Article

# Measurements of inclusive W and Z cross sections in pp collisions at √s = 7 TeV The CMS collaboration

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Politecnico di Bari, Bari, Italy
(Impact Factor: 6.11). 01/2011; 2011(1):080. DOI: 10.1007/JHEP01(2011)080

ABSTRACT

Measurements of inclusive W and Z boson production cross sections in pp collisions at Ös = 7 \sqrt {s} = 7 TeV are presented, based on 2.9 pb−1 of data recorded by the CMS detector at the LHC. The measurements, performed in the electron and muon decay channels, are
combined to give

s( \textpp ® \textWX ) B( \textW ® ln ) = 9.95±0.07( \textstat. )±0.28( \textsyst. )±1.09 \sigma \left( {{\text{pp}} \to {\text{W}}X} \right) \times \mathcal{B}\left( {{\text{W}} \to \ell \nu } \right) = 9.95\pm 0.07\left( {{\text{stat}}{.}} \right)\pm 0.28\left( {{\text{syst}}{.}} \right)\pm 1.09 (lumi.) nb and

s( \textpp ® \textZX ) B( Z ® l+ l- ) = 0.931±0.026( \textstat. )±0.023( \textsyst. )±0.102 \sigma \left( {{\text{pp}} \to {\text{Z}}X} \right) \times \mathcal{B}\left( {Z \to {\ell^{+} }{\ell^{-} }} \right) = 0.931\pm 0.026\left( {{\text{stat}}{.}} \right)\pm 0.023\left( {{\text{syst}}{.}} \right)\pm 0.102 (lumi.) nb, where ℓ stands for either e or μ. Theoretical predictions, calculated at the next-to-next-to-leading order in QCD using recent parton distribution functions,
are in agreement with the measured cross sections. Ratios of cross sections, which incur an experimental systematic uncertainty
of less than 4%, are also reported.

KeywordsHadron-Hadron Scattering

### Full-text

Available from: Niki Saoulidou
JHEP01(2011)080
Published for SISSA by Springer
Received: December 13, 2010
Accepted: December 27, 2010
Published: January 19, 2011
Measurements of inclusive W and Z cross sections in
pp collisions at
s = 7 TeV
The CMS collaboration
Abstract: Measurements of inclusive W and Z boson production cross sections in pp
collisions at
s = 7 TeV are presented, based on 2.9 pb
1
of data recorded by the CMS
detector at the LHC. The measurements, performed in the electron and muon decay chan-
nels, are combined to give σ(pp WX) ×B(W ) = 9.95 ±0.07 (stat.) ±0.28 (syst.) ±
1.09 (lumi.) nb and σ(pp ZX) × B(Z 
+

) = 0.931 ± 0.026 (stat.) ± 0.023 (syst.) ±
0.102 (lumi.) nb, where  stands for either e or µ. Theoretical predictions, calculated at
the next-to-next-to-leading order in QCD using recent parton distribution functions, are
in agreement with the measured cross sections. Ratios of cross sections, which incur an
experimental systematic uncertainty of less than 4%, are also reported.
Keywords: Hadron-Hadron Scattering
ArXiv ePrint: 1012.2466
Open Access, Copyright CERN,
for the beneﬁt of the CMS Collaboration
doi:10.1007/JHEP01(2011)080
Page 1
JHEP01(2011)080
Contents
1 Introduction 1
2 The CMS detector 2
3 Lepton reconstruction and identiﬁcation 3
3.1 Electrons 3
3.2 Muons 4
4 Missing transverse energy 5
5 Lepton selection eﬃciencies 5
5.1 Electrons 6
5.2 Muons 7
6 Event selection and signal extraction 8
6.1 W boson selection 9
6.1.1 Electrons 9
6.1.2 Muons 10
6.2 Z boson selection 11
6.2.1 Electrons 11
6.2.2 Muons 12
7 Systematic uncertainties 13
8 Results 15
9 Conclusions 19
The CMS collaboration 24
1 Introduction
The inclusive production of W and Z bosons is an important benchmark process at hadron
colliders. Measurements of σ (pp WX)×B (W ) and σ (pp ZX)×B(Z
+

),
where  = e or µ, test calculations based on higher-order perturbative QCD and parton
distribution functions (PDF). Such calculations are supported by measurements at the
SppS [1, 2] and Tevatron [35] pp colliders. We report the extension of these measurements
to signiﬁcantly higher energies, namely, with pp collisions at a center-of-mass energy of
7 TeV provided by the Large Hadron Collider (LHC). The data were collected from April
through August, 2010, by the Compact Muon Solenoid (CMS) experiment, and correspond
1
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JHEP01(2011)080
to an integrated luminosity of (2.88 ± 0.32) pb
1
. Recently, the ATLAS Collaboration
published measurements of cross sections for inclusive W and Z productions at the LHC
based on approximately 0.34 pb
1
[6]. In this article, “Z boson production” includes γ
exchange within the mass range 60 to 120 GeV.
High-p
T
electrons and muons are used for selecting W and Z 
+

candidate
events. In addition to a high-p
T
lepton, W events are characterized by signiﬁcant missing
transverse energy (E/
T
) due to the escaping neutrino. The reconstruction of electrons and
muons is detailed in section 3, along with lepton identiﬁcation and isolation requirements,
and the E/
T
reconstruction is described in section 4.
The measurements of cross sections are based on the formula σ ×B = N/(A ×ε ×L),
where N is the number of signal events, A is the ﬁducial and kinematic acceptance, ε is the
selection eﬃciency for events in the acceptance, and L is the integrated luminosity. The
value of A is aﬀected by PDF and renormalization scale uncertainties, while the value of ε
is susceptible to errors from triggering and reconstruction. In order to control the eﬃciency
uncertainties, we concentrate on the extraction of corrections to the eﬃciencies obtained
from the simulation; these correction factors come from eﬃciency ratios ρ = ε
sim
derived
by measuring ε and ε
sim
in the same way on data and simulations, respectively. In eﬀect,
we replace the product A × ε by the product F × ρ, where F = A × ε
sim
is the fraction of
generated events selected in the simulation. The values for ρ are derived from data, and
hence their uncertainties are experimental; the uncertainties on F derive from the theo-
retical uncertainties on A. In order to exploit this distinction between experimental and
theoretical uncertainties, we also report cross section measurements deﬁned within the re-
stricted acceptance dictated by the detector coverage and minimum transverse momentum;
these values incur essentially no theoretical uncertainty.
In section 5 we determine electron and muon selection eﬃciency correction factors from
the data. The selection of events for the W and Z samples and the extraction of signal
event yields are outlined in section 6, followed by a discussion of systematic uncertainties
in section 7. Finally, the results are reported and brieﬂy discussed in section 8.
In the following section, a brief description of the CMS detector is provided.
2 The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m inter-
nal diameter, providing a magnetic ﬁeld of 3.8 T. Within the ﬁeld volume are a silicon
pixel and strip tracker, an electromagnetic calorimeter (ECAL) and a brass/scintillator
hadron calorimeter (HCAL). Muons are detected in gas-ionization detectors embedded in
the steel return yoke. In addition to the barrel and endcap detectors, CMS has extensive
forward calorimetry.
CMS uses a right-handed coordinate system, with the origin at the nominal interaction
point, the x-axis pointing to the center of the LHC ring, the y-axis pointing up (perpen-
dicular to the LHC plane), and the z-axis along the anticlockwise-beam direction. The
polar angle θ is measured from the positive z-axis and the azimuthal angle φ is measured
in radians in the xy-plane. The pseudorapidity is given by η = ln(tan θ/2).
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JHEP01(2011)080
The inner tracker measures charged particle trajectories in the pseudorapidity range
|η| < 2.5. It consists of 1 440 silicon pixel and 15 148 silicon strip detector modules. It
provides an impact parameter resolution of 15 µm and a transverse momentum (p
T
)
resolution of about 1% for charged particles with p
T
40 GeV.
The electromagnetic calorimeter consists of nearly 76 000 lead tungstate crystals which
provide coverage in pseudorapidity |η| < 1.479 in a cylindrical barrel region (EB) and
1.479 < |η| < 3.0 in two endcap regions (EE). A preshower detector consisting of two
planes of silicon sensors interleaved with a total of 3 X
0
of lead is located in front of the EE.
The ECAL has an ultimate energy resolution of better than 0.5% for unconverted photons
with transverse energies above 100 GeV. The energy resolution is 3% or better for the
range of electron energies relevant for this analysis. The hadronic calorimeter is a sampling
device with brass as passive material and scintillator as active material. The combined
calorimeter cells are grouped in projective towers of granularity η × φ = 0.087 × 0.087
at central rapidities and 0.175 × 0.175 at forward rapidities.
Muons are detected in the pseudorapidity window |η| < 2.4, with detection planes
based on three technologies: drift tubes, cathode strip chambers, and resistive plate cham-
bers. A high-p
T
muon originating from the interaction point produces track segments in
typically three or four muon stations. Matching these segments to tracks measured in the
inner tracker results in a p
T
resolution between 1 and 2% for p
T
values up to 100 GeV.
The ﬁrst level (L1) of the CMS trigger system, composed of custom hardware proces-
sors, is designed to select the most interesting events in less than 1 µs using information
from the calorimeters and muon detectors. The High Level Trigger (HLT) processor farm
further decreases the event rate to a few hundred hertz, before data storage.
A more detailed description of CMS can be found elsewhere [7].
3 Lepton reconstruction and identiﬁcation
Events in which hadronic jets mimic an electron or a muon can contaminate the W and
Z samples. Such fake leptons, as well as real leptons arising from decays of heavy-ﬂavour
hadrons or decays in ﬂight of light mesons within jets, are suppressed by imposing limits
on additional energy recorded near the projected impact point of the candidate lepton
in the calorimeters, as well as on the energy of charged particles reconstructed in the
inner tracker near the direction of the candidate lepton. We deﬁne isolation variables for
the three subsystems: I
rel
ECAL
=
P
E
T
(ECAL)/p

T
, I
rel
HCAL
=
P
E
T
(HCAL)/p

T
and I
rel
trk
=
P
p
T
(tracks)/p

T
, where p

T
is the transverse momentum of the lepton candidate. The
scalar sums of transverse energy (E
T
) and transverse momentum (p
T
) are performed for
objects falling within a cone R =
p
(∆η)
2
+ (∆φ)
2
< 0.3 around the lepton candidate,
the energy deposits and the track associated with the lepton candidate being excluded from
the sums. We also deﬁne a combined isolation variable, I
rel
comb
= I
rel
ECAL
+ I
rel
HCAL
+ I
rel
trk
.
3.1 Electrons
Events with high-E
T
electrons are selected online when they pass a L1 trigger ﬁlter that
requires a coarse-granularity region of the ECAL to have E
T
> 5 GeV. They subsequently
3
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JHEP01(2011)080
must pass an HLT [8] ﬁlter that requires an ECAL cluster with E
T
> 15 GeV, using the
full granularity of the ECAL and E
T
measurements corrected using oﬄine calibration [9].
Electrons are identiﬁed oﬄine as clusters of ECAL energy deposits matched to tracks
from the silicon tracker. The ECAL clusters are designed to collect the largest fraction of
the energy of the original electron, including energy radiated along its trajectory. They
must fall in the ECAL ﬁducial volume of |η| < 1.44 for EB clusters or 1.57 < |η| < 2.5
for EE clusters. The transition region from 1.44 < |η| < 1.57 is excluded as it leads to
lower-quality reconstructed clusters, due mainly to services and cables exiting between the
barrel and endcap calorimeters. Electron tracks are reconstructed using an algorithm [10]
that accounts for possible energy loss due to bremsstrahlung in the tracker layers. The
energy of an electron candidate with E
T
> 20 GeV is essentially determined by the ECAL
cluster energy, while its momentum direction is determined by that of the associated track.
Particles misidentiﬁed as electrons are suppressed by requiring that the η and φ coordinates
of the track trajectory extrapolated to the ECAL match the η and φ coordinates of the
ECAL cluster, by requiring a narrow ECAL cluster width in η, and by limiting the HCAL
energy measured in a cone of R < 0.15 around the ECAL cluster direction.
Electrons from photon conversions are suppressed by requiring one hit in the innermost
pixel layer for the reconstructed electron track. Furthermore, electrons are rejected when
a partner track is found that is consistent with a photon conversion, based on the opening
angle and the separation in the transverse plane at the point at which the electron and
partner tracks are parallel.
For both the W and Z analyses an electron candidate is considered isolated if I
rel
trk
<
0.09, I
rel
ECAL
< 0.07 and I
rel
HCAL
< 0.10 in the barrel region; I
rel
trk
< 0.04, I
rel
ECAL
< 0.05 and
I
rel
HCAL
< 0.025 in the endcap regions.
The electron selection criteria were obtained by optimizing signal and background
levels according to simulation-based studies. The optimization was done for EB and EE
separately. We use the same criteria for the W eν and Z e
+
e
channels; these select
approximately 75% of the reconstructed electrons in the data with clusters in the ECAL
ﬁducial volume and E
T
> 20 GeV, and reduce the fake electron background by two orders
of magnitude.
More details and studies of electron reconstruction and identiﬁcation can be
found in ref. [11].
3.2 Muons
Events with high-p
T
muons are selected online if the data from the muon chambers satisfy
the L1 muon trigger, and if a muon candidate reconstructed from both muon chamber and
tracker data satisﬁes the HLT. An HLT threshold of p
T
> 9 GeV for muons in the range
|η| < 2.1 is chosen as the baseline for the analysis.
Oﬄine, a number of quality requirements are imposed. Muon candidates can be recon-
structed by two diﬀerent algorithms: one starts from inner-tracker information (“tracker
muons”), and another starts from segments in the muon chambers (“global muons”). We
demand that muon candidates for this analysis be reconstructed by both algorithms. We
also demand signals in at least two muon stations, and require that χ
2
/N
dof
< 10 for a
4
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JHEP01(2011)080
global ﬁt containing all valid tracker and muon hits, where N
dof
is the number of degrees
of freedom. The ﬁrst condition ensures a sensible momentum estimate at the muon trig-
ger level, and further suppresses remaining punch-through and sail-through hadrons. The
second condition suppresses contributions from light-meson decays-in-ﬂight.
In order to ensure a precise estimate of momentum and impact parameter, only tracks
with more than 10 hits in the tracker and at least one hit in the pixel detector are used.
Cosmic-ray muons are rejected by requiring an impact parameter relative to the nominal
beam axis of less than 2 mm. Studies of cosmic-ray muons conﬁrm that the high-p
T
cosmic
muon contamination is negligible.
As in the case of electrons, isolation criteria are applied. For both W and Z analyses,
a muon candidate is considered isolated if I
rel
comb
< 0.15.
More details and studies of muon reconstruction and identiﬁcation can be
found in ref. [12].
4 Missing transverse energy
An accurate E/
T
measurement is essential for distinguishing a W signal from QCD mul-
tijet production backgrounds. We proﬁt from the application of the particle ﬂow (PF)
algorithm [13], which provides superior E/
T
reconstruction performance at the energy scale
of W boson production. The algorithm combines information from the inner tracker, the
muon chambers, and all the calorimetry cells to classify reconstructed objects according to
particle type (electron, muon, photon, charged or neutral hadron), thereby allowing precise
energy corrections, and also providing a signiﬁcant degree of redundancy that reduces the
sensitivity of the E/
T
measurements to miscalibrations of the calorimetry.
Anomalous noise signals can spoil the E/
T
measurements. A dedicated eﬀort to identify
and remove such noise in the ECAL and HCAL, based on cosmic-ray and control samples
as well as collision data, has successfully reduced the impact of such noise to a negligible
level; there is no discernible diﬀerence in the E/
T
distributions for W events from
data and from simulation [14].
The E/
T
is the modulus of the transverse missing momentum vector, computed as the
negative of the vector sum of all reconstructed transverse momenta of particles identiﬁed
with the PF algorithm. The E/
T
resolution for inclusive multijet samples and for W
events is reproduced well by the simulation. The resolution worsens by about 10% when
there is more than one primary vertex; this occurs in about 40% of the events in the
considered data set, and has a negligible impact on the extraction of the W signal yields
described below.
5 Lepton selection eﬃciencies
The eﬃciencies for lepton reconstruction, identiﬁcation, isolation and trigger eﬃciencies
are obtained from data. Correction factors for the values extracted from the simulation
are determined with a tag-and-probe method exercised on Z 
+

samples in both data
and simulation. This procedure adequately removes any systematic uncertainties coming
5
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JHEP01(2011)080
from imperfections in the simulation, even though the kinematic distributions of leptons
in the Z 
+

sample diﬀer slightly from those in the selected W sample.
The tag-and-probe sample for the measurement of a given eﬃciency contains events
selected with two lepton candidates. One lepton candidate, called the “tag,” satisﬁes tight
identiﬁcation and isolation requirements. The other lepton candidate, called the “probe,”
is selected with criteria that depend on the eﬃciency being measured. The invariant mass
of the tag and probe lepton candidates must fall in the range 60–120 GeV. The signal
yields are obtained for two exclusive subsamples of events in which the probe lepton passes
or fails the selection criteria considered. Fits are performed to the invariant-mass distribu-
tions of the pass and fail subsamples, including a term that accounts for the background.
The measured eﬃciency is deduced from the relative level of signal in the pass and fail
subsamples; its uncertainty includes a systematic contribution from the ﬁtting procedure.
The correction factors are obtained as ratios of tag-and-probe eﬃciencies for the data
and for the simulation. They are used to compute the signal selection eﬃciency ratios
ρ, and their uncertainties are propagated as systematic uncertainties on these quantities,
except in the Z µ
+
µ
analysis, for which the eﬃciencies and yields are determined
simultaneously.
The eﬃciency of the lepton isolation requirements can also be measured using a
“random-cone” technique. In the inclusive W or Z sample, energy contributing to the
isolation variables comes mainly from the underlying event, which can be sampled in di-
rections uncorrelated with the lepton directions in a particular event. We use leptons in
simulated signal events to deﬁne directions in data events where the isolation energies can
be measured and compared to the requirements of the analysis; this ensures a sampling
of phase space that mimics the leptons in real data events. Studies with simulation verify
that this technique provides values for the isolation eﬃciency that are accurate to about
0.5% for muons and 1% for electrons.
5.1 Electrons
The electron selection eﬃciency is the product of three components: 1) the reconstruction
eﬃciency, 2) the identiﬁcation and isolation eﬃciency, and 3) the trigger eﬃciency. Eﬃ-
ciencies are evaluated for the barrel and endcap regions, and for the two possible electron
charges, separately.
The reconstruction eﬃciency is the probability of ﬁnding a reconstructed track when
the electron cluster is within the ECAL ﬁducial volume. The probe is selected as an ECAL
cluster of reconstructed transverse energy greater than 20 GeV. To reduce backgrounds,
which are not insigniﬁcant, we use a tight selection on the tag and require the probe to
pass additional loose shower shape and isolation requirements; these are known from simu-
lations to be uncorrelated with the reconstruction eﬃciency. The measured reconstruction
eﬃciency is the fraction of probes reconstructed as electron tracks. For the EB and EE elec-
trons we measure a reconstruction eﬃciency of (98.6±0.5)% and (96.2±0.8)%, respectively.
The resulting correction factors are consistent with unity.
The eﬃciency of electron identiﬁcation, isolation, and conversion rejection require-
ments is estimated relative to the sample of reconstructed electrons. The tag selection
6
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JHEP01(2011)080
does not need to be tight, and no additional criteria on the probe are imposed. In the
barrel, we measure a selection eﬃciency of (79.1 ± 1.8)%, to be compared to 85.5% for
the simulation, resulting in a correction factor of 0.925 ± 0.021. In the endcaps, an eﬃ-
ciency of (69.2 ± 2.0)% is measured, where 74.9% is expected from simulation, resulting
in a correction factor of 0.924 ± 0.027. The random-cone technique is used to cross check
the eﬃciency of the electron isolation requirements. The results conﬁrm the values within
1.0% for EB and 1.8% for EE electrons, respectively.
Finally, we obtain combined L1 and HLT trigger eﬃciencies from identiﬁed and isolated
electron candidates as probes. We measure (98.9 ± 0.3)% in the barrel, and (99.2 ± 0.5)%
in the endcaps, leading to correction factors consistent with unity. These tag-and-probe
eﬃciencies are conﬁrmed by measurements made with a sample of minimum-bias events
selected with scintillation counters and a sample of events selected by an HLT algorithm
that has minimum-bias requirements at L1 and a complete emulation of the oﬄine ECAL
cluster reconstruction.
The charge misidentiﬁcation for electrons in the simulated W sample is (0.67±0.01)%.
We infer a data/simulation charge misidentiﬁcation correction factor of 1.2
+0.4
0.3
by com-
paring the fraction of events with electrons of same electric charge in data and simulation
samples. This correction factor is included in the results for W
±
cross sections, as well as
their ratio, and its error propagated to the systematic uncertainties on these quantities.
The products of all correction factors for the electron selection are 0.919 ± 0.022 for
the EB and 0.926 ± 0.028 for the EE.
When combining the correction factors, we take into account the relative acceptance
of electrons from W decays in the EB and EE. We obtain the eﬃciency ratio for W eν
events: ρ
W
= 0.921 ± 0.036; and separately by charge: ρ
W
+
= 0.917 ± 0.046 and ρ
W
=
0.927 ± 0.047. We infer a signal selection eﬃciency of (72.1 ± 2.8)% for W eν events
with the electron cluster in the ECAL ﬁducial volume and E
T
> 20 GeV.
In the Z e
+
e
analysis, one electron candidate is allowed to fail the trigger criteria;
the eﬃciency ratio is ρ
Z
= 0.856 ± 0.050 and the corrected signal selection eﬃciency for
Z e
+
e
events with both electron clusters in ECAL ﬁducial volume and E
T
> 20 GeV
is (56.2 ± 3.3)%. This number is derived from the corrected overall electron selection
eﬃciencies, which are (78.3 ±2.9)% and (66.8 ±2.9)% in the EB and EE, respectively, and
taking into account the expected fractions of Z e
+
e
events with EB-EB, EB-EE and
EE-EE combinations of electrons, which are 52%, 37% and 11%, respectively.
5.2 Muons
The muon reconstruction and selection eﬃciency has ﬁve distinguishable compo-
nents: 1) the eﬃciency to ﬁnd a track in the inner tracker, 2) the eﬃciency to ﬁnd a
track in the muon chambers, and, for a muon candidate, 3) the eﬃciency to pass the qual-
ity requirements, 4) the eﬃciency to pass the isolation requirements, and 5) the probability
to pass the L1 trigger and HLT.
Muon eﬃciencies are extracted from the sample of candidate Z µ
+
µ
events. The
tag muon must pass all muon selection criteria. The invariant mass of the tag-and-probe
7
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JHEP01(2011)080
muon candidates is formed; invariant-mass distributions are produced for exclusive cate-
gories of events where the probe muon passes or fails various eﬃciency requirements. Si-
multaneous ﬁts to those distributions allow the number of signal events and the eﬃciencies
to be extracted.
The inner-tracker eﬃciency is studied using well-reconstructed tracks in the muon
chambers as probes. The eﬃciency for tracking in the muon chambers is tested with tracker
muons satisfying very loose matching to muon track segments. To measure the eﬃciency
of quality requirements, the probe muon must pass all the selection criteria except those
on the χ
2
and on the impact distance to the beam axis. Finally, the isolation eﬃciency is
measured using muons that pass the quality requirements, and the trigger eﬃciency using
muons that in addition are isolated.
The following eﬃciencies are obtained: for inner tracking, (99.1 ± 0.4)%; for muon
tracking, (96.4±0.5)%; for quality requirements, (99.7±0.3)%; for isolation, (98.5 ±0.4)%;
and for trigger, (88.3 ± 0.8)%. All correction factors are consistent with unity, except for
the trigger eﬃciency, for which the correction factor is 0.947 ± 0.009.
Isolation eﬃciencies have also been measured using the random-cone technique, and
the results conﬁrm the tag-and-probe value for the isolation eﬃciency quoted above: 98.7%
for W µν and 98.5% for Z µ
+
µ
.
The overall muon selection eﬃciency is (82.8 ± 1.0)%, to be compared to the value
of 88.7% obtained from the simulation; the eﬃciency ratio is ρ
W
= 0.933 ± 0.012. There
is no signiﬁcant diﬀerence between the eﬃciency ratios for positive and negative muons:
ρ
W
+
= 0.935 ± 0.018 and ρ
W
= 0.931 ± 0.019, respectively.
6 Event selection and signal extraction
The data used for these measurements were collected from April to August 2010. We
used only those data-taking periods passing the standard CMS quality criteria, which
allow no anomalous or faulty behavior for the inner tracker, the calorimeters, and the
muon chambers.
Several large samples of simulated events were used to evaluate the signal and back-
ground eﬃciencies and to validate our analysis techniques. Samples of electroweak pro-
cesses with W and Z production, both for signal and background events, were produced
with POWHEG [1517], interfaced with the PYTHIA [18] parton-shower generator. QCD
events with muons, electrons, or jets likely to be misidentiﬁed as electrons in the ﬁnal
state were studied with PYTHIA, as were other minor backgrounds such as tt and certain
electroweak processes (W τν, Z τ
+
τ
, WW, WZ, and ZZ). We do not consider the
diboson channels (WW, WZ, and ZZ) as part of the W and Z signals in order to facilitate
the comparison of our results to theoretical predictions, which do not take these contri-
butions into account. Generated events were processed through the full GEANT4 [19]
detector simulation, trigger emulation, and event reconstruction chain.
8
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JHEP01(2011)080
6.1 W boson selection
The W events are characterized by a prompt, energetic, and isolated lepton, and signiﬁcant
missing energy. The main backgrounds are QCD multijet events and Drell-Yan events in
which one lepton fails the selection. The QCD background is reduced by requiring the lep-
ton to be isolated; the remaining events do not have large E/
T
and can be distinguished from
signal events on a statistical basis. The Drell-Yan background is suppressed by rejecting
events with a second lepton candidate.
To measure the signal yields, we choose to ﬁt the E/
T
distribution in the electron
channel and the M
T
distribution in the muon channel, where M
T
=
p
2p
T
E/
T
(1 cos φ);
φ is the angle between the missing transverse momentum and the lepton transverse
momentum. QCD backgrounds are estimated from data, as explained below. According to
the simulation, W τ ν makes a small relative contribution; backgrounds from Z τ
+
τ
,
tt, and diboson production are negligible in both electron and muon channels.
6.1.1 Electrons
The W eν candidate events are required to have one identiﬁed electron with an ECAL
cluster of E
T
> 20 GeV in the ECAL ﬁducial volume. If a second electron candidate
satisfying looser criteria and with E
T
> 20 GeV is present in the event, the event is rejected.
The fraction of signal events selected in the simulation is F
W
= 0.446 ±0.006, with F
W
+
=
0.459 ± 0.007 and F
W
= 0.428 ± 0.008. The number of events selected in the data is
28 601, with 15 859 positive and 12 742 negative electrons.
The W eν signal is extracted from an unbinned maximum likelihood ﬁt of the
observed E/
T
distribution to the sum of signal and background shapes. The QCD back-
ground shape, which accounts for both QCD multijet production and direct-photon pro-
duction with the photon converting in the detector, can be modeled by a modiﬁed
Rayleigh distribution,
f(E/
T
) = E/
T
× exp
E/
2
T
2(σ
0
+ σ
1
E/
T
)
2
!
.
This function can be understood as describing ﬂuctuations of the missing transverse mo-
mentum vector around zero due to measurement errors; the resolution term, σ
0
+ σ
1
E/
T
,
increases with E/
T
to account for tails in the E/
T
measurement. This function describes
well the QCD background shape in the simulation, over the full range of E/
T
, as well as
E/
T
distributions from signal-free samples obtained by inverting the identiﬁcation or isola-
tion criteria.
The signal distributions are derived from simulation, separately for W
+
and W
, and
receive an event-by-event correction in bins of the W transverse momentum, determined
from a study of the hadronic recoil distributions of Z e
+
e
events in the data [14]. In ﬁts
to the E/
T
distributions, the free parameters are the W signal yield, the QCD background
yield, and the shape parameters σ
0
and σ
1
.
We extract the inclusive yield N
W
from a ﬁt where the expected ratio for σ
W
+
W
is assumed. It has been checked that the result was insensitive to this assumption. Fig-
ure 1 (a) shows the E/
T
distribution of the inclusive W eν sample and the results of
9
Page 10
JHEP01(2011)080
the likelihood ﬁt; the ﬁt function describes the data well, with a p-value of 0.49 for the
Kolmogorov-Smirnov test. The inclusive yield is N
W
= 11 895 ± 115 events.
The signals for the W
+
e
+
ν and W
e
ν channels are extracted from a si-
multaneous ﬁt to the individual E/
T
distributions, in which the QCD background shape
parameters σ
0
and σ
1
are constrained to be the same for both samples. The yields are
N
W
+
= 7 193 ±89 for W
+
e
+
ν and N
W
= 4 728 ±73 for W
e
ν, with a negligible
correlation. Because the two ﬁts are independent, the relation N
W
= N
W
+
+ N
W
is not
exactly satisﬁed, but holds to within 0.2%.
6.1.2 Muons
The W µν candidate events are required to have a muon with p
T
> 20 GeV and
|η| < 2.1. If a second muon with p
T
> 10 GeV is present, the event is rejected in order to
reduce the contribution from Drell-Yan events. The fraction of signal events selected from
the simulation is F
W
= 0.462 ±0.005, with F
W
+
= 0.477 ±0.005 and F
W
= 0.441 ±0.005.
The number of selected events is 18 571, including 10 682 with positive and 7 889 with
negative muons.
The W µν signal yield is extracted from a binned likelihood ﬁt to the observed
M
T
distribution, which is taken to be the sum of diﬀerent contributions: W µν signal,
QCD background, electroweak (EWK) backgrounds, and tt. The shapes of the signal and
background components (templates) are taken from the simulation, except for the QCD
background, which is obtained from data, as described below. The normalization of the
QCD background and the W µν yield are free parameters in the ﬁt. The EWK and tt
backgrounds are normalized to the W µν yield on the basis of simulations and expected
relative cross sections.
The QCD template used in the ﬁt is obtained from a high-purity QCD sample referred
to as the inverted sample. This sample is selected by applying the same criteria as in
the signal selection except the isolation requirement, which is reversed: I
rel
comb
> 0.20. The
shape of the QCD template from the inverted sample in the data agrees well with that
obtained in the simulation. Studies of simulated QCD events show that a small bias in
the shape is induced by the isolation requirement. This bias comes from the correlation of
the isolation variable with the
P
E
T
in the event. We correct the template on the basis of
a linear relation between M
T
and I
rel
comb
. In the simulation, we obtain an excellent match
between the corrected template from the inverted sample and the actual template from
the non-inverted sample. We compare the yields obtained when ﬁtting with diﬀerent QCD
templates, namely, corrected template in the data and uncorrected templates obtained
from the inverted sample in the data and from the non-inverted sample in the simulation.
We take the maximum diﬀerence in yields as an estimate of the systematic uncertainty
from the modeling of the QCD background shape.
As in the case of electrons, the signal template receives an event-by-event correction
in bins of the W transverse momentum determined from a study of the hadronic recoil
distributions of Z µ
+
µ
events in the data.
Figure 1 (b) shows the ﬁt to the observed M
T
spectrum of the inclusive W µν sam-
ple; the ﬁt distribution describes the data well, with a p-value of 0.34 for the Kolmogorov-
10
Page 11
JHEP01(2011)080
[GeV]
T
E
0 20 40 60
number of events / 2.5 GeV
0
1
2
3
3
10×
data
ν e W
t EWK+t
QCD
CMS
= 7 TeVs
at
-1
2.9 pb(a)
[GeV]
T
M
0 20 40 60 80 100 120
number of events / 4 GeV
0
0.5
1
1.5
3
10×
data
νµ W
t EWK+t
QCD
CMS
= 7 TeVs
at
-1
2.9 pb(b)
Figure 1. The W signal distributions: (a) E/
T
distribution for the selected W eν sample; (b) M
T
distributions for the selected W µν sample. The points represent the data. Superimposed are
the results of the maximum likelihood ﬁts for signal plus backgrounds, in yellow; all backgrounds,
in orange; QCD backgrounds, in violet. The dashed lines represent the signal distributions.
Smirnov test. The inclusive yield is N
W
= 12 257 ± 111. The charge-speciﬁc yields are
N
W
+
= 7 445 ± 87 and N
W
= 4 812 ± 69. Here, we ﬁt simultaneously for the inclusive
yield N
W
and the ratio N
W
+
/N
W
so that, by construction, N
W
= N
W
+
+ N
W
.
6.2 Z boson selection
To identify Z 
+

decays, a pair of identiﬁed leptons is required, with dilepton in-
variant mass in the range 60 < M

+

< 120 GeV. Backgrounds are very low, including
backgrounds from QCD processes. In the Z e
+
e
channel, the yield is obtained by count-
ing the number of selected events and making a small correction for backgrounds. In the
Z µ
+
µ
channel, yield and lepton eﬃciencies are ﬁtted simultaneously. No correction is
made for γ
exchange.
6.2.1 Electrons
The Z e
+
e
candidate events are required to have two electrons satisfying the same
selection criteria as the electrons selected in the W eν sample. Both electrons must
have an ECAL cluster with E
T
> 20 GeV in the ECAL ﬁducial volume. The fraction of
signal events selected in the simulation is F
Z
= 0.285 ± 0.005.
The Z mass peaks in the data exhibit small shifts, on the order of 1 to 2%, with respect
to the simulated distributions. From these shifts, we determine ECAL cluster energy scale
correction factors of 1.015 ± 0.002 and 1.033 ± 0.005 for barrel and endcap electrons,
respectively. The uncertainties on these correction factors are propagated as systematic
uncertainties on the yield. Applying these corrections to electron candidates in the data,
we select 677 events, with the dielectron invariant mass shown in ﬁgure 2 (a), along with
11
Page 12
JHEP01(2011)080
the predicted distribution, after the energy scale correction of the data and normalization
of the simulation.
Three techniques are used to estimate the background originating from events in which
one or both electron candidates are misidentiﬁed jets or photons. The ﬁrst method mea-
sures the probability of jets to be misidentiﬁed as electron from a large sample of events
selected with a jet trigger. The second method is based on counting events with elec-
tron candidates of same electric charge, after taking into account the probability of wrong
charge assignment. The third method uses a ﬁt to the track isolation variable to extract
the fractions of signal and QCD background. The three methods are independent and give
consistent results. Combining them, we estimate the QCD background in our sample to
be 0.4 ±0.4 events. Backgrounds from other processes with true electrons (Z τ
+
τ
, di-
bosons, and tt) are estimated from the simulation. The total background in the Z e
+
e
sample is estimated to be 2.8 ± 0.4 events.
6.2.2 Muons
In the Z µ
+
µ
channel, event yields and muon selection eﬃciencies are extracted from
a simultaneous ﬁt. The tag-and-probe sample is built from events containing two muon
candidates with p
T
> 20 GeV and |η| < 2.1. The tag muon satisﬁes the identiﬁcation and
isolation criteria used in the W µν selection; the probe muon is selected as either a
tracker or global muon. The tag-and-probe sample is divided into ﬁve mutually-exclusive
samples of events, according to the quality of the probe muon, as described above. In the
signal sample, the probe muon fulﬁlls all the identiﬁcation and isolation criteria, and at
least one of the muon candidates satisﬁes the trigger requirement. This sample contains 913
events. The distribution of the dimuon invariant mass is shown in ﬁgure 2 (b), compared
with distributions based on simulations normalized to the measured cross section.
The background is negligible in the signal sample. The mass spectrum in that sample
is used as a model for the signal shapes in other samples, where backgrounds are modeled
by products of a polynomial and an exponential function. The yields and eﬃciencies are
extracted from a joint binned maximum likelihood ﬁt to all mass spectra. The Z µ
+
µ
signal yield is already corrected for eﬃciency by virtue of the parameterization used in
the ﬁt; the corrected yield is N
Z
Z
= 1 050 ± 35 events and the signal acceptance is
A
Z
= 0.398 ± 0.005.
The muon momentum scale and resolution are veriﬁed in diﬀerent p
T
regions from the
study of lower-mass dimuon resonances (J/ψ and Υ), the cosmic-ray muon endpoint [20],
the matching of tracker muons and global muons, the W transverse momentum spectrum,
and the Z mass lineshape. From the observed agreements with the simulation, we ﬁnd that
no momentum corrections are needed.
The QCD multijet background in the signal sample is estimated to be 0.048 ± 0.002
event. Including or neglecting this background in the simultaneous ﬁt changes the yield by
0.2%, which we take as a systematic uncertainty on the background. A further systematic
uncertainty stems from the modeling of the shapes of signal and background; we estimate
this uncertainty to be 1%. The contributions from other backgrounds (Z τ
+
τ
, dibosons,
and tt) are small, according to simulations, and amount to 3.5 ± 0.2 events in total.
12
Page 13
JHEP01(2011)080
) [GeV]
-
e
+
M(e
60 80 100 120
number of events / 2 GeV
0
50
100
150
data
-
e
+
e Z
CMS
= 7 TeVs
at
-1
2.9 pb(a)
) [GeV]
-
µ
+
µM(
60 80 100 120
number of events / 2 GeV
0
100
200
300
data
-
µ
+
µ Z
CMS
= 7 TeVs
at
-1
2.9 pb(b)
Figure 2. The Z signal distributions: (a) dielectron mass spectrum for the selected Z e
+
e
sample; (b) dimuon mass spectrum for the selected Z µ
+
µ
sample. The points represent
the data and the histograms, the simulation. Backgrounds are negligible and are not represented
in the plots.
7 Systematic uncertainties
The largest uncertainty for the cross section measurement comes from the estimation of the
integrated luminosity. CMS uses signals from the forward hadronic (HF) calorimeters to
measure the instantaneous luminosity in real time with an absolute normalization obtained
with Van der Meer scans, from which we infer the size of the colliding beams and thereby
the luminosity, with minimal reliance on simulations [21]. The total luminosity uncertainty
amounts to 11% and is expected to diminish in the future.
Aside from luminosity, the main source of experimental uncertainty in our measure-
ments comes from the propagation of uncertainties on the eﬃciency ratios obtained by the
tag-and-probe method. This amounts to 3.9% and 1.4% for W eν and W µν analy-
ses, respectively. In the Z e
+
e
channel, we conservatively neglect the anti-correlation
between eﬃciencies and yields, which are extracted separately from the same sample; the
eﬃciency uncertainties amount to 5.9%. In the Z µ
+
µ
analysis, yield and eﬃciencies
are determined simultaneously, and therefore the eﬃciency uncertainties are part of the
statistical error from the ﬁt. Corrections of 0.5% and 1.0% are applied to the W µν and
Z µ
+
µ
event yields, respectively, to account for a loss of events due to barrel muon
triggers that failed timing requirements and for which the tracker data were not read out
properly. These corrections are determined from the data, and lead to a 0.5% systematic
uncertainty in both channels.
Sub-dominant systematic uncertainties come from the lepton energy/momentum scale
and resolution. Electron energy correction factors are approximately 1% to 3% in the barrel
and endcap calorimeters, from the observed shift of the Z mass peak. In the W eν
13
Page 14
JHEP01(2011)080
case, the electron energy scale has an impact on the E/
T
distribution for the signal; we
apply typical energy scale corrections to electrons in the simulation (before E
T
threshold
selection) and recompute the E/
T
. From variations of the signal yields from the ﬁt, we assign
a 2.0% systematic uncertainty to the W eν cross section. In the Z e
+
e
analysis,
the E
T
threshold and mass window requirements lead to a 0.6% uncertainty due to the
energy scale uncertainty. Studies of the Z µ
+
µ
line shape show that data/simulation
momentum scale shifts larger than 0.4% can be excluded, which imply small uncertainties
of 0.3% in the W µν analysis, and 0.2% in the Z µ
+
µ
analysis.
The E/
T
energy scale is aﬀected by our limited knowledge of the intrinsic hadronic recoil
response. We observe minor discrepancies when comparing hadronic recoil distributions in
data and simulation, and assign an uncertainty of 1.8% in the W eν analysis due to the
E/
T
energy scale. In the muon channel, this uncertainty is estimated by reﬁtting the M
T
distribution with the signal shape predicted by the simulation. The variation in the signal
yield with respect to the reference result is 0.4%.
In the W eν channel, the systematic uncertainty due to background subtraction
is obtained by comparing ﬁts to various background-dominated distributions: the sample
selected with inverted identiﬁcation criteria in the data, and the samples selected with and
without inverted identiﬁcation criteria in the QCD simulation. We quantify the diﬀerences
in the tails of these three distributions by an extra parameter in our analytical background
function. Using a set of pseudo-experiments to estimate the impact of such diﬀerences on
the results of the nominal ﬁt, we evaluate the uncertainty due to background subtraction
in the W eν analysis to be 1.3%. In the W µν analysis the QCD background shape
is tested by reﬁtting the M
T
spectrum with the background shape ﬁxed to QCD-enriched
sample expectations. This choice provides the maximum variation (2.0%) in the signal
yield with respect to the reference ﬁt.
The background from fake electrons in the Z e
+
e
sample is estimated from data,
as described in section 6.2.1. The uncertainty on this background is 0.1% of the total
Z yield. The expected background to Z µ
+
µ
is 0.5%, with an uncertainty of 0.2%.
Further uncertainty arises from the ﬁt model of the backgrounds in subsamples where
one of the muon candidates fails the selection. We estimate this uncertainty to be 1%.
Uncertainties from the normalization of electroweak and tt backgrounds are negligible in
both W and Z channels.
Theoretical uncertainties in the W cross section measurement aﬀect the estima-
tion of the acceptance. The Monte Carlo estimates are based on simulations that use a next-
to-leading order (NLO) generator (POWHEG) as input. Events are re-weighted at gener-
ator level according to diﬀerent PDF set assumptions (CTEQ6.6 [22], MSTW08NLO [23],
NNPDF2.0 [24]). The observed variations in the acceptance are less than 1.2%. Remaining
theoretical uncertainties associated with the treatment of initial-state radiation, ﬁnal-state
QED radiation, missing electroweak eﬀects, and renormalization and factorization scale
assumptions amount to approximately 1.5%.
Table 1 shows a summary of the systematic uncertainties for the W and Z cross sec-
tion measurements.
14
Page 15
JHEP01(2011)080
Source W eν W µν Z e
+
e
Z µ
+
µ
Lepton reconstruction & identiﬁcation 3.9 1.5 5.9 0.5
Momentum scale & resolution 2.0 0.3 0.6 0.2
E/
T
scale & resolution 1.8 0.4 n/a n/a
Background subtraction/modeling 1.3 2.0 0.1 0.2 1.0
PDF uncertainty for acceptance 0.8 1.1 1.1 1.2
Other theoretical uncertainties 1.3 1.4 1.3 1.6
Total 5.1 3.1 6.2 2.3
Table 1. Systematic uncertainties of the four cross section measurements, in percent. “n/a” means
the source does not apply. A common luminosity uncertainty of 11% applies to all channels.
8 Results
All theoretical predictions quoted in this section are computed at the next-to-next-to-
leading order (NNLO) with the program FEWZ [25, 26] and the MSTW08 set of PDFs.
The uncertainties correspond to 68% conﬁdence levels obtained by combining the PDF and
α
S
errors from the MSTW08, CTEQ6.6, and NNPDF2.0 groups and adding the NNLO
scale uncertainties in quadrature, as prescribed by the PDF4LHC working group [27].
For all measurements we present results for electron and muon channels separately
and, assuming lepton universality in W and Z decays, for the combined lepton channel.
The electron and muon channels are combined by maximizing a likelihood that accounts
for the individual statistical and systematic uncertainties and their correlations. For cross
section measurements, correlations are only numerically relevant for theoretical uncertain-
ties, including the PDF uncertainties on the acceptance values. For cross section ratio
measurements, the correlations of lepton eﬃciencies are taken into account in each lepton
channel, with other experimental uncertainties assumed uncorrelated; in the combination
of lepton channels, we assume fully-correlated uncertainty for the acceptance factor, with
other uncertainties assumed uncorrelated.
The measured cross sections times branching ratio for W, W
+
, W
and Z production
are reported in table 2, for the electron, muon, and combined lepton ( = e or µ) channels,
along with predictions at the NNLO in QCD. The reported Z boson production cross
sections pertain to the invariant mass range 60 < M

+

< 120 GeV, and are corrected for
the ﬁducial and kinematic acceptance but not for γ
exchange.
The ratio of cross sections for W and Z production is
R
W/Z
=
[ σ × B](W)
[ σ × B](Z)
=
N
W
N
Z
ρ
Z
ρ
W
F
Z
F
W
=
N
W
N
Z
ε
Z
ε
W
A
Z
A
W
,
where A
W
and A
Z
are the ﬁducial and kinematic acceptances for W and Z
+

,
respectively, and ε
W
and ε
Z
are the selection eﬃciencies for W and Z signal events in
the acceptance. The uncertainty from A
W
/A
Z
is determined from Monte Carlo generator
studies to be approximately 1%.
15
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JHEP01(2011)080
Channel σ × B (nb) NNLO (nb)
W
eν 10.04 ± 0.10 (stat.) ± 0.52 (syst.) ± 1.10 (lumi.)
10.44 ± 0.52µν 9.92 ± 0.09 (stat.) ± 0.31 (syst.) ± 1.09 (lumi.)
9.95 ± 0.07 (stat.) ± 0.28 (syst.) ± 1.09 (lumi.)
W
+
e
+
ν 5.93 ± 0.07 (stat.) ± 0.36 (syst.) ± 0.65 (lumi.)
6.15 ± 0.29µ
+
ν 5.84 ± 0.07 (stat.) ± 0.18 (syst.) ± 0.64 (lumi.)

+
ν 5.86 ± 0.06 (stat.) ± 0.17 (syst.) ± 0.64 (lumi.)
W
e
ν 4.14 ± 0.06 (stat.) ± 0.25 (syst.) ± 0.45 (lumi.)
4.29 ± 0.23µ
ν 4.08 ± 0.06 (stat.) ± 0.15 (syst.) ± 0.45 (lumi.)

ν 4.09 ± 0.05 (stat.) ± 0.14 (syst.) ± 0.45 (lumi.)
Z
e
+
e
0.960 ± 0.037 (stat.) ± 0.059 (syst.) ± 0.106 (lumi.)
0.972 ± 0.042µ
+
µ
0.924 ± 0.031 (stat.) ± 0.022 (syst.) ± 0.102 (lumi.)

+

0.931 ± 0.026 (stat.) ± 0.023 (syst.) ± 0.102 (lumi.)
Table 2. Summary of production cross section times branching ratio measurements and their
theoretical predictions.
Quantity Ratio NNLO
R
W/Z
e 10.47 ± 0.42 (stat.) ± 0.47 (syst.)
10.74 ± 0.04µ 10.74 ± 0.37 (stat.) ± 0.33 (syst.)
10.64 ± 0.28 (stat.) ± 0.29 (syst.)
R
+/
e 1.434 ± 0.028 (stat.) ± 0.082 (syst.)
1.43 ± 0.04µ 1.433 ± 0.026 (stat.) ± 0.054 (syst.)
 1.433 ± 0.020 (stat.) ± 0.050 (syst.)
Table 3. Summary of the cross section ratio measurements and their theoretical predictions.
The ratio of cross sections for W
+
and W
production is
R
+/
=
[ σ × B](W
+
)
[ σ × B](W
)
=
N
W
+
N
W
ρ
W
ρ
W
+
F
W
F
W
+
=
N
W
+
N
W
ε
W
ε
W
+
A
W
A
W
+
,
where A
W
+
and A
W
are the ﬁducial and kinematic acceptances for W
+

+
ν and
W

ν, respectively, and ε
W
+
and ε
W
+
are the selection eﬃciencies for W
+
and
W
signal events in the acceptance. The uncertainty from A
W
+
/A
W
is determined from
Monte Carlo generator studies to be approximately 2%.
The measurements of the R
W/Z
and R
+/
cross section ratios are reported in table 3,
along with their theoretical predictions.
We also report the cross sections as measured within the ﬁducial and kinematic ac-
ceptance, thereby eliminating the PDF uncertainties from the results. In eﬀect, these un-
certainties are transferred to the theoretical predictions, allowing for a cleaner separation
of experimental and theoretical uncertainties. For each channel the ﬁducial and kinematic
acceptance is deﬁned by the fraction of events with lepton p
T
greater than 20 GeV after
ﬁnal-state QED radiation, and with pseudorapidity in the range |η| < 2.5 for electrons and
|η| < 2.1 for muons.
16
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JHEP01(2011)080
Channel σ × B in acceptance A (nb) A
W eν 6.04 ± 0.06 (stat.) ± 0.31 (syst.) ± 0.66 (lumi.) 0.601 ± 0.005
W
+
e
+
ν 3.69 ± 0.05 (stat.) ± 0.22 (syst.) ± 0.41 (lumi.) 0.622 ± 0.006 p
T
> 20 GeV
W
e
ν 2.36 ± 0.04 (stat.) ± 0.14 (syst.) ± 0.26 (lumi.) 0.571 ± 0.009 |η| < 2.5
Z e
+
e
0.460 ± 0.018 (stat.) ± 0.028 (syst.) ± 0.051 (lumi.) 0.479 ± 0.005
W µν 5.21 ± 0.05 (stat.) ± 0.15 (syst.) ± 0.57 (lumi.) 0.525 ± 0.006
W
+
µ
+
ν 3.16 ± 0.04 (stat.) ± 0.10 (syst.) ± 0.35 (lumi.) 0.541 ± 0.006 p
T
> 20 GeV
W
µ
ν 2.05 ± 0.03 (stat.) ± 0.06 (syst.) ± 0.22 (lumi.) 0.502 ± 0.006 |η| < 2.1
Z µ
+
µ
0.368 ± 0.012 (stat.) ± 0.007 (syst.) ± 0.040 (lumi.) 0.398 ± 0.005
Table 4. Summary of production cross section measurements in restricted ﬁducial and kinematic
acceptances. The p
T
and |η| criteria restricting the acceptance for electrons and muons, and the
resulting acceptance values, are also given.
Quantity Ratio (CMS/Theory) Lumi. Uncertainty
σ × B
W 0.953 ± 0.028 (exp.) ± 0.048 (theo.)
±0.11
W
+
0.953 ± 0.029 (exp.) ± 0.045 (theo.)
W
0.954 ± 0.034 (exp.) ± 0.051 (theo.)
Z 0.960 ± 0.036 (exp.) ± 0.040 (theo.)
R
W/Z
0.990 ± 0.038 (exp.) ± 0.004 (theo.)
nil
R
+/
1.002 ± 0.038 (exp.) ± 0.028 (theo.)
Table 5. The ratios of the W and Z cross section times branching ratio measurements to their
theoretical predictions, and of the measured cross section ratios to their theoretical predictions.
The uncertainty in the integrated luminosity cancels out in the latter ratios.
The measurements of cross sections in restricted acceptance regions are reported in ta-
ble 4, along with the acceptance values, computed using the POWHEG generator, which is
complete to the NLO and interfaced with PYTHIA for ﬁnal-state radiation (FSR). Accep-
tance values from FEWZ, which is complete to the NNLO but lacks FSR, are compatible
with those from POWHEG. The quoted errors on the acceptances are due to the PDF un-
certainties. Since the acceptances are diﬀerent for electrons and muons, these cross section
values cannot be combined. The diﬀerence in acceptance for W
+
and W
, larger in the
electron channel, is a consequence of the pseudorapidity distributions of
+
and `
from
boson decays, which reﬂect not only the diﬀerent x distributions of quarks and antiquarks
in the proton, but also a distinction between valence and sea quarks at a given x due to
the V–A interaction.
Summaries of the measurements are given in ﬁgures 3, 4, 5, and 6, illustrating the
consistency of the measurements in the electron and muon channels, as well as the con-
ﬁrmation of theoretical predictions computed at the NNLO in QCD with state-of-the-art
PDF sets. For each reported measurement, the statistical error is represented in black and
the total experimental uncertainty, obtained by adding in quadrature the statistical and
systematic uncertainties, in dark blue. For the cross section measurements, the luminosity
uncertainty is added linearly to the experimental uncertainty, and is represented in green.
The dark-yellow vertical line represents the theoretical prediction, and the light-yellow
vertical band is the theoretical uncertainty, interpreted as a 68% conﬁdence interval, as
described above.
17
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JHEP01(2011)080
) [nb]ν l B( W × WX ) ( pp σ
0 2 4 6 8 10 12
= 7 TeVs at
-1
2.9 pbCMS
[with PDF4LHC 68% CL uncertainty]
NNLO, FEWZ+MSTW08 prediction
0.52 nb± 10.44
ν eW
nb
lumi
1.10±
syst
0.52±
stat
0.10±10.04
νµ W
nb
lumi
1.09±
syst
0.31±
stat
0.09±9.92
(combined) ν lW
nb
lumi
1.09±
syst
0.28±
stat
0.07±9.95
Figure 3. Summary of the W boson production cross section times branching ratio measurements.
ll ) [nb] B( Z × ZX ) ( pp σ
0 0.2 0.4 0.6 0.8 1 1.2
= 7 TeVs at
-1
2.9 pbCMS
[with PDF4LHC 68% CL uncertainty]
NNLO, FEWZ+MSTW08 prediction, 60-120 GeV
0.04 nb± 0.97
eeZ
nb
lumi
0.11±
syst
0.06±
stat
0.04±0.96
µµ Z
nb
lumi
0.10±
syst
0.02±
stat
0.03±0.92
(combined) ll Z
nb
lumi
0.10±
syst
0.02±
stat
0.03±0.93
Figure 4. Summary of the Z boson production cross section times branching ratio measurements.
The agreement of theoretical predictions with our measurements is quantiﬁed in table 5
and illustrated in ﬁgure 7. There, the experimental uncertainty (”exp”) is computed as the
sum in quadrature of the statistical uncertainty and the systematic uncertainties aside from
the theoretical uncertainties associated with the acceptance. The theoretical uncertainty
(”theo”) is computed by adding in quadrature the variations of the central value when the
renormalization scale is varied, and the PDF uncertainty. Figure 8 (a) represents the CMS
measurements together with measurements at lower-energy hadron colliders. The increase
of the W and Z cross sections with energy is conﬁrmed. Figure 8 (b) shows the good
agreement between CMS and ATLAS measurements in pp collisions at
s = 7 TeV.
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JHEP01(2011)080
B ](Z)× σ B ](W) / [ × σ = [
W/Z
R
0 2 4 6 8 10 12 14
= 7 TeVs at
-1
2.9 pbCMS
[with PDF4LHC 68% CL uncertainty]
NNLO, FEWZ+MSTW08 prediction
0.04 ±10.74
ee, Z ν eW
syst
0.47±
stat
0.42±10.47
µµ , Z νµ W
syst
0.33±
stat
0.37±10.74
(combined) ll , Z ν lW
syst
0.29±
stat
0.28±10.64
Figure 5. Summary of the R
W/Z
cross section ratio measurements.
)
-
B ](W× σ) / [
+
B ](W× σ = [
+/-
R
0 0.5 1 1.5
= 7 TeVs at
-1
2.9 pbCMS
[with PDF4LHC 68% CL uncertainty]
NNLO, FEWZ+MSTW08 prediction
0.04±1.43
ν eW
syst
0.08±
stat
0.03±1.43
νµ W
syst
0.05±
stat
0.03±1.43
(combined) ν lW
syst
0.05±
stat
0.02±1.43
Figure 6. Summary of the R
+/
cross section ratio measurements.
9 Conclusions
We have performed measurements of inclusive W and Z boson production cross sections in
pp collisions at
s = 7 TeV using (2.88±0.32) pb
1
of data recorded by the CMS detector
at the LHC. We ﬁnd internal consistency between measurements in the electron and muon
channels and report their combination. We also report ratios of W to Z and W
+
to W
production cross sections. The theoretical predictions agree with our measurements, as
illustrated in ﬁgure 7.
19
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JHEP01(2011)080
Ratio (CMS/Theory)
0.6 0.8 1 1.2 1.4
= 7 TeVs at
-1
2.9 pbCMS
B ( W )× σ
theo.
0.048±
exp.
0.028±0.953
)
+
B ( W× σ
theo.
0.045±
exp.
0.029±0.953
)
-
B ( W× σ
theo.
0.051±
exp.
0.034±0.954
B ( Z )× σ
theo.
0.040±
exp.
0.036±0.960
W/Z
R
theo.
0.004±
exp.
0.038±0.990
+/-
R
theo.
0.028±
exp.
0.038±1.002
lumi. uncertainty: 11%±
Figure 7. Summary of the ratios of the CMS measurements to their theoretical predictions.
The luminosity uncertainty (±11%), which aﬀects only the cross section times branching ratio
measurements, is represented by a shaded area.
Collider Energy [TeV]
B [nb]× σ
-1
10
1
10
-1
CMS, 2.9 pb
CDF Run II
D0 Run I
UA2
UA1
Theory: NNLO, FEWZ and MSTW08 PDFs
pp
pp
0.5 1 2
5 7
10 20
W
+
W
-
W
Z
(a)
7 TeV
0.5
1
2
3
4
5
7
10
20
B [nb]× σ
ATLAS CMS
-1
0.34 pb
-1
2.9 pb
W
Z
-
W
+
W
lumi.
11%±
(b)
Figure 8. (a) Measurements of inclusive W and Z production cross sections times branching ratio
as a function of center-of-mass energy for CMS and experiments at lower-energy colliders. The lines
are the NNLO theory predictions. (b) Comparison of the ATLAS and CMS W and Z production
cross sections times branching ratios. The error bars are the statistical and systematic uncertainties
added in quadrature, except for the uncertainty on the integrated luminosity, whose value is shown
separately as a band.
20
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JHEP01(2011)080
Aside from the luminosity uncertainty, which cancels in the ratios, the systematic
uncertainties are comparable to the statistical ones in our measurements. The experimental
uncertainties are smaller than those on the theoretical predictions; they are typically less
than 4%. This suggests that the inclusive measurements of W and Z cross sections can
potentially be used to normalize the LHC luminosity at the 5% level or better [28]. As
most of the systematic uncertainties are statistical in nature, they will decrease with larger
data samples, and also beneﬁt from an improved understanding of the CMS detector.
Acknowledgments
We wish to congratulate our colleagues in the CERN accelerator departments for the ex-
cellent performance of the LHC machine. We thank the technical and administrative staﬀ
at CERN and other CMS institutes. This work was supported by the Austrian Federal
Ministry of Science and Research; the Belgium Fonds de la Recherche Scientiﬁque, and
Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding Agencies (CNPq, CAPES,
FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chi-
nese Academy of Sciences, Ministry of Science and Technology, and National Natural Sci-
ence Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian
Ministry of Science, Education and Sport; the Research Promotion Foundation, Cyprus;
the Estonian Academy of Sciences and NICPB; the Academy of Finland, Finnish Ministry
of Education, and Helsinki Institute of Physics; the Institut National de Ph