1, 2] motivates further studies to establish its nature
and determine the coupling of the new boson to b quarks. Furthermore, for models featuring
an extended Higgs sector, such as two-Higgs-doublet models [3–6], an interesting discovery
channelisφ → Zφ withthesubsequentdecayφ → bb,whereφ areneutralHiggsbosons.
1 2 2 1,2
Since the mass difference m −m may be large, the Higgs decay would consist of a pair of
φ1 φ2
collinearbquarksproducedinassociationwithaZboson.
Of particular interest is the measurement of angular correlations of b hadrons, especially at
small opening angles, where significant theoretical uncertainties in the description of the col-
linear production of b quarks remain. Several theoretical predictions, obtained with different
techniquesandapproximations, canbetested. Tree-levelcalculationsallowingforlargenum-
bers of extra partons in the matrix elements (as initial- and final-state radiation) are available.
These are provided by MADGRAPH [7, 8], ALPGEN [9], and SHERPA [10], in both the five- and
four-flavourapproaches,i.e.byconsideringthefiveorfourlightestquarkflavoursinthepro-
ton parton distribution function (PDF) sets. Next-to-leading-order (NLO) calculations have
been performed in both the five-flavour (MCFM) [11] and four-flavour [12, 13] approaches. A
fullyautomatedNLOcomputationmatchedtoapartonshowersimulationisimplementedby
the aMC@NLO event generator [14, 15]. A detailed discussion of b-quark production in the
differentcalculationschemesisavailableinRef.[16].
From the experimental point of view, the study of b-hadron pair production using the stan-
dard jet-based b-tagging methods [17] suffers from geometrical limitations due to the jet cone
size. Hadroniccascadesfromb-quarkpairsatsmallangularseparationcanmergeintoasingle
jet, making this region of phase space difficult to access using jet-based b-tagging techniques.
To overcome this obstacle, an alternative method is used, consisting of the identification of b
hadronsfromdisplacedsecondaryvertices,whicharereconstructedfromtheirchargeddecay
products. This approach is implemented in the inclusive secondary vertex finder (IVF) [18].
The IVF exploits the excellent tracking capabilities of the CMS detector and, being indepen-
dent of the jet reconstruction, extends the sensitivity to small angular separations and softer
b-hadrontransversemomenta(p ).
T
Four variables are used to parametrise the angular correlations in the Zbb final state: ∆R ,
BB
∆φ , min∆R , and A . The angular correlation between the b hadrons is described by
BB ZB ZBB
twovariables, ∆R and ∆φ , theangularseparationbetweentheflightdirectionsofthetwo
BB BB
particles in (η,φ) and in the transverse plane, respectively. The variable ∆R is defined as
BB
∆R = (cid:112)(∆φ )2+(∆η )2, where ∆φ and ∆η are the azimuthal (in radians) and pseu-
BB BB BB BB BB
dorapidity separations. The pseudorapidity is defined as η = −ln[tan(θ/2)], where θ is the
polaranglerelativetotheanticlockwisebeamdirection. The∆R distributionconstitutesadi-
BB
recttestofthemodellingofthedifferentpp → ZbbXproductionmodes. Thisquantityallows
the identification of the contribution from the qi → ZbbX subprocesses (where i = q, g) for
which the scattering amplitude modelling is based on Feynman diagrams with g → bb split-
ting. Leadingorder diagrams for these subprocesses are shownin Figs. 1 (a) and (b), together
with diagrams representative of other pp → Zbb production modes: emission of a Z boson
fromab-quarkline(c),andb-quarkfusiongg → Zbb(d).
2 1 Introduction
q Z g q q b g b
Z g Z
b b Z
q q q b
g b g b g b
(a) (b) (c) (d)
Figure 1: Tree-level Feynman diagrams for (a,b) qi → ZbbX subprocesses (where i = q,g)
involving g → bb splitting; (c) qq → Zbb with the emission of a Z boson from a b quark; and
(d)gg → Zbb.
∆
Asecondvariable,theangularseparationbetweenthebhadronsinthetransverseplane, φ ,
BB
is also considered because it is a better observable for the back-to-back configuration. Since
the relative fraction of quark- and gluon-initiated subprocesses is correlated with the Z-boson
momentum pZ,thedifferential∆R and∆φ distributionsaremeasuredindifferentintervals
T BB BB
of pZ.
T
Twoadditionalangularvariablesareconsidered: theangularseparationbetweentheZboson
and the closest b hadron in the (η,φ) plane, min∆R , and the asymmetry between the b-
ZB
hadronemissiondirectionsandtheZproductiondirection, A ,definedas
ZBB
max∆R −min∆R
A = ZB ZB, (1)
ZBB max∆R +min∆R
ZB ZB
wheremax∆R isthedistancebetweentheZbosonandthefurtherbhadron. Configurations
ZB
in which the two b hadrons are emitted symmetrically with respect to the Z direction yield a
value of A close to zero. Emission of additional gluon radiation in the final state results
ZBB
in a nonzero value of A . Hence, the A variable helps to indirectly test the validity of
ZBB ZBB
quantum chromodynamics (QCD) at higher orders of the perturbative series. The min∆R
ZB
variable identifies events with the Z boson in the vicinity of one of the two b hadrons, and is
thereforeusefulfortestingNLOcorrectionsinvolvingZradiationfromaquark[19].
The contribution of the qi → ZbbX subprocesses to the total production is illustrated in Fig. 2
as a function of each of the four variables described above. The distributions are shown for
both the nonboosted (all pZ) and the boosted (pZ > 50GeV) regions of the Z transverse mo-
T T
mentum. For all the variables, the contribution of the qi → ZbbX subprocesses differs from
the contribution of gg → ZbbX. The qi → ZbbX subprocesses are dominant in the following
regions: ∆R < 1,∆φ < 0.75,min∆R > 3.2,and A < 0.05.
BB BB ZB ZBB
In this analysis, the differential production cross sections for the process pp → ZbbX (hence-
forth the processes are denoted by their final state, here “Zbb”) as functions of the four kine-
maticvariableslistedaboveareevaluatedfromCMSdata. Thesecrosssectionsaregivenatthe
hadron level and compared to the predictions provided by several of the Monte Carlo (MC)
generatorsmentionedabove. Thetotalcrosssectionisalsomeasured. Theresultsaregivenfor
differentregionsof pZ. Becauseofthelimitedsizeoftheavailabledatasample,thedifferential
T
measurements are calculated in the nonboosted and boosted regions. The total cross section
is evaluated for pZ larger than 0, 40, 80, and 120GeV. Z bosons are reconstructed in the e+e−
T √
and µ+µ− decay modes. The analysis exploits the full 2011 data set recorded at s = 7TeV,
corresponding to an integrated luminosity of (5.2±0.1)fb−1. Measurements of the Z-boson
production cross section in association with one or two b-tagged jets at the LHC have been
reportedpreviouslybytheATLASandCMSCollaborations[20,21].
3
n n n
bi bi 0.1 CMS Simulation total bi
/ / s = 7 TeV qifi ZbbX/
ss d1/ ss d1/0.08 Malla pdZTGraph 4F ggfi ZbbssX d1/ pZT > 50 GeV
0.06
0.04
0.02
00 0.50.11 1.05.2 2 02.3.5 30.43.5 04.5 0 00..56 1 0.17.5 20.82.5 03.9 3.5 14
D R A D R
BB ZBB BB
bin bin0.09 CMS Simulation total bin
ss/ d1/ ss/ d1/00..0078 Maslla p=dZT G7 rTaepVh 4F qgigfifi Z ZbbbbXssX/ d1/ pZT > 50 GeV
0.06
0.05
0.04
0.03
0.02
0.01
00 0.05.1 10.21.5 0.32 02.4.5 03.5 0 0.06.5 01.7 1.05.8 2 0.92.5 13
D f A D f
BB ZBB BB
n n n
bi bi CMS Simulation total bi
/ / s = 7 TeV qifi ZbbX/
ss d1/ ss d1/ 1 Malla pdZTGraph 4F ggfi ZbbssX d1/ pZT > 50 GeV
10-1
10-2
10-3
00 0.50.11 1.05.2 2 02.3.5 30.43.5 04.5 0 00..56 1 0.17.5 20.82.5 03.9 3.5 14
minD R AminD R
ZB ZBB ZB
n n n
bi bi 10 CMS Simulation total bi
/ / s = 7 TeV qifi ZbbX/
ss d1/ ss d1/ 1 Malla pdZTGraph 4F ggfi ZbbssX d1/ pZT > 50 GeV
10-1
10-2
10-3
00 0.2 00.2.4 0.6 00.4.8 10 0.60.2 0.4 0.80.6 0.8 1 1
A A A
ZBB ZBBZBB
Figure 2: Distribution of ∆R (first row), ∆φ (second row), min∆R (third row), and A
BB BB ZB ZBB
(fourth row) as predicted by MADGRAPH in the four-flavour scheme, in the nonboosted (left)
andboosted(right)regionsoftheZ transversemomentum. Thecomponentfromgg → ZbbX
isrepresentedbythehatchedhistogram,whilethecontributionfromqi → ZbbXsubprocesses
(wherei = q,g)isrepresentedbytheshadedhistogram. Theunshadedhistogramcorresponds
tothesumofthetwocomponents.
4 3 Eventreconstructionandselection
Thepaperisorganisedasfollows: thedescriptionoftheCMSexperimentandsimulatedsam-
ples are given in Section 2; the event reconstruction and selection are presented in Section 3;
themeasurementtechniqueisexplainedinSection4;thesystematicuncertaintiesarediscussed
in Section 5; the theoretical uncertainties associated with different models of Zbb production
are summarized in Section 6; the results and conclusions are presented in Sections 7 and 8,
respectively.
2 CMS detector and simulated samples
AdetaileddescriptionoftheCMSexperimentcanbefoundinRef.[22]. Themainsubdetectors
used in this analysis are the silicon tracker, the electromagnetic calorimeter (ECAL), and the
muonsystem. Thetrackerconsistsofsiliconpixelandstripdetectormodulesandisimmersed
in a 3.8T magnetic field, which enables the measurement of charged particle momenta over
the pseudorapidity range |η| < 2.5. The electromagnetic calorimeter consists of nearly 76000
leadtungstatecrystals,whichprovidecoveragefor|η| (cid:46) 1.48inacylindricalbarrelregionand
1.48 (cid:46) |η| (cid:46) 3.0intwoendcapregions,exceptforainsensitivegapintheregion1.442 < |η| <
1.566 between the ECAL barrel and endcap. Muons are identified in the range |η| < 2.4 by
gas-ionisation detectors embedded in the steel return yoke. The first level of the CMS trigger
system consists of custom hardware processors and uses information from the calorimeters
and muon system to select the most interesting events in less than 1µs. The high level trigger
processorfarmfurtherdecreasestheeventratetolessthan300Hzbeforedatastorage.
Samples of signal and background events are produced using various event generators to es-
timate the signal purity, efficiency, and detector acceptance, with the CMS detector response
modelledinextensivedetailwith GEANT4 [23].
The Zbb signal sample is produced with the MADGRAPH 1.4.8 generator in the four-flavour
approach. Nobquarksarepresentintheinitialstate,whileuptotwoadditionallightpartons
are produced in association with the Z boson and the two b quarks. The PDF set is CTEQ6L1
andthesimulationofpartonshower,hadronisation,andmultipartoninteractionsisdonewith
PYTHIA 6.4.2.4 [24]. The background samples are Z plus jets, where the additional jets are
from light quarks or gluons (u, d, c, s, g), top pair production (tt), and Z pair production. The
Z+jetssampleisextractedfromaDrell–Yaninclusivesampleproducedwith MADGRAPH in
the five-flavour approach and interfaced with PYTHIA. The tt sample is also produced with
the MADGRAPH generatorinterfacedwith PYTHIA,whilethedibosonZZsampleisgenerated
with PYTHIA. The tune considered in PYTHIA is Z2∗, which is the Z1 tune [25] with the PDF
setchangedtoCTEQ6L1andminormodificationsoftheunderlyingeventmodelling,namely
PARP(90) = 0.227andPARP(82) = 1.921.
Additional interactions per bunch crossing (pileup) are included in the simulation with the
distributionofpileupinteractionsmatchingthatobservedindata.
3 Event reconstruction and selection
Thefirststepoftheanalysisistheonlineeventselectionwiththeloosestavailabledimuonand
dielectrontriggersinordertoenrichthesamplewithZ → µ+µ− ande+e− decays. Thedielec-
tron trigger line requires loose electron identification and isolation and imposes 17 and 8GeV
transversemomentumthresholdsonthetwoelectroncandidates,respectively. Thetransverse
momentumthresholdsofthemuontriggerline,whichchangedwithtimetocopewithincreas-
inginstantaneousluminosity,wereinitially7GeVonbothmuoncandidates,then13or17GeV
5
ononecandidateand8GeVontheother.
Muon candidates are then required to pass tight selection requirements to ensure high pu-
rity [26]. Electron candidates are reconstructed from energy deposits in the ECAL, and must
satisfy the standard CMS electron identification criteria [27]. Leptons are required to have
p > 20GeV, and to be within the pseudorapidity range |η| < 2.4. Prompt leptons are
T
selected by requiring a distance of closest approach between the track and the primary pp
interaction (identified as the vertex with the largest quadratic sum of its constituent tracks’
p ) smaller than 200µm. A requirement is applied on the lepton isolation, computed using
T
the particle-flow technique [28], which exploits the information from all subdetectors to indi-
vidually identify the particles produced in the collisions. The isolation, defined as the ratio
between the scalar sum of the transverse momentum or transverse energy (E ) of the parti-
T
cles within a ∆R < 0.4 (0.3) cone around the muon (electron) and its transverse momentum,
(∑ p +∑ E +∑ E )/p , must be at most 0.15. In order to ensure
chargedhad. T neutralhad. T photon T T
thattheselectionisstableregardingthelargeandvaryingnumberofprimaryinteractions,the
chargedparticle-flowcandidatesarerequiredtobeassociatedwiththeselectedprimaryvertex
(PV).Inaddition,acorrectionisappliedtosubtracttheenergycontributionofneutralhadrons
andphotonsproducedinpileupinteractions. Thiscorrectionisestimatedeventbyeventfrom
themedianoftheenergydensitydistributionandappliedwithintheisolationcone[29].
Onlyeventswithtwooppositelychargedsame-flavourleptoncandidateswithinvariantmass
between 60 and 150GeV are selected. The signal region is then defined as the 81 < M <
(cid:96)(cid:96)
101GeVintervaltoreducethecontaminationfromttevents.
Events containing b hadrons are selected by applying the inclusive vertex finder technique.
The secondary vertex (SV) reconstruction on which the IVF is based is initiated by the iden-
tification of a set of “seed” tracks that are significantly displaced with respect to the primary
vertex. Such tracks are selected by requiring their three-dimensional impact parameter to be
larger than 50µm, and their impact parameter (IP) significance S = IP/σ larger than 1.2,
IP IP
where σ is defined from the uncertainties on both the PV position and the point of closest
IP
approachbetweenthetrackandthePV.Additionaltracksareclusteredtogetherwiththeseed
tracks if they fulfil several requirements. First, the distance of closest approach of a track to
the seed must not exceed 500µm, and its significance must be smaller than 4.5. Second, the
anglebetweenthevectordefinedbythePVandthepointofclosestapproachontheseedtrack
and the seed track direction at the vertex has to be smaller than 45◦ so only forward tracks
from b-hadron decays are retained. Secondary vertices are built from the seeds and clustered
tracks[30].
TheSVfour-momentumiscalculatedas p = ∑p wherethesumisoveralltracksassociated
SV i
withthatvertex. Thepionmasshypothesisisusedforeverytracktoobtainitsenergy E. The
i
vertexmassm isgivenbym2 = E2 −p2 .
SV SV SV SV
The IVF technique establishes a list of b-hadron (B) candidates from the reconstructed SVs.
If two SVs are present, they can potentially be the signature of a b → cX decay chain and are
mergedintoasingleBcandidateifthefollowingconditionsarefulfilled: i)∆R(SV ,SV ) < 0.4,
1 2
ii) the sum of the invariant masses of track candidates associated with the vertices is smaller
than5.5GeV,andiii)cosδ > 0.99,whereδistheanglebetweenthevectorfromthepositionof
the SV that is closer to the PV to the position of the other SV and the three-momentum of the
vertex with larger decay length. The flight distance significance of a B candidate is calculated
from the distance between the PV and SV divided by its uncertainty. More details of the SV
andBcandidatereconstructioncanbefoundinRef.[18].
6 4 Crosssectionmeasurement
V)160 V)160
e CMS L = 5.2 fb-1 data e CMS L = 5.2 fb-1 data
G140 G140
3 s = 7 TeV signal+background 3 s = 7 TeV signal+background
s)/(120 background s)/(120 background
ent100 ent100
v v
e e
N( 80 N( 80
60 60
40 40
20 20
0 0
60 70 80 90 100 110 120 130 140 150 60 70 80 90 100 110 120 130 140 150
dimuon invariant mass (GeV) dielectron invariant mass (GeV)
Figure3: Fitresultsforthedimuon(left)anddielectron(right)invariantmassdistributionsfor
events with two leptons and two B candidates selected as described in Section 3. The dashed
lineshowsthefittedbackgroundcomponentandthesolidlinethesumofthefittedsignaland
backgroundcomponents,whicharedescribedinthetext. Theverticaldashedlinesindicatethe
boundariesofthesignalregion. Thepointswitherrorsrepresentthedata.
The flight distance L is defined as the length of the three-dimensional vector connecting the
primaryandsecondaryvertices. ItssignificanceS isobtainedbydividingLbyitsuncertainty,
L
calculated as quadratic sum of the PV and SV position uncertainties. A b hadron candidate is
retainedifS > 5,|η| < 2, p > 8GeV,andinvariantmassm > 1.4GeV. TheBcandidatemass
L T
andflightdistancesignificancecuts,alongwiththerequirementofatleastthreetracksassoci-
ated with the secondary vertex, are the most effective requirements for rejecting background
eventsfromZccproduction.
Events that have exactly two B candidates are retained. The resulting dimuon and dielectron
invariant masses are shown between 60 and 150GeV in Fig. 3. In total, 330 (223) events pass
alltheselectionrequirementsinthemuon(electron)channelinthe81 < M < 101GeVsignal
(cid:96)(cid:96)
massregion. ThankstotheexcellentperformanceoftheCMStrackingsystem,theIVFangular
resolutionisapproximately0.02for∆R and∆φ and0.03formin∆R and A .
BB BB ZB ZBB
The main source of background contamination in the final sample is top-quark pair produc-
tion. The tt fraction is assessed from an unbinned maximum-likelihood fit to the measured
dileptoninvariantmassdistributionasdescribedinSection4. Thefityieldsattcontamination
ofapproximately30%intheinclusiveeventsample,andofabout23%for pZ > 50GeV.
T
The measured and simulated distributions of the most significant event properties are com-
pared at the detector level, as shown in Fig. 4. The measured distributions of mass and trans-
verse momentum of the leading B candidate, i.e. that with the largest p , as well as pZ, agree
T T
withMCpredictionswithinuncertainties.
4 Cross section measurement
The differential and total cross sections are obtained by subtracting the background and cor-
rectingfordetectoracceptance, signalefficiency, andpurity. Thecorrectionfactorsrefertothe
kinematicphasespaceforeventswithexactlytwobhadronsandaleptonpairfromaZdecay.
The b hadrons have p > 15GeV and pseudorapidity |η| < 2. Each lepton has p > 20GeV,
T T
|η| < 2.4, and the dilepton invariant mass is 81 < M < 101GeV. The differential cross sec-
(cid:96)(cid:96)
tions are measured for pZ > 0GeV and pZ > 50GeV. In the former case, the bin sizes are 0.7,
T T
0.53, 0.84, and 0.2 for ∆R , ∆φ , min∆R , and A , respectively. In the latter, the corre-
BB BB ZB ZBB
7
N(events)/(0.56 GeV)111112024680000000 CsM =S 7 L T =e V5.2 fb-1 dDDTdMaiTYYbCtbo++a asslbitroganht.t ,ucncertainty N(events)/(8 GeV)111122246802000000 CsM =S 7 L T =e V5.2 fb-1 dDDTdMaiTYYbCtbo++a asslbitroganht.t ,ucncertainty N(events)/(15 GeV)11180240000 CsM =S 7 L T =e V5.2 fb-1 dDDTdMaiTYYbCtbo++a asslbitroganht.t ,ucncertainty
100 60
80
80
60 60 40
40 40 20
20 20
0 0 0
C 2 C 2 C 2
M M M
a/ 11.5 2 2.5 3 3.5 4 4.5 5 5.5 a/ 110 20 30 40 50 60 70 80 90 100 a/ 10 20 40 60 80 100 120 140 160 180 200 220
dat 01.5 2 2.5 3 3.5 4 4.5 5 5.5 dat 010 20 30 40 50 60 70 80 90 100 dat 00 20 40 60 80 100 120 140 160 180 200 220
leading B-candidate mass (GeV) leading B-candidate p(GeV) Z candidate p (GeV)
T T
Figure 4: Distribution of the leading B candidate invariant mass (left), transverse momentum
(centre), and pZ (right) for the muon and electron channels combined, in the signal region
T
(81 < M < 101GeV). The CMS data are represented by solid points and the MC simulation
(cid:96)(cid:96)
bystackedhistograms. TheshadedregionrepresentsthestatisticaluncertaintyintheMCpre-
diction. Thefractionofsignalandtopbackgroundinthesimulationisextractedbymeanafit
(Fig.3)andthesumisnormalisedtothenumberofentriesinthedata. Thebottomplotsshow
the ratio of measured and simulated numbers of entries in each bin with the MC uncertainty
representedbythedottedarea.
sponding values are 0.84, 0.63, 1.0, and 0.25. Since the IVF angular resolution is significantly
smallerthanthebinsizeforallthemeasureddistributions,nounfoldingprocedureisapplied
tomeasurethehadron-leveldifferentialcrosssections.
Thehadron-leveldifferentialcrosssectioniscalculatedfrom
SB
σ = F(nµ ,ne )· α,j ·P · 1, (2)
α,j α,j α,j (cid:101)2B α,j L
α,j
where
N(cid:96)
n(cid:96) = α,j , (3)
α,j (cid:101)(cid:96) ·A(cid:96)
α,j α,j
with (cid:96) = e, µ. For each bin j of the angular variable α, indicating one of the four variables
definedinSection1, thenumberofsignalevents N(cid:96) isextractedfromanextendedunbinned
α,j
maximum-likelihood fit to the lepton pair invariant mass distribution. A Breit–Wigner distri-
butionconvolvedwithaGaussianresolutionfunctionisusedforthesignalandathird-degree
Chebychev polynomial distribution for the background, as shown in Fig. 3. The signal shape
parameters are evaluated from data while the background parameters are obtained from sim-
ulation. N(cid:96) is corrected for the dilepton reconstruction and selection efficiency (cid:101)(cid:96) and ac-
α,j α,j
ceptance A(cid:96) . The corrected yields n(cid:96) in the muon and electron channels are found to be in
α,j α,j
agreement,withinstatisticaluncertainties.
The two channels are combined into a single measurement F(nµ ,ne ) using the BLUE algo-
α,j α,j
rithm[31,32], whichperformsaweightedaverageoftheinputvaluestakingintoaccountthe
respectiveuncertaintiesandtheircorrelations.
Theresultingyieldiscorrectedfortheb-hadronpairidentificationefficiency(cid:101)2B,theb-hadron
α,j
purityP ,andtheintegratedluminosityL. ThefactorSB correctsforeventswithbhadrons
α,j α,j
with p < 15GeV.
T
8 5 Systematicuncertainties
Thedileptontriggerefficiencyisestimatedfromdatawithatag-and-probemethod,asafunc-
tionoftheleptonkinematics. Itisapproximately93%forthedimuonand98%forthedielectron
trigger selections. The lepton offline reconstruction and selection efficiencies, around 80% for
muon and 50% for electron pairs, are obtained from simulation and are rescaled to match the
valuesmeasuredindatawithatag-and-probeprocedure,asafunctionoftheleptonpseudora-
pidity.
Thetotalb-hadronidentificationefficiencyisestimatedusingmultijeteventscontainingsemilep-
tonicdecaysofb-hadronsandfromeventsenrichedwithtopquarks. Inaddition,adedicated
studyisperformedtoverifythattheefficiencymeasurementsarevalidfortheinclusivevertex
findingalgorithmaswell.
The efficiency for identifying b-hadron pairs, which ranges between 8% and 10%, is corrected
by applying a factor of 0.88 to account for the discrepancy observed between the measured
and simulated efficiency. This scale factor is measured from data, in the same way as it is
done for the Simple Secondary Vertex method that identifies b hadrons inside jets [17]. This
studyrequirestheassociationoftheverticesreconstructedwiththeIVFwithjetsandexploits
the features of muons produced in semileptonic decays of the b hadrons, namely their high
transverse momenta with respect to the jet axis. The purity P and correction factor SB are
α,j α,j
evaluatedtobeabout85%and97%,respectively,basedonMCsimulation.
The same method is used to derive the total cross section for different ranges of pZ. The ex-
T
tendedmaximum-likelihoodfitandtheproceduretoextractthecorrectionfactorsareapplied
tothecorrespondingeventsample.
5 Systematic uncertainties
Thefollowinguncertaintiesonthedifferentialcrosssectionsareconsidered:
• Uncertaintyincombineddileptonsignal
The procedure to combine the muon and electron channels takes into account the
systematic uncertainties on the N(cid:96) yields and on the dilepton efficiency correction
α,j
factors. Thesystematicuncertaintyaffectingtheresultingcombinationisestimated
bytheBLUEalgorithm,andisapproximately±2%. Moredetailsaregivenbelow.
– Uncertaintyinthesignalyield
Thesystematicuncertaintyassociatedwiththeextractionof N(cid:96) fromthe
α,j
extended unbinned maximum-likelihood fit is estimated by varying the
shapeparameterswithintheiruncertainties. Forthesignal,theshapepa-
rameters are the Breit–Wigner mean and width, as well as the Gaussian
standard deviation. For the background, the parameters of the Cheby-
chevpolynomialdistributionareconsidered. Avariationofthesefactors
leadstoasignalyielduncertaintybelow±2%.
– Uncertaintyinthetriggerefficiencyandtheleptonefficiencyscalefactors
The lepton reconstruction and selection efficiency corrections are com-
putedwiththeMCsimulation,andrescaledtomatchtheefficiencyvalues
measuredfromdatawiththetag-and-probemethod. Thecorresponding
systematic uncertainty is estimated by varying the scale factors and the
trigger efficiency extracted from data within their systematic uncertain-
ties, mostly due to the background shape parametrisation. The resulting
variation is ±0.5% for the muon channel and ±1% for the electron chan-