# Search for narrow resonances in the lepton final state at CMS

G. Kukartsev  Department of Physics and Astronomy, Brown University,
Providence, RI, USA

###### Abstract

We discuss the results of searches for high-mass narrow resonances decaying
into pairs of leptons using pp collisions at 7 TeV delivered by LHC and
collected with the CMS detector in 2010 and 2011. These include searches for
the ${Z^{0}}^{\prime}$ bosons and RS gravitons.

##  I Introduction

Several theoretical models predict new $\mathrm{\,Te\kern-1.00006ptV}$-scale
resonances decaying into a pair of leptons. Models of particular interest for
the presented analysis include the Sequential Standard Model (SSM) with
standard-model-like couplings, and certain grand-unification-motivated models
($\Psi$) Leike:1998wr . Both predict narrow $Z^{0}$-boson-like states
(${Z^{0}}^{\prime}$). We also consider Kaluza-Klein excitations in the
Randall-Sundrum (RS) model of extra dimensions ($G_{\mathtt{KK}}$)
Randall:1999vf ; Randall:1999ee . We use the four listed models as benchmarks
while we search for a narrow resonance, which is similar to the SSM
${Z^{0}}^{\prime}$, in the dimuon and the dielectron channels. We perform a
likelihood-based shape analysis of the reconstructed dilepton invariant mass
($m_{ll}$) spectra. The approach provides robustness against uncertainties in
the absolute background rate.

The recent searches for ${Z^{0}}^{\prime}\to l^{+}l^{-}$ and
$G_{\mathtt{KK}}\to l^{+}l^{-}$ were published by the Tevatron experiments
D0_RS ; D0_Zp ; CDF_RS ; CDF_Zp . There are indirect constraints from LEP-II
delphi ; aleph ; opal ; l3 .

##  II Detector and Experiment

CMS is a general-purpose particle detector located at the LHC proton-proton
collider at CERN. A prominent feature of the detector is a superconducting
solenoid with the internal diameter of 6$\rm\,m$ and an axial field of 3.8 T.
The solenoid encloses the pixel detector, the silicon tracker, the crystal
electromagnetic calorimeter (ECAL) and the brass and scintillator hadron
calorimeter (HCAL). Outside the solenoid there is a steel flux return yoke
instrumented with the gas ionization detectors, which constitute the CMS muon
system. A diagram of the detector is shown in Figure 1. Further details can be
found elsewhere JINST . For the presented results, 1.1$\mbox{\,fb}^{-1}$ of
integrated luminosity were used.

Figure 1: The CMS detector.

##  III Data and Monte Carlo

The presented results were obtained using the data recorded by the CMS
experiment in 2011. The data were taken using proton-proton colliding beams
with the center-of-mass energy of $7\mathrm{\,Te\kern-1.00006ptV}$. The size
of the dataset corresponds to an integrated luminosity of approximately
$1.1\mbox{\,fb}^{-1}$. The size of the data sample used in the dielectron
analysis is $25\mbox{\,pb}^{-1}$ smaller due to different quality requirements
for the data.

The signal and background processes were modeled using Monte Carlo
simulations. Depending on the process, PYTHIA v6.424 Sjostrand:2006za ,
MADGRAPH MADGRAPH  and POWHEG v1.1 Alioli:2008gx ; Nason:2004rx ;
Frixione:2007vw  event generators together with the CTEQ6L1 Pumplin:2002vw
parton distribution function (PDF) set were used. The full CMS detector
simulation was done with GEANT4 GEANT4 . The generated events were passed
through the CMS trigger simulation and full reconstruction sequence.

##  IV Event Selection

We developed dedicated selection criteria for each of the two dilepton
channels under consideration. Even though the underlying physics processes
under study are similar, reconstruction of different lepton flavors in the
detector differs substantially. For electrons, we reconstruct the transverse
energy using calorimeter information, while the muon reconstruction is based
on the tracking and the muon systems for the measurement of the transverse
momenta. Dilepton invariant mass reconstruction deteriorates for higher values
in the dimuon channel and improves in the dielectron channel. We require the
muons to be reconstructed with the opposite charge, and do not impose this
restriction on dielectron pairs. For the dimuon pairs reconstruction, we
reduce systematic uncertainty by performing data-driven studies with cosmic-
ray muons. The dielectron channel entails higher background rates from
misreconstructed strong scattering signal, and requires tighter selection,
which leads to lower efficiency and acceptance.

###  IV.1 Trigger

For the dimuon pair event candidates, we used a single muon trigger with
sufficiently high minimum transverse momentum requirement
($p_{T}>30\mathrm{\,Ge\kern-1.00006ptV}$). The muon was firstly required to be
detected in the muon system, and then matched to a track in the silicon
tracker. For dielectron pairs, the trigger requires two sufficiently energetic
deposits ($33\mathrm{\,Ge\kern-1.00006ptV}$) in ECAL, with at least one of the
deposits matched to level-one deposit. The corresponding deposit in HCAL must
be small (less than $15\%$). In later portions of the dataset, a match to the
activity in the silicon pixel tracker was required.

###  IV.2 Lepton Reconstruction and Pile-up

Standard CMS techniques apply to the reconstruction, calibration and
identification of the leptons MUO-10-004-PAS ; EGMPAS ; EWK-10-002-PAS . For
all leptons, the reconstructed track was required to be consistent with the
beam interaction point, to be topologically isolated from the hadronic
signatures, and to be sufficiently energetic in the plane transverse to the
beam axis ($p_{T}>35\mathrm{\,Ge\kern-1.00006ptV}$ for muons and electrons in
the ECAL barrel, $p_{T}>40\mathrm{\,Ge\kern-1.00006ptV}$ for endcap
electrons). The muons are then reconstructed via a global fit of the tracker
and the muon system information with proper quality requirements met: there
should be enough hits (more than 10) in the silicon tracker, at least 1 hit in
the pixel detector, and a track reconstructed in the tracker and extrapolated
to the muon system must be compatible with the hits in the muon system, with
hits in at least 2 of the muon stations. The transverse impact parameter
relative to the beam interaction point is required to be less than
$0.2\rm\,cm$. The electrons are reconstructed as an ECAL cluster matched to a
track in the silicon tracker. The ECAL cluster seeds the track in the pixel
detector, which in turn seeds the track in the tracker. Each track must have
at least five hits, and a hit in each of the three pixel layers. The
reconstructed electron candidate must be within either barrel ($|\eta|<1.442$)
or endcap ($1.56<\eta<2.5$) ECAL acceptance regions, and less than $5\%$ of
the energy must be deposited in HCAL.

Leptons are required to be isolated from other activity in the tracker, in
order to suppress background from jets misreconstructed as leptons, and from
non-prompt leptons. The isolation is defined using a cone $\delta
R=\sqrt{(\delta\eta)^{2}+(\delta\phi)^{2}}$ centered on the lepton axis where
$\eta$ is pseudo-rapidity and $\phi$ is the azimuthal angle relative to the
beam axis.

For the muon, the sum of transverse momenta of all other tracks, consistent
with the primary vertex, in the cone of $0.3$ must be less than $10\%$ of the
muon $p_{T}$. The efficiency of this isolation requirement was shown to be
stable with the number of primary vertexes as indication of robustness against
pile-up in a higher instantaneous luminosity regime.

For the electron, the sum of all track $p_{T}$ in the cone of $0.04$ is
required to be less than $7\mathrm{\,Ge\kern-1.00006ptV}$ in the barrel of
ECAL, and less than $15\mathrm{\,Ge\kern-1.00006ptV}$ for the endcap. The
tracks are required to be consistent with the reconstructed primary vertex.
The calorimeter isolation for the electrons requires that the sum of $E_{T}$
of all deposits in the ECAL and the HCAL to be less than
$0.03E_{T}+2\mathrm{\,Ge\kern-1.00006ptV}$ relative to the the electron
$E_{T}$. For the electrons in endcap, we exploit the HCAL segmentation along
the beam axis. The isolation energy is required to be less than
$0.03\cdot\max{(0,E_{T}-50\mathrm{\,Ge\kern-1.00006ptV})}+2.5\mathrm{\,Ge\kern-1.00006ptV}$
where $E_{T}$ is determined from ECAL and the first layer of HCAL. In the
second layer, the HCAL $E_{T}$ must be less than
$0.5\mathrm{\,Ge\kern-1.00006ptV}$. Additionally, the shape of the transverse
energy deposit is required to be compatible with the expected electron signal,
and a good match in $\eta$ and $\phi$ with the corresponding track is
required.

###  IV.3 Lepton pair selection

We select events with two reconstructed leptons: either muons or electrons,
originating from a well-reconstructed primary vertex. The vertex must be
within $2\rm\,cm$ from the beam interaction point in the transverse plane, and
within $24\rm\,cm$ along the beam axis, to suppress cosmic ray background. For
the muon pair event candidates, an additional protection against cosmic muons
is required as an opening angle between the two muons being less than
$(\pi-0.02)$.

For the dimuon events, we require opposite charges for the two muons as it
reduces the fraction of events with a large mismeasurement of the momentum. We
suppress events with many poorly reconstructed tracks in order to reduce beam
background. At least one muon has to match a high-level trigger (HLT) muon. As
an additional quality requirement, the muon pair is required to be consistent
with a common vertex.

For the electron pair events, at least one of the electrons is required to be
reconstructed in the barrel part of the detector. In order to suppress
background from photon conversions, we impose requirement on the distance to
the nearest track and an opening angle with it.

###  IV.4 Efficiency and Acceptance

We measure efficiency of triggering, lepton reconstruction and identification
with “tag-and-probe” method MUO-10-004-PAS ; EWK-10-002-PAS . We use a pure
sample of dimuon pairs requiring that their invariant mass is consistent with
the Z boson mass
($60\mathrm{\,Ge\kern-1.00006ptV}<m_{\mathtt{ll}}<120\mathrm{\,Ge\kern-1.00006ptV}$).
One of the muons in the pair is reconstructed with stringent quality
requirements (tag), and the other is used as a probe for efficiency estimates.
Contributing factors also include track reconstruction and electron
clustering. We measure the single muon trigger efficiency to be $95.0\%\pm
0.3\%$ in the barrel and $89.9\%\pm 0.4\%$ in the endcap. The efficiency of
the muon identification is measured to be $96.4\%\pm 0.2\%$ in the barrel and
$96.0\%\pm 0.3\%$ in the endcap. The efficiency of the track reconstruction in
the internal tracker is found to be above $99\%$ in the whole acceptance
range. Figure 2 represents the overall acceptance and efficiency values for
the dielectron channel, as a function of the dilepton invariant mass. Similar
behavior with higher overall acceptance and efficiency values is observed in
the dimuon channel.

Figure 2: Acceptance and efficiency (left) and invariant mass resolution
(right), dielectron channel.

##  V Resolution

We study detector performance using Standard Model processes with W and Z
mesons and their leptonic final states. We also use cosmic muons. The muon
momentum resolution ranges from $1\%$ at few tens of
$\mathrm{\,Ge\kern-1.00006ptV}$ (Z boson peak scale) to approximately $10\%$
above $1\mathrm{\,Te\kern-1.00006ptV}$. Tracker-based reconstruction yields
better performance at low momenta, while the muons reconstructed in the muon
system have better resolution at high momenta. However, energy loss in the
steel yoke and showers in the muon chambers can spoil the global fit. We find
that adding muon system hits to the tracker-based fit improves resolution for
muons with $p_{T}$ greater than approximately
$200\mathrm{\,Ge\kern-1.00006ptV}$ PTDR2 . The most comprehensive algorithm
(”Tune P”) makes track-by-track decisions about which hits in which subsystems
to use. The resolution is also sensitive to the alignment of the muon and the
tracker systems.

Unlike for muons, the electron energy resolution improves with energy. The
ECAL resolution is better than $0.5\%$ for unconverted photons with transverse
energies above $100\mathrm{\,Ge\kern-1.00006ptV}$. The invariant mass
resolution of dielectron pairs is modeled with a Crystal Ball function and
obtained from Monte Carlo simulation, with additional smearing applied. The
smearing is obtained from comparisons of the Z-boson peak fits in data and
Monte Carlo simulation of the $Z\to ee$ process. At
$1\mathrm{\,Te\kern-1.00006ptV}$, the dielectron invariant mass resolution is
approximately $1.3\%$ when both electrons are in the barrel acceptance region,
and approximately $2.4\%$ when one of the electrons is in the endcap region.
For the electrons in the barrel section of the detector, energy scale is
established using neutral pions and checked using the Z peak.

##  VI Background

The Drell-Yan process produces the dominant irreducible background, with the
next biggest contribution from the top pair and other top-like processes (tW,
diboson and $Z\to\tau\tau$). The remaining background comes from jet
misidentification as leptons ($1\%-5\%$ depending on the channel), and from
cosmic muons in the dimuon channel. We found that the contribution from the
latter, and from diphoton processes misreconstructed as dielectrons are
negligible. Figures 3 and 4 depict the observed dilepton data overlaid with
the background components. The individual components are normalized to next-
to-leading order, and then to the Z-boson peak in data.

Figure 3: Dimuon invariant mass (left) and the corresponding cumulative
spectrum (right). Individual components are normalized to NLO and then
together to the Z-boson peak.

Figure 4: Dielectron invariant mass (left) and the corresponding cumulative
spectrum (right). Individual components are normalized to NLO and then
together to the Z-boson peak.

The overall background rate and the shape of the dilepton invariant mass
distribution are taken from the Drell-Yan Monte Carlo corrected to next-to-
next-to-leading-order with FEWZz v1.X FEWZ , PYTHIA v6.409 and CTEQ6.1 PDF
Stump:2003yu . For the purposes of setting the limits on the dilepton
resonance cross section, the variation in the shape due to added top-like and
other background sources ($5\%-10\%$), the uncertainties in k-factor,
generator choice and PDF sets are covered conservatively by a background rate
uncertainty of $20\%$($15\%$) in the dimuon (dielectron) channel.

As a cross check of the top-like background model, we compare data and Monte
Carlo distributions of the dilepton invariant mass where the flavor and
electric charge of the two leptons are required to be different (“e$\mu$”
method). The reasoning is that if the two leptons do not originate from a
resonance, there is no special reason for them to be of the same flavor. For
each dielectron and dimuon event, we expect to observe nearly two $e\mu$
events (the actual ratio is slightly different due to different efficiencies
for electrons and muons). Figure 5 demonstrates the comparison between data
and Mote Carlo for the $e\mu$ events, which we find satisfactory.

Figure 5: Invariant mass of an electron and a muon of the opposite charge.

##  VII Statistical Inference

We set $95\%$ C.L. upper limits on the cross section ratio as defined in
Equation 5, assuming uniform prior on the parameter of interest and Lognormal
likelihood constraint terms on the nuisance parameters in order to model
systematic uncertainties. We use the likelihood formalism to estimate the
model parameters (via maximum likelihood, ML), and to build a likelihood ratio
to be used as a test statistic. In the Bayesian methods the likelihood is
further multiplied by priors to obtain the posterior pdf. We define the
unbinned likelihood for a data set as

$\L({\bm{x}}|{\bm{\theta}},{\bm{\nu}})=\prod_{i=1}^{N}f(x_{i}|{\bm{\theta}},{\bm{\nu}}),$
(1)

where the product is over the events in the data set ${\bm{x}}$,
$f(x|{\bm{\theta}},{\bm{\nu}})$ is the probability density function of the
observable $x$, $x_{i}$ is the value of the observable in the $i-$th event,
${\bm{\theta}}$ is a vector of the model parameters of interest, ${\bm{\nu}}$
is a vector of nuisance parameters.

It is often convenient and advantageous to define an extended likelihood by
adding the Poisson term. It provides the normalization of the data in terms of
the event yield:

$\L({\bm{x}}|\mu,{\bm{\theta}},{\bm{\nu}})=\frac{\mu^{N}e^{-\mu}}{N!}\prod_{i=1}^{N}f(x_{i}|{\bm{\theta}},{\bm{\nu}}),$
(2)

where $N$ is the number of events in the data sample $\\{x_{i}\\}$, $\mu$ is
the Poisson mean number of events. In the following we will use extended
likelihoods everywhere.

It is useful to define the profile likelihood ratio test statistic

$t_{\theta}=-2\ln\lambda({\bm{\theta}})=-2\ln{\frac{\L_{\mathtt{B}}({\bm{\theta}},\hat{\hat{{\bm{\nu}}}}_{\mathtt{B}})}{\L_{\mathtt{S+B}}({\bm{\theta}},\hat{\hat{{\bm{\nu}}}}_{\mathtt{SB}})}},$
(3)

where $\L_{\mathtt{B}}$ and $\L_{\mathtt{S+B}}$ are the likelihood values for
the background-only and for the signal-plus-background models, and
${\bm{\nu}}_{\mathtt{B}}$ is a subset of ${\bm{\nu}}_{\mathtt{SB}}$. The _hat_
notation ($\hat{\,\,\,}$) symbolizes the ML estimator, i.e.
$\hat{{\bm{\theta}}}$ is the value of ${\bm{\theta}}$ that maximizes the
likelihood for a given model. The double hat notation ($\hat{\hat{\,\,\,}}$)
stands for a conditional ML estimator for a given value of a parameter of
interest, i.e. $\hat{\hat{{\bm{\nu}}}}$ is the value of ${\bm{\nu}}$ that
maximizes the likelihood for a given model, for a given value of
${\bm{\theta}}$.

There are several ${Z^{0}}^{\prime}$ models that we consider in the analysis.
In the Sequential Standard Model (SSM), the ${Z^{0}}^{\prime}$ has the same
couplings as the standard model $Z$ boson. The $\Psi$ model is based on an
$E_{6}$ gauge symmetry. For the models overview see Z-Boson searches in
Nakamura:2010zzi . We use the SSM model by default everywhere unless
explicitly stated otherwise.

For the ${Z^{0}}^{\prime}$ search, we define the signal-plus-background
likelihood as

$\L_{\mathtt{S+B}}({\bm{m}}|\theta,{\bm{\nu}})=\frac{\mu^{N}e^{-\mu}}{N!}\prod_{i=1}^{N}\left(\frac{\mu_{\mathtt{S}}(\theta)}{\mu}f_{\mathtt{S}}(m_{i}|{\bm{\nu}}_{\mathtt{S}})+\frac{\mu_{\mathtt{B}}}{\mu}f_{\mathtt{B}}(m_{i}|{\bm{\nu}}_{\mathtt{B}})\right),$
(4)

where ${\bm{m}}$ is the dataset in which $m_{i}$ is the value of the
observable $m$ (the invariant mass of the lepton pair) in $i$-th event,
$\theta$ denotes the parameter of interest, either the cross section or the
cross section ratio, as defined further, ${\bm{\nu}}$ is the vector of the
nuisance parameters, $f_{\mathtt{S}}$ and $f_{\mathtt{B}}$ are the PDFs for
the signal and the background (specific shapes are defined later in the
document), $N$ is the total number of events observed, $\mu_{\mathtt{S}}$ and
$\mu_{\mathtt{B}}$ are the expected signal and the background event yields,
respectively, and $\mu=\mu_{\mathtt{S}}+\mu_{\mathtt{B}}$ is the total number
of events expected. Note that the expected signal yield $\mu_{\mathtt{S}}$ is
a function of the parameter of interest. The parameter of interest is the
cross section ratio

$R_{\sigma}=\frac{\sigma_{{Z^{0}}^{\prime}\to\ell^{+}\ell^{-}}}{\sigma_{Z^{0}\to\ell^{+}\ell^{-}}},$
(5)

where $\sigma_{Z^{0}\to\ell^{+}\ell^{-}}$ is the cross section multiplied by
the branching ratio for $pp\to Z^{0}\to\ell^{+}\ell^{-}$. Such an approach
allows to exclude the uncertainty on the integrated luminosity from the
measurement. In this case, we parameterize the expected signal yield as

$\mu_{\mathtt{S}}=N_{Z}\cdot
R_{\sigma}\cdot\frac{\epsilon_{\mathtt{sel}}({Z^{0}}^{\prime})\cdot{\cal
A}({Z^{0}}^{\prime})\cdot}{\epsilon_{\mathtt{sel}}(Z^{0})\cdot{\cal
A}(Z)}\equiv N_{Z}\cdot R_{\sigma}\cdot R_{\epsilon}\cdot R_{{\cal A}}.$ (6)

Here $N_{Z}$ is the observed number of $Z^{0}$ events, and $R_{\epsilon}\cdot
R_{{\cal A}}$ denotes the fraction in Equation 6. The PDF, which represents
the ${Z^{0}}^{\prime}$ signal model, is

$f_{\mathtt{S}}(m_{ll}|M,\Gamma,w)=\mathtt{BW}(m_{ll}|M,\Gamma)\otimes\mathtt{Gaussian}(0,w),$
(7)

where $m_{ll}$ is the invariant mass of the two leptons (the observable),
$\mathtt{BW}$ stands for the resonant Breit-Wigner shape, $\Gamma$ is its
width, $w$ is the width of the Gaussian resolution function. For combining
multiple analysis channels, the corresponding likelihoods are multiplied
together in order to build the combined likelihood.

##  VIII Systematic uncertainty

We combine all systematic uncertainties into three components that we treat
independently: an uncertainty on signal sensitivity (includes uncertainties on
signal and Z acceptances and efficiencies and on the Z event count), the
background rate uncertainty, which is described in Section VI, and the mass
scale uncertainty in the dielectron channel ($1\%$).

##  IX Results

We present reconstructed dilepton invariant mass distributions in the CMS data
in Figures 3 and 4 superimposed with the individual background components from
Monte Carlo. We use the mass spectra to set $95\%$ C.L. Bayesian upper limits
on the dilepton resonance cross section ratio (Equation 5). We use several
popular theoretical models to set lower limits on the corresponding resonance
masses, including the Sequential Standard Model ${Z^{0}}^{\prime}$. Figure 6
displays the observed limits overlaid with the median expected limits and 1-
and 2-standard deviation quantile bands. Theoretical estimates for four
popular theoretical models are overlaid as well. Figure 7 displays similar
limit plots for the combination of the dimuon and dielectron channels. the
likelihood ratio in Equation 3 is asymptotically distributed as a $\chi^{2}$
distribution with number of degrees of freedom equal to the difference in the
numbers of free parameters between the two models.

By combining the two channels, we exclude ${Z^{0}}^{\prime}$ masses for the
SSM and E6-motivated $\Psi$ model below 1940$\mathrm{\,Ge\kern-1.00006ptV}$
and 1620$\mathrm{\,Ge\kern-1.00006ptV}$, respectively. The corresponding
limits in the individual dimuon(dielectron) channels are
1780(1730)$\mathrm{\,Ge\kern-1.00006ptV}$ and
1440(1440)$\mathrm{\,Ge\kern-1.00006ptV}$. Combined analysis excludes masses
of the RS Kaluza-Klein gravitons for couplings of 0.05 and 0.10 at
1450$\mathrm{\,Ge\kern-1.00006ptV}$ and 1780$\mathrm{\,Ge\kern-1.00006ptV}$.
The corresponding dimuon(dielectron) numbers are
1240(1300)$\mathrm{\,Ge\kern-1.00006ptV}$ and
1640(1590)$\mathrm{\,Ge\kern-1.00006ptV}$.

Figure 6: Exclusion limits on the dilepton resonance cross section times
branching fraction relative to the Z-boson standard model production, dimuon
channel (left) and dielectron channel (right).  Figure 7: Combined dimuon and
dielectron channel exclusion limits on the dilepton resonance cross section
times branching fraction relative to the Z-boson standard model production.

We identify the most signal-like patterns in the data. They correspond to a
dimuon resonance at 1080$\mathrm{\,Ge\kern-1.00006ptV}$ and a dielectron
resonance at 950$\mathrm{\,Ge\kern-1.00006ptV}$, with local significances of
1.7 and 2.2 standard deviations, respectively. Corrected for the “trials
factor” (a consideration that a signal-like fluctuation can happen at an
arbitrary mass value), the significances become 0.3 and 0.2 standard
deviations, respectively. Combined analysis suggest a dilepton resonance-like
signature at 970$\mathrm{\,Ge\kern-1.00006ptV}$ with local significance of 2.1
and significance corrected for the trials factor of 0.2 standard deviations.
Figures 8 and 9 display the sampling distributions of the likelihood ratio
test statistic (3) obtained from ensembles of background-only
pseudoexperiments, used for estimating significances including the trials
factor corrections, overlaid with the value from data.

Figure 8: Significance in the dimuon channel (left) and in the dielectron
channel (right). A histogram corresponds to an ensemble of background-only
pseudoexperiments. The red line is a value observed in data. A plotted value
corresponds to the most signal-like pattern in a dataset, in a fine scan of
the spectrum over the allowed invariant mass values.  Figure 9: Combined
significance in the two channels. A histogram corresponds to an ensemble of
background-only pseudoexperiments. The red line is a value observed in data. A
plotted value corresponds to the most signal-like pattern in a dataset, in a
fine scan of the spectrum over the allowed invariant mass values.

##  X Conclusion

The CMS Collaboration has searched for high-mass narrow resonances in the
dilepton invariant mass spectra in the dimuon and the dielectron channels,
using 1.1$\mbox{\,fb}^{-1}$ of integrated luminosity recorded by the CMS
detector operating at the LHC proton-proton collider at CERN, with the center-
of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$. The individual channel and
combined spectra are consistent with the Standard Model expectations. The 95%
C.L. upper limits have been set on the product of the new resonance production
cross section and the corresponding branching fraction relative to the
Standard Model Z boson production. Mass limits have been set on the resonances
predicted by the SSM and $\Psi$ ${Z^{0}}^{\prime}$ models, and on the RS
Kaluza-Klein gravitons for couplings of 0.05 and 0.1.

###### Acknowledgements.

We wish to congratulate our colleagues in the CERN accelerator departments for
the excellent performance of the LHC machine. We thank the technical and
administrative staff at CERN and other CMS institutes, and acknowledge support
from: FMSR (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP
(Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS
(Colombia); MSES (Croatia); RPF (Cyprus); Academy of Sciences and NICPB
(Estonia); Academy of Finland, ME, and HIP (Finland); CEA and CNRS/IN2P3
(France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH
(Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF
and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI
(Mexico); PAEC (Pakistan); SCSR (Poland); FCT (Portugal); JINR (Armenia,
Belarus, Georgia, Ukraine, Uzbekistan); MST and MAE (Russia); MSTD (Serbia);
MICINN and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei);
TUBITAK and TAEK (Turkey); STFC (United Kingdom); DOE and NSF (USA).

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