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 = 7TeV
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−1of 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 → ?ν) = 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
2 The CMS detector2
3 Lepton reconstruction and identification
4 Missing transverse energy5
5 Lepton selection efficiencies
6 Event selection and signal extraction
6.1W boson selection
6.2Z boson selection
7Systematic uncertainties 13
The CMS collaboration24
The inclusive production of W and Z bosons is an important benchmark process at hadron
colliders. Measurements of σ (pp → WX)×B(W → ?ν) 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 [3–5] pp colliders. We report the extension of these measurements
to significantly higher energies, namely, with pp collisions at a center-of-mass energy of
7TeV 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 –
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. In this article, “Z boson production” includes γ∗
exchange within the mass range 60 to 120GeV.
High-pTelectrons and muons are used for selecting W → ?ν and Z → ?+?−candidate
events. In addition to a high-pTlepton, 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 /Treconstruction 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/εsimderived
by measuring ε and εsimin the same way on data and simulations, respectively. In effect,
we replace the product A × ε by the product F × ρ, where F = A × εsimis 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
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(tanθ/2).
– 2 –
The inner tracker measures charged particle trajectories in the pseudorapidity range
|η| < 2.5. It consists of 1440 silicon pixel and 15148 silicon strip detector modules. It
provides an impact parameter resolution of ∼ 15µm and a transverse momentum (pT)
resolution of about 1% for charged particles with pT≈ 40GeV.
The electromagnetic calorimeter consists of nearly 76000 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 X0of 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-pTmuon 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 pTresolution between 1 and 2% for pTvalues up to 100GeV.
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 1µs 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 .
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: Irel
objects falling within a cone ∆R =
the energy deposits and the track associated with the lepton candidate being excluded from
the sums. We also define a combined isolation variable, Irel
?(∆η)2+ (∆φ)2< 0.3 around the lepton candidate,
T, where p?
Tis the transverse momentum of the lepton candidate. The
scalar sums of transverse energy (ET) and transverse momentum (pT) are performed for
Events with high-ETelectrons are selected online when they pass a L1 trigger filter that
requires a coarse-granularity region of the ECAL to have ET> 5GeV. They subsequently
– 3 –
must pass an HLT  filter that requires an ECAL cluster with ET> 15GeV, using the
full granularity of the ECAL and ETmeasurements corrected using offline calibration .
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 
that accounts for possible energy loss due to bremsstrahlung in the tracker layers. The
energy of an electron candidate with ET> 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 Irel
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 ET> 20 GeV, and reduce the fake electron background by two orders
More details and studies of electron reconstruction and identification can be
found in ref. .
ECAL< 0.07 and Irel
HCAL< 0.025 in the endcap regions.
HCAL< 0.10 in the barrel region; Irel
trk< 0.04, Irel
ECAL< 0.05 and
Events with high-pTmuons 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 pT> 9GeV 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 χ2/Ndof< 10 for a
– 4 –
global fit containing all valid tracker and muon hits, where Ndofis 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-pTcosmic
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 Irel
More details and studies of muon reconstruction and identification can be
found in ref. .
4 Missing transverse energy
An accurate E /Tmeasurement is essential for distinguishing a W signal from QCD mul-
tijet production backgrounds. We profit from the application of the particle flow (PF)
algorithm , which provides superior E /Treconstruction 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 /Tmeasurements to miscalibrations of the calorimetry.
Anomalous noise signals can spoil the E /Tmeasurements. 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 /Tdistributions for W → ?ν events from
data and from simulation .
The E /Tis 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 /Tresolution for inclusive multijet samples and for W → ?ν
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
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 –
from imperfections in the simulation, even though the kinematic distributions of leptons
in the Z → ?+?−sample differ slightly from those in the selected W → ?ν 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
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.
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
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 –
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
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
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: ρW= 0.921 ± 0.036; and separately by charge: ρW+ = 0.917 ± 0.046 and ρW− =
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 ET> 20 GeV.
In the Z → e+e−analysis, one electron candidate is allowed to fail the trigger criteria;
the efficiency ratio is ρZ= 0.856 ± 0.050 and the corrected signal selection efficiency for
Z → e+e−events with both electron clusters in ECAL fiducial volume and ET> 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.
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 –
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 χ2and 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 ρW= 0.933 ± 0.012. There
is no significant difference between the efficiency ratios for positive and negative muons:
ρW+ = 0.935 ± 0.018 and ρW− = 0.931 ± 0.019, respectively.
6Event 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
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 [15–17], interfaced with the PYTHIA  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 
detector simulation, trigger emulation, and event reconstruction chain.
– 8 –
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 /Tand 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 /Tdistribution in the electron
channel and the MTdistribution in the muon channel, where MT=?2pTE /T(1 − cos∆φ);
momentum. QCD backgrounds are estimated from data, as explained below. According to
the simulation, W → τν makes a small relative contribution; backgrounds from Z → τ+τ−,
tt, and diboson production are negligible in both electron and muon channels.
∆φ is the angle between the missing transverse momentum and the lepton transverse
The W → eν candidate events are required to have one identified electron with an ECAL
cluster of ET > 20GeV in the ECAL fiducial volume. If a second electron candidate
satisfying looser criteria and with ET> 20GeV is present in the event, the event is rejected.
The fraction of signal events selected in the simulation is FW= 0.446±0.006, with FW+ =
0.459 ± 0.007 and FW− = 0.428 ± 0.008. The number of events selected in the data is
28601, with 15859 positive and 12742 negative electrons.
The W → eν signal is extracted from an unbinned maximum likelihood fit of the
observed E /Tdistribution 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
This function can be understood as describing fluctuations of the missing transverse mo-
mentum vector around zero due to measurement errors; the resolution term, σ0+ σ1E /T,
increases with E /Tto account for tails in the E /Tmeasurement. This function describes
well the QCD background shape in the simulation, over the full range of E /T, as well as
E /Tdistributions from signal-free samples obtained by inverting the identification or isola-
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 . In fits
to the E /Tdistributions, the free parameters are the W signal yield, the QCD background
yield, and the shape parameters σ0and σ1.
We extract the inclusive yield NWfrom a fit where the expected ratio for σW+/σW−
is assumed. It has been checked that the result was insensitive to this assumption. Fig-
ure 1 (a) shows the E /Tdistribution of the inclusive W → eν sample and the results of
f(E /T) = E /T× exp
2(σ0+ σ1E /T)2
– 9 –
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 NW= 11895 ± 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 /Tdistributions, in which the QCD background shape
parameters σ0 and σ1 are constrained to be the same for both samples. The yields are
NW+ = 7193±89 for W+→ e+ν and NW− = 4728±73 for W−→ e−ν, with a negligible
correlation. Because the two fits are independent, the relation NW= NW+ + NW− is not
exactly satisfied, but holds to within 0.2%.
The W → µν candidate events are required to have a muon with pT > 20 GeV and
|η| < 2.1. If a second muon with pT> 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 FW= 0.462±0.005, with FW+ = 0.477±0.005 and FW− = 0.441±0.005.
The number of selected events is 18571, including 10682 with positive and 7889 with
The W → µν signal yield is extracted from a binned likelihood fit to the observed
MTdistribution, 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: Irel
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?ETin the event. We correct the template on the basis of
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 MTspectrum of the inclusive W → µν sam-
ple; the fit distribution describes the data well, with a p-value of 0.34 for the Kolmogorov-
comb> 0.20. The
a linear relation between MTand Irel
comb. In the simulation, we obtain an excellent match
– 10 –
0 20 4060
number of events / 2.5 GeV
= 7 TeVs
0 204060 80 100120
number of events / 4 GeV
= 7 TeVs
Figure 1. The W signal distributions: (a) E /Tdistribution for the selected W → eν sample; (b) MT
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 NW = 12257 ± 111. The charge-specific yields are
NW+ = 7445 ± 87 and NW− = 4812 ± 69. Here, we fit simultaneously for the inclusive
yield NWand the ratio NW+/NW− so that, by construction, NW= NW+ + NW−.
Z boson selection
To identify Z → ?+?−decays, a pair of identified leptons is required, with dilepton in-
variant mass in the range 60 < M?+?− < 120GeV. 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.
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 ET> 20GeV in the ECAL fiducial volume. The fraction of
signal events selected in the simulation is FZ= 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
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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.
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 pT> 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 NZ/εZ = 1050 ± 35 events and the signal acceptance is
AZ= 0.398 ± 0.005.
The muon momentum scale and resolution are verified in different pTregions from the
study of lower-mass dimuon resonances (J/ψ and Υ), the cosmic-ray muon endpoint ,
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.
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number of events / 2 GeV
= 7 TeVs
number of events / 2 GeV
= 7 TeVs
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 . 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
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JHEP01(2011)080 Download full-text
case, the electron energy scale has an impact on the E /Tdistribution for the signal; we
apply typical energy scale corrections to electrons in the simulation (before ETthreshold
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 ETthreshold 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 /Tenergy 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 /Tenergy scale. In the muon channel, this uncertainty is estimated by refitting the MT
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 MTspectrum 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 → ?ν 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 , MSTW08NLO ,
NNPDF2.0 ). 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-
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