-titleHadron Collider Physics Symposium 2011 11institutetext: LPSC-Grenoble, CNRS/IN2P3, UJF, INPG

# Search for extra dimensions in the diphoton final state with ATLAS

Quentin Buat On behalf of the ATLAS Collaboration<EMAIL_ADDRESS>
###### Abstract

The large difference between the Planck scale and the electroweak scale, known
as the hierarchy problem, has been addressed in some models through the
existence of extra spatial dimensions. A search for evidence of extra spatial
dimensions has been performed, through an analysis of the diphoton final state
in data recorded in 2011 with the ATLAS detector at the CERN Large Hadron
Collider. The analysis uses a dataset of 2.12 $fb^{-1}$ of proton-proton
collisions at $\sqrt{s}=7$ TeV. The diphoton invariant mass spectrum is
observed to be in good agreement with the expected Standard Model (SM)
background. We set 95$\%$ CL lower limits on the scale related to virtual
graviton exchange process in the context of the Arkani-Hamed, Dimopoulos,
Dvali model (ADD) and on the lightest Kaluza Klein excitation mass in the
context of the Randall-Sundrum model (RS).

##  1 Introduction

Recently, there has been great interest in models which address the hierarchy
problem through the existence of extra spatial dimensions. In this analysis we
search for evidence of extra spatial dimensions in the context of the ADD
ADDPaper  and RS RSPaper  models. This analysis briefly summarized here, is
described in more detail in GravPaper .

In the ADD context, _n_ flat extra spatial dimensions are postulated with a
compactification radius R. The gravity is the only field that propagates in
those extra dimensions and acquires Kaluza Klein (KK) modes. In the ADD
context, resolving the hierarchy problem implies small values of 1/R. This
leads to an almost continuous KK spectrum of the graviton mass.
Experimentally, an ADD signal will contribute through virtual graviton
exchange to the diphoton invariant mass spectrum. This process can be
parametrized as a function of the number of extra dimensions _n_ and an
ultraviolet cutoff ($M_{s}$). Several formalisms exist in the literature to
define $M_{s}$, referred to here as GRW GRW , HLZ HLZ  and Hewett Hewett .

The RS model postulates a 5-dimensional space-time bounded by two (3+1) branes
with the SM particles localized on one of the branes. The fifth dimension has
a ”warped” geometry which allows to naturally generate TeV scales from the
Planck scale. The fundamental Planck scale ($M_{Pl}$) on one brane is related
to the apparent scale ($\Lambda_{\pi}$) on the other brane by the relation
$\Lambda_{\pi}=\overline{M}_{Pl}\exp{(-k\pi r_{c})}$ where $k$ is the
curvature scale of the extra dimension, $r_{c}$ the compactification radius
and $\overline{M}_{Pl}=\frac{M_{Pl}}{\sqrt{8\pi}}$. The observed hierarchy of
scales can be naturally reproduced by this model with $kr_{c}\approx 11$. In
the minimal RS model, gravitons are the only particles that propagate in the
bulk. Consequently a series of massive KK excitations is predicted with a mass
splitting of the order of 1 TeV. Finally the RS model can be expressed in
terms of the coupling $k/\overline{M}_{Pl}$ and the mass of the lightest KK
excitation ($m_{G}$). Experimentally the presence of a RS signal can be probed
as a narrow resonance in the diphoton invariant mass spectrum.

##  2 Photon reconstruction and identification

A complete description of the ATLAS detector can be found in DetectorPaper .
In this analysis we look for final states with two photons. Therefore we rely
on the inner tracker and the calorimetric system of the detector. The tracking
system of ATLAS is composed of layers of silicon-based and straw-tube
detectors surrounded by a 2 T magnetic field for momentum measurements. It
allows to measure the tracks of the 30% of photons converting in $e^{+}e^{-}$
pairs before reaching the calorimeter. The photon energy deposit is measured
by the Liquid Argon (LAr) electromagnetic calorimeter, covering the region
$0<|\eta|<1.37$ and $1.52<|\eta|<2.37$. It is segmented in three longitudinal
layers. Most of the energy of the electromagnetic (EM) shower is recovered by
the second layer which has a granularity of
$\Delta\eta\times\Delta\phi=0.025\times 0.025$. The first layer with a thinner
segmentation is designed to reject jets dominated by neutral hadrons such as a
$\pi^{0}$ or a $\eta$. Indeed, such a hadron may decay into two photons which
can be identified by resolving the two maxima in the first layer of the LAr
calorimeter. In the central region ($|\eta|<1.81$), a presampler is used to
evaluate the energy lost in the upstream material. The hadronic calorimeter,
composed of scintillating tiles-iron sampling for the central part
($|\eta|<1.7$) and of liquid-argon-copper/tungsten sampling for $|\eta|>1.7$
is used to measure the leakage of energy of the photon candidates. A complete
description of the reconstruction and identification of photons with ATLAS can
be found in ATLASphotons .

##  3 Trigger and Data selection

The events are recorded using a trigger requiring at least two photon
candidates with transverse energy $E_{T}^{\gamma}>20$ GeV and satisfying
identification requirements based on the leakage of energy into the hadronic
calorimeter and the transverse width of the EM shower. This trigger is fully
efficient for high mass diphoton events passing the offline selection
requirements. Events are required to have at least one primary collision
vertex, with at least three reconstructed tracks. Selected events have at
least two photon candidates, each with $E_{T}^{\gamma}>25$ GeV and lying
outside the transition region between the barrel and endcap calorimeters. In
addition, the two photons are required to satisfy standard quality criteria
and to lie outside detector regions where their energy is not measured in an
optimal way. The two highest $E_{T}^{\gamma}$ photon candidates have to
satisfy a set of identification requirements on the hadronic leakage and on
the lateral width of the EM shower. The requirements on the EM shower use the
thin granularity of the first sampling to achieve a high purity of the
selected photon sample. The isolation transverse energy $E_{T}^{iso}$ for each
photon is calculated ATLASphotons  by summing over the cells within a cone of
radius $\Delta R=\sqrt{(\eta-\eta^{\gamma})^{2}+(\phi-\phi^{\gamma})^{2}}<0.4$
around the direction of the photon. Then the energy deposit of the photon
itself is subtracted as well as the soft jet activity of the underlying event
ambientenergy . In addition, $E_{T}^{iso}$ is corrected for the leakage of the
photon energy into the isolation ring. To further reduce the jet background,
an isolation cut of $E_{T}^{iso}<5$ GeV is applied on the two leading photons.
For all events the two photons with the highest $E_{T}^{\gamma}$ values are
considered and the diphoton invariant mass has to exceed 140 GeV. A total of
6846 events are selected.

##  4 Monte Carlo Simulation Studies

Monte Carlo (MC) simulations were performed to study the detector response to
various scenarios of ADD and RS models as well as to perform studies of the SM
background.

The SM diphoton background was simulated with PYTHIA 6.424 pythia  and
MRST2007LOMOD MRST2007lomod  parton distribution functions (PDFs). The PYTHIA
events were reweighted as a function of the diphoton invariant mass to the
differential cross section predicted by the NLO calculation of DIPHOX 1.3.2
diphox  . The reweighting factor decreased smoothly from $\approx 1.6$ for
$m_{\gamma\gamma}=140$ GeV to 1 for large masses.

SHERPA 1.2.3 sherpa  with CTEQ6L cteq66  PDFs was used to simulate the various
ADD scenarios. The ADD MC samples were used to determine the signal acceptance
($A$) and selection efficiency ($\epsilon$). The acceptance varied for the
various ADD implementations and fell from typical values of $\approx 20$% for
$M_{S}=1.5$ TeV down to $\approx 15$% for $M_{S}=3$ TeV. The selection
efficiency, for events within the detector acceptance, was found to be
$\approx 70$%.

RS model MC signal samples were produced with PYTHIA 6.424 for a range of
$m_{G}$ and $k/\overline{M}_{Pl}$ values, using the MRST2007LOMOD PDFs. The
products of $A\times\epsilon$ for the RS signal models were in the range
$\approx(53-60)$%, slowly rising with increasing graviton mass. The
reconstructed shape of the graviton resonance was modeled by a Breit-Wigner
(BW) lineshape convoluted with a double-sided Crystal Ball function to
describe the detector response. The natural width of the BW was fixed
according to the expected theoretical value, which varies as the square of
$k/\overline{M}_{Pl}$. As an example, the value of the width for
$k/\overline{M}_{Pl}=0.1$ increases from $\approx 8$ GeV for $m_{G}=800$ GeV
to $\approx 30$ GeV for $m_{G}=2200$ GeV. Fitting this mass dependence
provides a parametrization used to describe signals with any values of $m_{G}$
and $k/\overline{M}_{Pl}$.

##  5 Background evalution

The SM $\gamma\gamma$ production is the largest background of this analysis.
The invariant mass spectrum shape was determined by PYTHIA reweighted by
DIPHOX NLO cross-section predictions.

The second significant background arises from a different physics object
(electron or jet) misidentified as a photon. This background, called reducible
background, is dominated by the production of $\gamma$ \+ jet or dijet events.
Studies have shown that the Drell Yan contribution can be neglected for events
with $m_{\gamma\gamma}>140$ GeV. The shape of the reducible background is
determined by a data-driven technique. By reverting the identification
criteria on the leading and/or subleading photon, we get three different
control samples enriched in $\gamma$ \+ jet, jet + $\gamma$ and dijet events.
The invariant mass spectra of the three samples are consistent and they are
merged to determine the reducible background shape. This shape is extrapolated
to high diphoton masses where the data control sample are statistically
limited.

The fraction of each background has been determined by a two dimensional
template fit method using the photon isolation variable, described in more
detail in SMdiphoton . Finally the background expectation is normalized to the
data in the invariant mass range [140, 400] GeV where the presence of any
possible ADD and RS signal has been excluded by previous searches.

##  6 Systematic uncertainties

The systematic uncertainty on the background estimation arises from three
different sources. The irreducible background uncertainty is obtained by
varying the scales of the models and the PDFs in DIPHOX while the reducible
background uncertainty is obtained by fitting the three control samples
described in section 5 with the functionnal form. The uncertainty on the
background estimation varies from $\approx$2% for the low mass region to
$\approx$20% at a mass of $\approx$2 TeV. For the signal, the PDFs uncertainty
is of 10-15% for ADD models and 5-10 % for RS models and the uncertainty on
the signal yields has been evaluated to be of 6.7 % for both ADD and RS
models.

##  7 Results and Interpretation

Figure 1 shows the observed invariant mass spectrum of diphoton events, with
statistical significance of the bin-by-bin difference between data and the
expected background at the bottom. This difference is measured in standard
deviations based on Poisson statistics. The small variations show the good
agreement between data and the estimated SM background. This is confirmed by
an analysis using the BUMPHUNTER bumphunter  tool, which yields a probability
of 0.28, given the background only hypothesis, to observe discrepancies as
large as the one observed in the bin by bin comparison. In the absence of any
significant deviation we set 95% CL on the signal cross sections, using a
bayesian approach bayes  with a flat prior. In the context of ADD models the
signal search region was chosen as $m_{\gamma\gamma}>1.1$ TeV by optimizing
the expected limit. The observed (expected) limit on the cross section due to
new physics is 2.49 (1.94) fb. This result can be translated into 95% CL lower
limits on $M_{s}$ for different numbers of extra dimensions and formalisms.
Table 1 summarizes the observed limits value. In the context of the RS models,
the observed invariant mass spectrum was compared to templates of the expected
background and various signal parametrizations. The limit is set as 95% CL on
the product of the cross-section $\times$ Branching ratio ($\sigma B$) as a
function of $m_{G}$. Then the cross-section limit is converted into a mass
limit using the theoretical dependence. Table 2 shows the limit in the
diphoton final state for various values of $k/\overline{M}_{Pl}$. By combining
with previously published ATLAS results zprime  from the dilepton final state,
we obtain a 95% CL limit on $\sigma B$ as a function of $m_{G}$ shown by the
top plot of figure 2. The result is also interpreted in the plane of
$k/\overline{M}_{Pl}$ versus $m_{G}$ (bottom plot of figure 2).

Figure 1: Observed invariant mass spectrum, superimposed with the predicted SM background and examples of signals for ADD and RS models. The bin-by-bin significance of the difference between data and background is shown in the lower panel. Table 1: 95% CL limits on $M_{S}$ (in TeV) for various implementations of the ADD model, using both LO (k-factor = 1) and NLO (k-factor = 1.70) theory cross section calculations. k-factor | GRW | Hewett | HLZ
---|---|---|---
Value |  | Pos | Neg | $n=3$ | $n=4$ | $n=5$ | $n=6$ | $n=7$
1 | 2.73 | 2.44 | 2.16 | 3.25 | 2.73 | 2.47 | 2.30 | 2.17
1.70 | 2.97 | 2.66 | 2.27 | 3.53 | 2.97 | 2.69 | 2.50 | 2.36
Table 2: 95% CL lower limits on $m_{G}$, for various values of $k/\overline{M}_{Pl}$. The $G\rightarrow\gamma\gamma$ channel alone and the combination with the dilepton results of Ref. zprime  are shown, using both LO (k-factor = 1) and NLO (k-factor = 1.75) theory cross section calculations. k-Factor Value | Channel(s) Used | 95% CL Limit [TeV]
---|---|---
$k/\overline{M}_{Pl}$ Value
0.01 | 0.03 | 0.05 | 0.1
1 | $G\to\gamma\gamma$ | 0.74 | 1.26 | 1.41 | 1.79
$G\to\gamma\gamma$/$ee$/$\mu\mu$ | 0.76 | 1.32 | 1.47 | 1.90
1.75 | $G\to\gamma\gamma$ | 0.79 | 1.30 | 1.45 | 1.85
$G\to\gamma\gamma$/$ee$/$\mu\mu$ | 0.80 | 1.37 | 1.55 | 1.95

Figure 2: (Top) Expected and observed 95% CL limits from the combination of
$G\rightarrow\gamma\gamma/ee/\mu\mu$ channels on $\sigma B$ as a function of
the graviton mass. The theory bands are drawn assuming a k-factor of 1.75.
(Bottom) The RS results interpreted in the plane of $k/\overline{M}_{Pl}$
versus graviton mass, and including recent results from other experiments
TevatronRS ; CMSggnew . The region above the curve is excluded at 95% CL.

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