Eur. Phys. J. C (2015) 75:147
DOI 10.1140/epjc/s10052-015-3364-2
Regular Article - Experimental Physics
Measurements of differential and double-differential Drell–Yan
cross sections in proton–proton collisions at
√
s = 8TeV
CMS Collaboration
∗
CERN, 1211 Geneva 23, Switzerland
Received: 2 December 2014 / Accepted: 19 March 2015 / Published online: 9 April 2015
© CERN for the benefit of the CMS collaboration 2015. This article is published with open access at Springerlink.com
Abstract Measurements of the differential and double-
differential Drell–Yan cross sections in the dielectron and
dimuon channels are presented. They are based on proton–
proton collision data at
√
s = 8 TeV recorded with the
CMS detector at the LHC and corresponding to an inte-
grated luminosity of 19.7 fb
−1
. The measured inclusive cross
section in the Z peak region (60–120 GeV), obtained from
the combination of the dielectron and dimuon channels, is
1138 ± 8 (exp) ± 25 (theo) ± 30 (lumi)pb, where the statis-
tical uncertainty is negligible. The differential cross section
dσ/dm in the dilepton mass range 15–2000 GeV is measured
and corrected to the full phase space. The double-differential
cross section d
2
σ/dm d|y| is also measured over the mass
range 20 to 1500 GeV and absolute dilepton rapidity from
0 to 2.4. In addition, the ratios of the normalized differen-
tial cross sections measured at
√
s = 7 and 8 TeV are pre-
sented. These measurements are compared to the predictions
of perturbative QCD at next-to-leading and next-to-next-to-
leading (NNLO) orders using various sets of parton distri-
bution functions (PDFs). The results agree with the NNLO
theoretical predictions computed with fewz 3.1 using the
CT10 NNLO and NNPDF2.1 NNLO PDFs. The measured
double-differential cross section and ratio of normalized dif-
ferential cross sections are sufficiently precise to constrain
the proton PDFs.
1 Introduction
At hadron colliders, Drell–Yan (DY) lepton pairs are pro-
duced via γ
∗
/Z exchange in the s channel. Theoretical cal-
culations of the differential cross section dσ/dm and the
double-differentialcross section d
2
σ/dm d|y|, where m is the
dilepton invariant mass and |y| is the absolute value of the
dilepton rapidity, are well established in the standard model
(SM) up to the next-to-next-to-leading order (NNLO) in per-
turbative quantum chromodynamics (QCD) [
1–4]. The rapid-
∗
e-mail:
cms-publication-committee-chair@cern.ch
ity distributions of the gauge bosons γ
∗
/Z are sensitive to the
parton content of the proton.
The rapidity and the invariant mass of the dilepton system
produced in proton–proton collisions are related at leading
order to the longitudinal momentum fractions x
+
and x
−
carried by the two interacting partons according to the for-
mula x
±
= (m/
√
s)e
±y
. Hence, the rapidity and mass dis-
tributions are sensitive to the parton distribution functions
(PDFs) of the interacting partons. The differential cross sec-
tions are measured with respect to |y| since the rapidity dis-
tribution is symmetric about zero. The high center-of-mass
energy at the CERN LHC permits the study of DY produc-
tion in regions of the Bjorken scaling variable and evolu-
tion scale Q
2
= x
+
x
−
s that were not accessible in previous
experiments [
5–10]. The present analysis covers the ranges
0.0003 < x
±
< 1.0 and 600 < Q
2
< 750,000 GeV
2
in the
double-differential cross section measurement. The differen-
tial cross section dσ/dm is measured in an even wider range
300 < Q
2
< 3,000,000 GeV
2
.
The increase in the center-of-mass energyat the LHC from
7 to 8 TeV provides an opportunity to measure the ratios and
double-differential ratios of cross sections of various hard
processes, including the DY process. Measurements of the
DY process in proton–proton collisions depend on various
theoretical parameters such as the QCD running coupling
constant, PDFs, and renormalization and factorization scales.
The theoretical systematic uncertainties in the cross section
measurements for a given process at different center-of-mass
energies are substantial but correlated, so that the ratios of
differential cross sections normalized to the Z boson pro-
duction cross section (double ratios) can be measured very
precisely [
11].
This paper presents measurements of the DY differential
cross section dσ/dm in the mass range 15 < m < 2000 GeV,
extending the measurement reported in [
12], and of the
double-differential cross section d
2
σ/dm d|y| in the mass
range 20 < m < 1500 GeV and absolute dilepton rapidity
from 0 to 2.4. In addition, the double ratios measured at 7
and 8 TeV are presented. The measurements are based on
123
147 Page 2 of 27 Eur. Phys. J. C (2015) 75 :147
a data sample of proton–proton collisions with a center-of-
mass energy
√
s = 8 TeV, collected with the CMS detector
and corresponding to an integrated luminosity of 19.7 fb
−1
.
Integrated luminosities of 4.8 fb
−1
(dielectron) and 4.5 fb
−1
(dimuon) at
√
s = 7 TeV are used for the double ratio mea-
surements.
Imperfect knowledge of PDFs [
13,14] is the dominant
source of theoretical systematic uncertainties in the DY cross
section predictions at low mass. The PDF uncertainty is
largerthan the achievable experimental precision, making the
double-differential cross section and the double ratio mea-
surements in bins of rapidity an effective input for PDF con-
straints. The inclusion of DY cross section and double ratio
data in PDF fits is expected to provide substantial constraints
for the strange quark and the light sea quark PDFs in the
small Bjorken x region (0.001 < x < 0.1).
The DY differential cross section has been measured by
the CDF, D0, ATLAS, and CMS experiments [
12,15–19].
The current knowledge of the PDFs and the importance of the
LHC measurements are reviewed in [
20,21]. Measuring the
DY differential cross section dσ/dm is important for various
LHC physics analyses. DY events pose a major source of
background for processes such as top quark pair production,
diboson production, and Higgs measurements with lepton
final states, as well as for searches for new physics beyond the
SM, such as the production of high-mass dilepton resonances.
The differential cross sections are first measured sep-
arately for both lepton flavors and found to agree. The
combined cross section measurement is then compared to
the NNLO QCD predictions computed with fewz 3.1 [
22]
using the CT10 NNLO PDF. The d
2
σ/dm d|y| measure-
ment is compared to the NNLO theoretical predictions com-
puted with fewz 3.1 using the CT10 and NNPDF2.1 NNLO
PDFs [
23,24].
2 CMS detector
The central feature of the CMS detector is a superconducting
solenoid of 6 m internal diameter and 13m length, providing
a magnetic field of 3.8 T. Within the field volume are a silicon
tracker, a crystal electromagnetic calorimeter (ECAL), and
a brass/scintillator hadron calorimeter (HCAL). The tracker
is composed of a pixel detector and a silicon strip tracker,
which are used to measure charged-particle trajectories and
cover the full azimuthal angle and the pseudorapidity interval
|η| < 2.5.
Muons are detected with four planes of gas-ionization
detectors. These muon detectors are installed outside the
solenoid and sandwiched between steel layers, which serve
both as hadron absorbers and as a return yokefor the magnetic
field flux. They are made using three technologies: drift tubes,
cathode strip chambers, and resistive-plate chambers. Muons
are measured in the pseudorapidity window |η| < 2.4. Elec-
trons are detected using the energy deposition in the ECAL,
which consists of nearly 76,000 lead tungstate crystals that
are distributed in the barrel region (|η| < 1.479) and two
endcap (1.479 < |η| < 3) regions.
The CMS experiment uses a two-level trigger system. The
level-1 trigger, composed of custom processing hardware,
selects events of interest at an output rate of 100kHz using
information from the calorimeters and muon detectors [
25].
The high-level trigger (HLT) is software based and further
decreases the event collection rate to a few hundred hertz
by using the full event information, including that from the
tracker [
26]. A more detailed description of the CMS detec-
tor, together with a definition of the coordinate system used
and the relevant kinematic variables, can be found in [
27].
3 Simulated samples
Several simulated samples are used for determining efficien-
cies, acceptances, and backgrounds from processes that result
in two leptons, and for the determination of systematic uncer-
tainties. The DY signal samples with e
+
e
−
and μ
+
μ
−
final
states are generated with the next-to-leading (NLO) genera-
tor powheg [
28–31] interfaced with the pythia v6.4.24 [32]
parton shower generator. pythia is used to model QED final-
state radiation (FSR).
The powheg simulated sample is based on NLO calcula-
tions, and a correction is applied to take into account higher-
order QCD and electroweak (EW) effects.Thecorrection fac-
tors binned in dilepton rapidity y and transverse momentum
p
T
are determined in each invariant-mass bin to be the ratio
of the double-differential cross sections calculated at NNLO
QCD and NLO EW with fewz 3.1 and at NLO with powheg,
as described in [
12]. The corresponding higher-order effects
depend on the dilepton kinematic variables. Higher-order
EW corrections are small in comparison to FSR corrections.
They increase for invariant masses in the TeV region [
33], but
are insignificant compared to the experimental precision for
the whole mass range under study. The NNLO QCD effects
are most important in the low-mass region. The effect of the
correction factors on the acceptance ranges up to 50 % in the
low-mass region (below 40 GeV), but is almost negligible in
the high-mass region (above 200 GeV).
The main SM background processes are simulated with
powheg (DY → τ
+
τ
−
, single top quark) and with Mad-
Graph [
34](tt, diboson eventsWW/WZ/ZZ). Both powheg
and MadGraph are interfaced with the tauola pack-
age [
35], which handles decays of τ leptons. The normal-
ization of the t
t sample is set to the NNLO cross section of
245.8pb [
36]. Multijet QCD background eventsare produced
with pythia.
All generated events are processed through a detailed sim-
ulation of the CMS detector based on Geant4 [37] and are
123
Eur. Phys. J. C (2015) 75 :147 Page 3 of 27 147
reconstructed using the same algorithms used for the data.
The proton structure is defined using the CT10 [
23]PDFs.
The simulation includes the effects of multiple interactions
per bunch crossing [
38] (pileup) with the simulated distribu-
tion of the number of interactions per LHC beam crossing
corrected to match that observed in data.
4 Object reconstruction and event selection
The events used in the analysis are selected with a dielec-
tron or a dimuon trigger. Dielectron events are triggered
by the presence of two electron candidates that pass loose
requirements on the electron quality and isolation with a
minimum transverse momentum p
T
of 17 GeV for one of
the electrons and 8 GeV for the other. The dimuon trigger
requires one muon with p
T
> 17 GeV and a second muon
with p
T
> 8GeV.
The offline reconstruction of the electrons begins with the
clustering of energy depositions in the ECAL. The energy
clusters are then matched to the electron tracks. Electrons are
identified by means of shower shape variables. Each electron
is required to be consistent with originating from the primary
vertex in the event. Energetic photons produced in a pp colli-
sion may interact with the detector material and convert into
an electron–positron pair. The electrons or positrons originat-
ing from such photon conversions are suppressed by requir-
ing that there be no more than one missing tracker hit between
the primary vertex and the first hit on the reconstructed track
matched to the electron; candidates are also rejected if they
form a pair with a nearby track that is consistent with a con-
version. Additional details on electron reconstruction and
identification can be found in [
39–42]. No charge require-
ments are imposed on the electron pairs to avoid inefficiency
due to nonnegligible charge misidentification.
At the offline muon reconstruction stage, the data from
the muon detectors are matched and fitted to data from the
silicon tracker to form muon candidates. The muon candi-
dates are required to pass the standard CMS muon iden-
tification and track quality criteria [
43]. To suppress the
background contributions due to muons originating from
heavy-quark decays and nonprompt muons from hadron
decays, both muons are required to be isolated from other par-
ticles. Requirements on the impact parameter and the opening
angle between the two muons are further imposed to reject
cosmic ray muons. In order to reject muons from light-meson
decays, a common vertex for the two muons is required.
More details on muon reconstruction and identification can
be found in [
12] and [43]. Events are selected for further
analysis if they contain oppositely charged muon pairs meet-
ing the above requirements. The candidate with the highest
χ
2
probability from a kinematic fit to the dimuon vertex is
selected.
Electron and muon isolation criteria are based on measur-
ing the sum of energy depositions associated with photons
and charged and neutral hadrons reconstructed and identi-
fied by means of the CMS particle-flow algorithm [
44–47].
Isolation sums are evaluated in a circular region of the (η,φ)
plane around the lepton candidate with R < 0.3 (where
R =
(η)
2
+ (φ)
2
), and are corrected for the contri-
bution from pileup.
Each lepton is required to be within the geometrical accep-
tance of |η| < 2.4. The leading lepton in the event is required
to have p
T
> 20 GeV and the trailing lepton p
T
> 10 GeV,
which corresponds to the plateau of the trigger efficiency.
Both lepton candidates in each event used in the offline anal-
ysis are required to match HLT trigger objects.
After event selection, the analysis follows a series of
steps. First, backgrounds are estimated. Next, the observed
background-subtracted yield is unfolded to correct for the
effects of the migration of events among bins of mass and
rapidity due to the detector resolution. The acceptance and
efficiency corrections are then applied. Finally, the migration
of events due to FSR is corrected. Systematic uncertainties
associated with each of the analysis steps are evaluated.
5 Background estimation
The major background contributions in the dielectron chan-
nel arise from τ
+
τ
−
and t
t processes in the low-mass region
and from QCD events with multiple jets at high invariant
mass. The background composition is somewhat different in
the dimuon final state. Multijet events and DY production of
τ
+
τ
−
pairs are the dominant sources of background in the
dimuon channel at low invariant mass and in the region just
below the Z peak. Diboson and t
t production followed by
leptonic decays are the dominant sources of background at
high invariant mass. Lepton pair production in γγ-initiated
processes, where both initial-state protons radiate a photon,
is significant at high mass. The contribution from this chan-
nel is treated as an irreducible background and is estimated
with fewz 3.1 [
48]. To correct for this background, a bin-
by-bin ratio of the DY cross sections with and without the
photon-induced contribution is calculated. This bin-by-bin
correction is applied after the mass resolution unfolding step,
whereas corrections for other background for which we have
simulated events are corrected before. This background cor-
rection is negligible at low mass and in the Z peak region,
rising to approximately 20% in the highest mass bin.
In the dielectron channel, the QCD multijet background
is estimated with a data sample collected with the trig-
ger requirement of a single electromagnetic cluster in the
event. Non-QCD events, such as DY, are removed from
the data sample using event selection and event subtraction
based on simulation, leaving a sample of QCD events with
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147 Page 4 of 27 Eur. Phys. J. C (2015) 75 :147
Entries per bin
1
10
2
10
3
10
4
10
5
10
6
10
7
10
data
ee→*/Zγ
ττ→
*/Zγ
EW
Wtt+Wt+ t
QCD
CMS
(8 TeV)
-1
19.7 fb
m(ee) [GeV]
Data/MC
0.5
1
1.5
1.5
20 50 100 200 500 1000 2000
Entries per bin
1
10
2
10
3
10
4
10
5
10
6
10
7
10
data
*/Zγ µµ→
ττ→*/Zγ
EW
Wtt+Wt+ t
QCD
CMS
(8 TeV)
-1
19.7 fb
) [GeV]µµm(
Data/MC
0.5
1
20 50 100 200 500 1000 2000
Fig. 1 The dielectron (left) and dimuon (right) invariant-mass spectra
observed in data and predicted by Monte Carlo (MC) simulation and
the corresponding ratios of observed to expected yields. The QCD mul-
tijet contributions in both decay channels are predicted using control
samples in data. The EW histogram indicates the diboson and W+jets
production. The simulated signal distributions are based on the NNLO-
reweighted powheg sample. No other corrections are applied. Error
bars are statistical only
characteristics similar to those in the analysis data sample.
This sample is used to estimate the probability for a jet to
pass the requirements of the electromagnetic trigger and to
be falsely reconstructed as an electron. This probability is
then applied to a sample of events with one electron and one
jet to estimate the background contribution from an electron
and a jet passing electron selection requirements. As the con-
tribution from two jets passing the electron selections is con-
sidered twice in the previous method, the contribution from
a sample with two jets multiplied by the square of the prob-
ability for jets passing the electron selection requirements is
further subtracted.
The QCD multijet background in the dimuon channel is
evaluated by selecting a control data sample before the isola-
tion and charge sign requirements are applied, following the
method described in [
49].
The largest background consists of final states with par-
ticles decaying by EW interaction, producing electron or
muon pairs, for example, t
t, τ
+
τ
−
, and WW. Notably, these
final states contain electron–muon pairs at twice the rate of
electron or muon pairs. These electron–muon pairs can be
cleanly identified from a data sample of eμ events and prop-
erly scaled (taking into account the detector acceptance and
efficiency) in order to calculate the background contribution
to the dielectron and dimuon channels.
Background yields estimated from an eμ data sample are
used to reduce the systematic uncertainty due to the limited
theoretical knowledge of the cross sections of the SM pro-
cesses. The residual differences between background con-
tributions estimated from data and simulation are taken into
account in the systematic uncertainty assignment, as detailed
in Sect.
9.
The dilepton yields for data and simulated events in bins
of invariant mass are reported in Fig.
1. The photon-induced
background is absorbed in the signal distribution so no cor-
rection is applied at this stage. As shown in the figure, the
background contribution at low mass is no larger than 5%
in both decay channels. In the high-mass region, background
contamination is more significant, reaching approximately
50% (30%) in the dielectron (dimuon) distribution.
6 Resolution and scale corrections
Imperfect lepton energy and momentum measurements can
affectthereconstructeddileptoninvariant-massdistributions.
Correcting for these effects is important in precise measure-
ments of differential cross sections.
A momentum scale correction to remove a bias in the
reconstructed muon momenta due to the differences in the
tracker misalignment between data and simulation and the
residual magnetic field mismodeling is applied following the
standard CMS procedure described in [
50].
The electron energy deposits as measured in the ECAL
are subject to a set of corrections involving information both
from the ECAL and the tracker, following the standard CMS
123
Eur. Phys. J. C (2015) 75 :147 Page 5 of 27 147
m(ee) (post-FSR) [GeV]
Fraction of events
-3
10
-2
10
-1
10
1
20
50
100
200 500
1000
2000
A
∈
∈× A
8 TeV
ee→*/Zγ
CMS
Simulation
) (post-FSR) [GeV]µµm(
Fraction of events
-3
10
-2
10
-1
10
1
20 50
100
200 500 1000 2000
A
∈
∈× A
8 TeV
µµ→*/Zγ
CMS
Simulation
Fig. 2 The DY acceptance, efficiency, and their product per invariant-mass bin in the dielectron channel (top) and the dimuon channel (bottom),
where “post-FSR” means dilepton invariant mass after the simulation of FSR
procedures for the 8 TeV data set [
51]. A final electron energy
scale correction, which goes beyond the standard set of cor-
rections, is derived from an analysis of the Z → e
+
e
−
peak
according to the procedure described in [
49], and consists of
a simple factor of 1.001 applied to the electron energies to
account for the different selection used in this analysis.
The detector resolution effects that cause a migration of
events among the analysis bins are corrected through an itera-
tive unfolding procedure [
52]. This procedure maps the mea-
sured lepton distribution onto the true one, while taking into
account the migration of events in and out of the mass and
rapidity range of this measurement.
The effects of the unfolding correction in the differen-
tial cross section measurement are approximately 50 (20)%
for dielectron (dimuon) channel in the Z peak region, where
the invariant-mass spectrum changes steeply. Less significant
effects, of the order of 15 % (5 %) in dielectron (dimuon)
channel, are observed in other regions. The effect on the
double-differential cross section measurement is less signif-
icant as both the invariant mass and rapidity bins are signif-
icantly wider than the respective detector resolutions. The
effect for dielectrons reaches 15 % in the 45–60 GeV mass
region and 5 % at high mass; it is, however, less than 1%
for dimuons over the entire invariant mass-rapidity range of
study.
7 Acceptance and efficiency
The acceptance A is defined as the fraction of simulated sig-
nal events with both leptons passing the nominal p
T
and
η requirements of the analysis. It is determined using the
NNLO reweighted powheg simulated sample, after the sim-
ulation of FSR.
The efficiency ǫ is the fraction of events in the DY simu-
lated sample that are inside the acceptance and pass the full
selection. The following equation holds:
Aǫ ≡
N
A
N
gen
N
ǫ
N
A
=
N
ǫ
N
gen
, (1)
where N
gen
is the number of generated signal events in a
given invariant-mass bin, N
A
is the number of events inside
the geometrical and kinematic acceptances, and N
ǫ
is the
number of events passing the event selection criteria. Figure
2
shows the acceptance, the efficiency, and their product as
functions of the dilepton invariant mass.
The DY acceptance is obtained from simulation. In the
lowest mass bin it is only about 0.5 %, rapidly increasing to
50% in the Z peak region and reaching over 90 % at high
mass.
The efficiency is factorized into the reconstruction, iden-
tification, and isolation efficiencies and the event trigger effi-
ciency. The factorization procedure takes into account the
asymmetric p
T
selections for the two legs of the dielec-
tron trigger. The efficiency is obtained from simulation,
rescaled with a correction factor that takes into account dif-
ferences between data and simulation. The efficiency correc-
tion factor is determined in bins of lepton p
T
and η using
Z → e
+
e
−
(μ
+
μ
−
) events in data and simulation with the
tag-and-probe method [
49] and is then applied as a weight to
simulated events on a per-lepton basis.
A typical dimuon event efficiency is 70–80% throughout
the entire mass range. In the dielectron channel, the efficiency
at low mass is only 20–40% because of tighter lepton iden-
tification requirements, and reaches 65% at high mass. The
trigger efficiency for events within the geometrical accep-
tance is greater than 98% (93 %) for the dielectron (dimuon)
signal. The efficiency is significantly affected by the pileup
123