Measurement of the inclusive isolated prompt photon cross section in pp collisions at $\sqrt{s}$ = 7 TeV with the ATLAS detector

Abstract

A measurement of the cross section for the inclusive production of isolated prompt photons in $pp$ collisions at a centre-of-mass energy $\sqrt(s)$ = 7 TeV is presented. The measurement covers the pseudorapidity ranges $|\eta^{\gamma}| < 1.37$ and $1.52 \leq |\eta^{\gamma}| < 1.81$ in the transverse energy range $15 \leq E^{\gamma}_T\ \leq 100~GeV$. The results are based on an integrated luminosity of $880~nb^{−1}$ , collected with the ATLAS detector at the Large Hadron Collider. Photon candidates are identified by combining information from the calorimeters and from the inner detector. Residual background in the selected sample is estimated from data based on the observed distribution of the transverse isolation energy in a narrow cone around the photon candidate. The results are compared to predictions from next-to-leading order perturbative QCD calculations.

Full text

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arXiv:1012.4389v2 [hep-ex] 21 Dec 2010
CERN-PH-EP-2010-068
Submitted to Phys. Rev. D
Measurement of the inclusive isolated prompt photon cross section in pp collisions at
√s = 7 TeV with the ATLAS detector
G. Aad et al.∗
(The ATLAS Collaboration)
(Dated: December 22, 2010)
A measurement of the cross section for the inclusive production of isolated prompt photons in
pp collisions at a centre-of-mass energy√s = 7 TeV is presented. The measurement covers the
pseudorapidity ranges |ηγ| < 1.37 and 1.52 ≤ |ηγ| < 1.81 in the transverse energy range 15 ≤ Eγ
100 GeV. The results are based on an integrated luminosity of 880 nb−1, collected with the ATLAS
detector at the Large Hadron Collider. Photon candidates are identified by combining information
from the calorimeters and from the inner tracker. Residual background in the selected sample is
estimated from data based on the observed distribution of the transverse isolation energy in a narrow
cone around the photon candidate. The results are compared to predictions from next-to-leading
order perturbative QCD calculations.
T<
PACS numbers: 13.25.Hw, 12.15.Hh, 11.30.Er
I.INTRODUCTION
Prompt photon production at hadron colliders pro-
vides a handle for testing perturbative QCD (pQCD)
predictions [1, 2]. Photons provide a colorless probe of
quarks in the hard partonic interaction and the subse-
quent parton shower. Their production is directly sen-
sitive to the gluon content of the proton through the
qg→
(LO). The measurement of the prompt photon produc-
tion cross section can thus be exploited to constrain the
gluon density function [3, 4]. Furthermore, photon identi-
fication is important for many physics signatures, includ-
ing searches for Higgs boson [5–7], graviton decays [8] to
photon pairs, decays of excited fermions [9], and decays
of pairs of supersymmetric particles characterized by the
production of two energetic photons and large missing
transverse energy [10–12].
Prompt photons include both “direct” photons, which
take part in the hard scattering subprocess (mostly
quark-gluon Compton scattering, qg → qγ, or quark-
antiquark annihilation, q¯ q → gγ), and “fragmenta-
tion” photons, which are the result of the fragmenta-
tion of a high-pT parton [13, 14].
an isolation criterion is applied based on the amount
of transverse energy inside a cone of radius R
?
ton direction in the pseudorapidity (η) and azimuthal
angle (φ) plane [15]. After the isolation requirement is
applied the relative contribution to the total cross section
from fragmentation photons decreases, though it remains
non-negligible especially at low transverse energies [14].
qγ process, which dominates at leading order
In this analysis,
=
(η − ηγ)2+ (φ − φγ)2= 0.4 centered around the pho-
∗Full author list given at the end of the article in Appendix C.
The isolation requirement also significantly reduces the
main background of non-prompt photon candidates from
decays of energetic π0and η mesons inside jets.
Early studies of prompt photon production were car-
ried out at the ISR collider [16, 17]. Subsequent stud-
ies, for example [18–20], further established prompt pho-
tons as a useful probe of parton interactions. More re-
cent measurements at hadron colliders were performed at
the Tevatron, in p¯ p collisions at a centre-of-mass energy
√s = 1.96 TeV. The measurement by the D0 Collabo-
ration [21] is based on 326 pb−1and covers a pseudo-
rapidity range |ηγ| < 0.9 and a transverse energy range
23 < Eγ
T< 300 GeV, while the measurement by the
CDF Collaboration [22] is based on 2.5 fb−1and covers a
pseudorapidity range |ηγ| < 1.0 and a transverse energy
range 30 < Eγ
T< 400 GeV. Both D0 and CDF measure
an isolated prompt photon cross section in agreement
with next-to-leading order (NLO) pQCD calculations,
with a slight excess seen in the CDF data between 30
and 50 GeV. Measurements of the inclusive prompt pho-
ton production cross section have also been performed
in ep collisions, both in photoproduction and deep in-
elastic scattering, by the H1 [23, 24] and ZEUS [25, 26]
Collaborations. The most recent measurement of the in-
clusive isolated prompt photon production was done with
2.9 pb−1at√s = 7 TeV by the CMS Collaboration [27].
That measurement, which covers 21 < Eγ
and |ηγ| < 1.45, is in good agreement with NLO predic-
tions for the full Eγ
Trange.
This paper describes the extraction of a signal of iso-
lated prompt photons using 880 nb−1of data collected
with the ATLAS detector at the Large Hadron Collider
(LHC). A measurement of the production cross section
in pp collisions at√s = 7 TeV is presented, in the pseu-
dorapidity ranges |ηγ| < 0.6, 0.6 ≤ |ηγ| < 1.37 and
1.52 ≤ |ηγ| < 1.81, for photons with transverse energies
T< 300 GeV

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between 15 GeV and 100 GeV.
The paper is organized as follows. The detector is de-
scribed in Section II, followed by a summary of the data
and the simulated samples used in the measurement in
Section III. Section IV introduces the theoretical predic-
tions to which the measurement is compared. Section V
describes the photon reconstruction and identification al-
gorithms; their performance is given in Section VI. Sec-
tion VII describes the methods used to estimate the resid-
ual background in the data and to extract the prompt
photon signal, followed by a discussion of the data correc-
tions for the cross section measurement in Section VIII.
The sources of systematic uncertainties on the cross sec-
tion measurement are discussed in Section IX. Section X
contains the main experimental results and the compar-
ison of the observed cross sections with the theoretical
predictions, followed by the conclusions in Section XI.
II. THE ATLAS DETECTOR
The ATLAS detector is described in detail in Refs. [28]
and [29]. For the measurement presented in this paper,
the calorimeter, with mainly its electromagnetic section,
and the inner detector are of particular relevance.
The inner detector consists of three subsystems: at
small radial distance r from the beam axis (50.5 <
r < 150 mm), pixel silicon detectors are arranged in
three cylindrical layers in the barrel and in three disks
in each end-cap; at intermediate radii (299 < r < 560
mm), double layers of single-sided silicon microstrip de-
tectors are used, organized in four cylindrical layers in
the barrel and nine disks in each end-cap; at larger radii
(563 < r < 1066 mm), a straw tracker with transition
radiation detection capabilities divided into one barrel
section (with 73 layers of straws parallel to the beam
line) and two end-caps (with 160 layers each of straws
radial to the beam line) is used. These three systems are
immersed in a 2 T axial magnetic field provided by a su-
perconducting solenoid. The inner detector has full cov-
erage in φ. The silicon pixel and microstrip subsystems
cover the pseudorapidity range |η| < 2.5, while the transi-
tion radiation tracker (TRT) acceptance is limited to the
range |η| < 2.0. The inner detector allows an accurate
reconstruction of tracks from the primary proton-proton
collision region, and also identifies tracks from secondary
vertices, permitting the efficient reconstruction of pho-
ton conversions in the inner detector up to a radius of
≈ 80 cm.
The electromagnetic calorimeter is a lead-liquid argon
(Pb-LAr) sampling calorimeter with an accordion geom-
etry. It is divided into a barrel section, covering the pseu-
dorapidity region |η| < 1.475, and two end-cap sections,
covering the pseudorapidity regions 1.375 < |η| < 3.2.
It consists of three longitudinal layers. The first one,
with a thickness between 3 and 5 radiation lengths, is
segmented into high granularity strips in the η direction
(width between 0.003 and 0.006 depending on η, with the
exception of the regions 1.4 < |η| < 1.5 and |η| > 2.4),
sufficient to provide an event-by-event discrimination be-
tween single photon showers and two overlapping showers
coming from a π0decay. The second layer of the electro-
magnetic calorimeter, which collects most of the energy
deposited in the calorimeter by the photon shower, has
a thickness around 17 radiation lengths and a granular-
ity of 0.025 × 0.025 in η × φ (corresponding to one cell).
A third layer, with thickness varying between 4 and 15
radiation lengths, is used to correct leakage beyond the
calorimeter for high energy showers. In front of the ac-
cordion calorimeter a thin presampler layer, covering the
pseudorapidity interval |η| < 1.8, is used to correct for
energy loss before the calorimeter. The sampling term a
of the energy resolution (σ(E)/E ≈ a/?E [GeV]) varies
largest contribution to the resolution up to about 200
GeV, where the global constant term, estimated to be
0.7% [30], starts to dominate.
The total amount of material before the first active
layer of the electromagnetic calorimeter (including the
presampler) varies between 2.5 and 6 radiation lengths
as a function of pseudorapidity, excluding the transition
region (1.37 ≤ |η| < 1.52) between the barrel and the
end-caps, where the material thickness increases to 11.5
radiation lengths.The central region (|η| < 0.6) has
significantly less material than the outer barrel (0.6 ≤
|η| < 1.37), which motivates the division of the barrel
into two separate regions in pseudorapidity.
A hadronic sampling calorimeter is located beyond the
electromagnetic calorimeter. It is made of steel and scin-
tillating tiles in the barrel section (|η| < 1.7), with depth
around 7.4 interaction lengths, and of two wheels of cop-
per and liquid argon in each end-cap, with depth around
9 interaction lengths.
A three-level trigger system is used to select events con-
taining photon candidates during data taking. The first
level trigger (level-1) is hardware based: using a coarser
cell granularity (0.1×0.1 in η ×φ) than that of the elec-
tromagnetic calorimeter, it searches for electromagnetic
clusters within a fixed window of size 0.2×0.2 and retains
only those whose total transverse energy in two adjacent
cells is above a programmable threshold. The second and
third level triggers (collectively referred to as the “high-
level” trigger) are implemented in software. The high-
level trigger exploits the full granularity and precision
of the calorimeter to refine the level-1 trigger selection,
based on improved energy resolution and detailed infor-
mation on energy deposition in the calorimeter cells.
between 10% and 17% as a function of |η| and is the
III.COLLISION DATA AND SIMULATED
SAMPLES
A.Collision Data
The measurement presented here is based on proton-
proton collision data collected at a centre-of-mass energy

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√s = 7 TeV between April and August 2010. Events
in which the calorimeters or the inner detector are not
fully operational, or show data quality problems, are ex-
cluded. Events are triggered using a single-photon high-
level trigger with a nominal transverse energy thresh-
old of 10 GeV, seeded by a level-1 trigger with nomi-
nal threshold equal to 5 GeV. The selection criteria ap-
plied by the trigger on shower shape variables computed
from the energy profiles of the showers in the calorime-
ters are looser than the photon identification criteria ap-
plied in the offline analysis, and allow ATLAS to reach
a plateau of constant efficiency close to 100% for true
prompt photons with Eγ
T> 15 GeV and pseudorapid-
ity |ηγ| < 1.81. In addition, samples of minimum-bias
events, triggered by using two sets of scintillator counters
located at z = ±3.5 m from the collision centre, are used
to estimate the single-photon trigger efficiency. The total
integrated luminosity of the sample passing data quality
and trigger requirements amounts to (880 ± 100) nb−1.
In order to reduce non-collision backgrounds, events
are required to have at least one reconstructed primary
vertex consistent with the average beam spot position
and with at least three associated tracks. The efficiency
of this requirement is expected to be greater than 99.9%
in events containing a prompt photon with Eγ
and lying within the calorimeter acceptance. The total
number of selected events in data after this requirement
is 9.6 million. The remaining amount of non-collision
background is estimated using control samples collected
with dedicated, low threshold triggers that are activated
in events where either no proton bunch or only one of the
two beams crosses the interaction region. The estimated
contribution to the final photon sample is less than 0.1%
and is therefore neglected.
T> 15 GeV
B. Simulated events
To study the characteristics of signal and back-
ground events, Monte Carlo (MC) samples are gener-
ated using PYTHIA 6.4.21 [31], a leading-order parton-
shower MC generator, with the modified leading order
MRST2007 [32] parton distribution functions (PDFs). It
accounts for QED radiation emitted off quarks in the
initial state (ISR) and in the final state (FSR). PYTHIA
simulates the underlying event using the multiple-parton
interaction model, and uses the Lund string model for
hadronisation [33]. The event generator parameters are
set according to the ATLAS MC09 tune [34], and the
detector response is simulated using the GEANT4 pro-
gram [35]. These samples are then reconstructed with
the same algorithms used for data. More details on the
event generation and simulation infrastructure are pro-
vided in Ref. [36]. For the study of systematic uncer-
tainties related to the choice of the event generator and
the parton shower model, alternative samples are also
generated with HERWIG 6.5 [37]. This generator also uses
LO pQCD matrix elements, but has a different parton
shower model (angle-ordered instead of pT-ordered), a
different hadronisation model (the cluster model) and a
different underlying event model, which is generated us-
ing the JIMMY package [38] with multiple parton interac-
tions enabled. The HERWIG event generation parameters
are also set according to the MC09 tune.
To study the main background processes, simulated
samples of all relevant 2→2 QCD hard subprocesses in-
volving only partons are used. The prompt photon con-
tribution arising from initial and final state radiation
emitted off quarks is removed from these samples in stud-
ies of the background.
Two different simulated samples are employed to study
the properties of the prompt photon signal. The first
sample consists of leading-order γ-jet events, and con-
tains primarily direct photons produced in the hard sub-
processes qg → qγ and q¯ q → gγ. The second signal sam-
ple includes ISR and FSR photons emitted off quarks in
all 2→2 QCD processes involving only quarks and glu-
ons in the hard scatter. This sample is used to study
the contribution to the prompt photon signal by photons
from fragmentation, or from radiative corrections to the
direct process, that are less isolated than those from the
LO direct processes.
Finally, a sample of W → eν simulated events is used
for the efficiency and purity studies involving electrons
from W decays.
IV. THEORETICAL PREDICTIONS
The expected isolated prompt photon production cross
section as a function of the photon transverse energy Eγ
is calculated with the JETPHOXMonte Carlo program [13],
which implements a full NLO QCD calculation of both
the direct and the fragmentation contributions to the to-
tal cross section. In the calculation performed for this
measurement, the total transverse energy carried by the
partons inside a cone of radius R = 0.4 in the η−φ space
around the photon direction is required to be less than
4 GeV. The NLO photon fragmentation function [39] and
the CTEQ 6.6 parton density functions [40] provided by
the LHAPDF package [41] are used. The nominal renor-
malization (µR), factorization (µF) and fragmentation
(µf) scales are set to the photon transverse energy Eγ
Varying the CTEQ PDFs within the 68% C.L. intervals
causes the cross section to vary between 5% and 2% as
ETincreases between 15 and 100 GeV. The variation of
the three scales independently between 0.5 and 2.0 times
the nominal scale changes the predicted cross section by
20% at low ET and 10% at high ET, while the varia-
tion of the isolation requirement between 2 and 6 GeV
changes the predicted cross section by no more than 2%.
The MSTW 2008 PDFs [42] are used as a cross-check of
the choice of PDF. The central values obtained with the
MSTW 2008 PDFs are between 3 and 5% higher than
those predicted using the CTEQ 6.6 PDFs.
The NLO calculation provided by JETPHOX predicts a
T
T.

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cross section at parton level, which does not include ef-
fects of hadronisation nor the underlying event and pileup
(i.e. multiple proton-proton interactions in the same
bunch crossing).The non-perturbative effects on the
cross section due to hadronisation are evaluated using the
simulated PYTHIA and HERWIG signal samples described in
Section IIIB, by evaluating the ratio of the cross section
before and after hadronisation and underlying event sim-
ulation. The ratios are estimated to be within 1% (2%)
of unity in PYTHIA (HERWIG) for all ET and η regions
under study. To account for the effect of the underly-
ing event and pileup on the measured isolation energy, a
correction to the photon transverse isolation energy mea-
sured in data is applied, using a procedure described in
Section VC.
V.
IDENTIFICATION AND ISOLATION
PHOTON RECONSTRUCTION,
A.Photon reconstruction and preselection
Photon reconstruction is seeded by clusters in the elec-
tromagnetic calorimeter with transverse energies exceed-
ing 2.5 GeV, measured in projective towers of 3×5 cells
in η × φ in the second layer of the calorimeter. An at-
tempt is made to match these clusters with tracks that
are reconstructed in the inner detector and extrapolated
to the calorimeter. Clusters without matching tracks are
directly classified as “unconverted” photon candidates.
Clusters with matched tracks are considered as elec-
tron candidates. To recover photon conversions, clusters
matched to pairs of tracks originating from reconstructed
conversion vertices in the inner detector are considered
as “converted” photon candidates. To increase the recon-
struction efficiency of converted photons, conversion can-
didates where only one of the two tracks is reconstructed
(and does not have any hit in the innermost layer of the
pixel detector) are also retained [29, 30].
The final energy measurement, for both converted and
unconverted photons, is made using only the calorimeter,
with a cluster size that depends on the photon classifica-
tion. In the barrel, a cluster corresponding to 3×5 (η×φ)
cells in the second layer is used for unconverted photons,
while a cluster of 3×7 (η × φ) cells is used for converted
photon candidates (to compensate for the opening be-
tween the conversion products in the φ direction due to
the magnetic field). In the end-cap, a cluster size of 5×5
is used for all candidates. A dedicated energy calibra-
tion [29] is then applied separately for converted and
unconverted photon candidates to account for upstream
energy loss and both lateral and longitudinal leakage.
Photon candidates with calibrated transverse energies
(Eγ
T) above 15 GeV are retained for the successive anal-
ysis steps. To minimise the systematic uncertainties re-
lated to the efficiency measurement at this early stage of
the experiment, the cluster barycenter in the second layer
of the electromagnetic calorimeter is required to lie in the
pseudorapidity region |ηγ| < 1.37, or 1.52 ≤ |ηγ| < 1.81.
Photon candidates with clusters containing cells over-
lapping with few problematic regions of the calorimeter
readout are removed. After the above preselection, 1.3
million photon candidates remain in the data sample.
B.Photon identification
Shape variables computed from the lateral and longitu-
dinal energy profiles of the shower in the calorimeters are
used to discriminate signal from background. The exact
definitions of the discriminating variables are provided
in Appendix A. Two sets of selection criteria (denoted
“loose” and “tight”) are defined, each based on indepen-
dent requirements on several shape variables. The se-
lection criteria do not depend on the photon candidate
transverse energy, but vary as a function of the photon
reconstructed pseudorapidity, to take into account varia-
tions in the total thickness of the upstream material and
in the calorimeter geometry.
1.Loose identification criteria
A set of loose identification criteria for photons is de-
fined based on independent requirements on three quan-
tities:
• the leakage Rhadin the first layer of the hadronic
compartment beyond the electromagnetic cluster,
defined as the ratio between the transverse energy
deposited in the first layer of the hadronic calorime-
ter and the transverse energy of the photon candi-
date;
• the ratio Rη between the energy deposits in 3 × 7
and 7 × 7 cells in the second layer of the electro-
magnetic calorimeter;
• the RMS width w2 of the energy distribution
along η in the second layer of the electromagnetic
calorimeter.
True prompt photons are expected to have small hadronic
leakage (typically below 1–2%) and a narrower energy
profile in the electromagnetic calorimeter, more concen-
trated in the core of the cluster, with respect to back-
ground photon candidates from jets.
The loose identification criteria on Rhad, Rη and w2
are identical for converted and unconverted candidates.
They have been chosen, using simulated prompt pho-
ton events, in order to obtain a prompt photon effi-
ciency, with respect to reconstruction, rising from 97%
at Eγ
both converted and unconverted photons [30]. The num-
ber of photon candidates in data passing the preselection
and loose photon identification criteria is 0.8 million.
T= 20 GeV to above 99% for Eγ
T> 40 GeV for

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2.Tight identification criteria
To further reject the background, the selection require-
ments on the quantities used in the loose identification
are tightened. In addition, the transverse shape along
the φ direction in the second layer (the variable Rφ, com-
puted from the ratio between the energy deposits in 3×3
and 3×7 cells) and the shower shapes in the first layer of
the calorimeter are examined. Several variables that dis-
criminate single photon showers from overlapping nearby
showers (in particular those which originate from neutral
meson decays to photon pairs) are computed from the
energy deposited in the first layer:
• the total RMS width ws,totof the energy distribu-
tion along η;
• the asymmetry Eratiobetween the first and second
maxima in the energy profile along η;
• the energy difference ∆E between the second max-
imum and the minimum between the two maxima;
• the fraction Fsideof the energy in seven strips cen-
tered (in η) around the first maximum that is not
contained in the three core strips;
• the RMS width ws,3of the energy distribution com-
puted with the three core strips.
The first variable rejects candidates with wide show-
ers consistent with jets. The second and third variables
provide rejection against cases where two showers give
separated energy maxima in the first layer. The last two
variables provide rejection against cases where two show-
ers are merged in a wider maximum.
The tight selection criteria are optimised indepen-
dently for unconverted and converted photons to account
for the quite different developments of the showers in each
case. They have been determined using samples of simu-
lated signal and background events prior to data taking,
aiming to obtain a average efficiency of 85% with respect
to reconstruction for true prompt photons with trans-
verse energies greater than 20 GeV [30]. About 0.2 mil-
lion photon candidates are retained in the data sample
after applying the tight identification requirements.
C.Photon transverse isolation energy
An experimental isolation requirement, based on the
transverse energy deposited in the calorimeters in a cone
around the photon candidate, is used in this measure-
ment to identify isolated prompt photons and to further
suppress the main background from π0(or other neu-
tral hadrons decaying in two photons), where the π0is
unlikely to carry the full original jet energy. The trans-
verse isolation energy (Eiso
T) is computed using calorime-
ter cells from both the electromagnetic and hadronic
calorimeters, in a cone of radius 0.4 in the η − φ space
around the photon candidate. The contributions from
5×7 electromagnetic calorimeter cells in the η −φ space
around the photon barycenter are not included in the
sum. The mean value of the small leakage of the photon
energy outside this region, evaluated as a function of the
photon transverse energy, is subtracted from the mea-
sured value of Eiso
T. The typical size of this correction is
a few percent of the photon transverse energy. After this
correction, Eiso
T
for truly isolated photons is nominally
independent of the photon transverse energy.
In order to make the measurement of Eiso
parable to parton-level theoretical predictions, such as
those described in Section IV, Eiso
by subtracting the estimated contributions from the un-
derlying event and from pileup. This correction is com-
puted on an event-by-event basis using a method sug-
gested in Refs. [43] and [44]. Based on the standard seeds
for jet reconstruction, which are noise-suppressed three-
dimensional topological clusters [28], and for two differ-
ent pseudorapidity regions (|η| < 1.5 and 1.5 < |η| <
3.0), a kT jet-finding algorithm [45, 46], implemented in
FastJet [47], is used to reconstruct all jets without any
explicit transverse momentum threshold. During recon-
struction, each jet is assigned an area via a Voronoi tessel-
lation [48] of the η−φ space. According to the algorithm,
every point within a jet’s assigned area is closer to that
jet than any other jet. The transverse energy density for
each jet is then computed from the ratio between the jet
transverse energy and its area. The ambient transverse
energy density for the event, from pileup and underlying
event, is taken to be the median jet transverse energy
density. Finally, this ambient transverse energy density
is multiplied by the area of the isolation cone to compute
the correction to Eiso
T.
The estimated ambient transverse energy fluctuates
significantly event-by-event, reflecting the fluctuations in
the underlying event and pileup activity in the data. The
mean correction to the calorimeter transverse energy in
a cone of radius R = 0.4 for an event with one pp interac-
tion is around 440 MeV in events simulated with PYTHIA
and 550 MeV in HERWIG. In the data, the mean correction
is 540 MeV for events containing at least one photon can-
didate with ET> 15 GeV and exactly one reconstructed
primary vertex, and increases by an average of 170 MeV
with each additional reconstructed primary vertex. The
average number of reconstructed primary vertices for the
sample under study is 1.56. The distribution of measured
ambient transverse energy densities for photons passing
the tight selection criteria is shown in Fig. 1. The im-
pact of this correction on the measured cross section is
discussed in Section IXB. For a consistent comparison of
this measurement to a theoretical prediction which incor-
porates an underlying event model, the method described
above should be applied to the generated final state in or-
der to evaluate and apply the appropriate event-by-event
corrections.
After the leakage and ambient-transverse-energy cor-
rections, the Eiso
Tdistribution for direct photons in sim-
Tdirectly com-
T
is further corrected

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Ambient Transverse Energy Density [GeV/Unit Area]
00.511.522.533.54 4.55
Entries / 100 MeV
0
2000
4000
6000
8000
10000
12000
ATLAS
∫
Data 2010,
-1
L dt = 880 nb
= 7 TeV s
Tight Photons
> 15 GeV
T
E
γ
FIG. 1. The measured ambient transverse energy densities,
using the jet-area method, for events with at least one tight
photon. The ambient transverse energy contains contribu-
tions from both the underlying event and pileup. The broad
distribution reflects the large event-to-event fluctuations.
ulated events is centered at zero, with an RMS width of
around 1.5 GeV (which is dominated by electronic noise
in the calorimeter). In the following, all photon candi-
dates with Eiso
T< 3 GeV are considered to be experimen-
tally isolated. This criterion can be related to a cut on
the transverse isolation energy calculated at the parton
level in PYTHIA, in order to mimic the isolation criterion
implemented in JETPHOX. This parton-level isolation is
the total transverse energy of all partons that lie inside
a cone of radius R = 0.4 around the photon direction
and originated from the same quark emitting the photon
in either ISR or FSR. The efficiency of the experimental
isolation cut at 3 GeV for photons radiated off partons
in PYTHIA is close to the efficiency of a parton-level isola-
tion cut at 4 GeV. This cut on the parton-level isolation
is equivalent to the same cut on a particle-level isolation,
which measures the transverse energy in a cone of radius
R = 0.4 around the photon after hadronisation (with the
underlying event removed). The experimental isolation
criterion is expected to reject roughly 50% of background
candidates with transverse energy greater than 15 GeV.
About 110 thousand photon candidates satisfy the
tight identification criteria and have Eiso
around 74 thousand are reconstructed as unconverted
photons and 36 thousand as converted photons.
transverse energy distribution of these candidates is
shown in Fig. 2. For comparison, the initial distribu-
tion of all photon candidates after the reconstruction and
preselection is also shown.
T
< 3 GeV:
The
[GeV]
T
E
γ
20 304050 6070 8090100
Entries/5 GeV
2
10
3
10
4
10
5
10
6
10
candidates)
γ
Data 2010 (all
) γ
Data 2010 (tight, isolated
-1
Ldt = 880 nb
∫
= 7 TeV, s
ATLAS
FIG. 2. Transverse energy distribution of photon candidates
selected in data, after reconstruction and preselection (open
triangles) and after requiring tight identification criteria and
transverse isolation energy lower than 3 GeV (full circles).
The photon candidates have pseudorapidity |ηγ| < 1.37 or
1.52 ≤ |ηγ| < 1.81.
VI.SIGNAL EFFICIENCY
A.Reconstruction and preselection efficiency
The reconstruction and preselection efficiency, εreco, is
computed from simulated events as a function of the true
photon transverse energy for each pseudorapidity interval
under study. It is defined as the ratio between the num-
ber of true prompt photons that are reconstructed – af-
ter preselection – in a certain pseudorapidity interval and
have reconstructed Eiso
T< 3 GeV, and the number of true
photons with true pseudorapidity in the same pseudora-
pidity interval and with particle-level transverse isolation
energy lower than 4 GeV. The efficiency of the require-
ment Eγ
T> 15 GeV for prompt photons of true transverse
energy greater than the same threshold is taken into ac-
count in Section VIII.
The reconstruction and preselection efficiencies are cal-
culated using a cross-section-weighted mixture of direct
photons produced in simulated γ-jet events and of frag-
mentation photons produced in simulated dijet events.
The uncertainty on the reconstruction efficiency due to
the difference between the efficiency for direct and frag-
mentation photons, and the unknown ratio of the two
in the final sample of selected signal photons, are taken
into account as sources of systematic uncertainty in Sec-
tion IXA.
The average reconstruction and preselection efficiency
for isolated prompt photons with |ηγ
|ηγ
to the inefficiency of the reconstruction algorithms at low
photon transverse energy (a few %), to the inefficiency
of the isolation requirement (5%) and to the acceptance
loss from a few inoperative optical links of the calorimeter
true| < 1.37 or 1.52 ≤
true| < 1.81 is around 82%; the 18% inefficiency is due

Page 7

7
readout [49].
B.Identification efficiency
The photon identification efficiency, εID, is similarly
computed as a function of transverse energy in each pseu-
dorapidity region. It is defined as the efficiency for recon-
structed (true) prompt photons, with measured Eiso
GeV, to pass the tight photon identification criteria de-
scribed in Section VB. The identification efficiency is
determined from simulation after shifting the photon
shower shapes by “shower-shape correction factors” that
account for the observed average differences between the
discriminating variables’ distributions in data and MC.
The simulated sample used contains all the main QCD
signal and background processes. The average differences
between data and simulation are computed after apply-
ing the tight identification criteria. The typical size of
the correction to the MC efficiency is −3% and is always
between −5% and zero. The photon identification effi-
ciency after all selection criteria (including isolation) are
applied is shown in Fig. 3 and in Table I, including the
systematic uncertainties that are discussed in more detail
in Section IXA. The efficiencies for converted photons
are, on average, 3-4% lower than for unconverted photons
with the same pseudorapidity and transverse energy.
T< 3
TABLE I. Isolated prompt photon identification efficiency in
the intervals of the photon pseudorapidity and transverse en-
ergy under study.
Eγ
[GeV]
T
Identification Efficiency
[%]
0.00 ≤ |ηγ| < 0.60 0.60 ≤ |ηγ| < 1.37 1.52 ≤ |ηγ| < 1.81
63.3 ± 6.663.5 ± 6.9
73.5 ± 6.1 73.5 ± 6.8
80.2 ± 5.480.8 ± 5.7
85.5 ± 4.585.3 ± 4.8
85.2 ± 3.989.3 ± 4.3
89.2 ± 3.392.1 ± 3.6
91.3 ± 3.194.1 ± 2.8
92.2 ± 2.694.8 ± 2.6
[15,20)
[20,25)
[25,30)
[30,35)
[35,40)
[40,50)
[50,60)
[60,100)
72.2 ± 8.4
81.6 ± 8.3
86.7 ± 6.6
90.4 ± 5.9
92.3 ± 5.0
93.5 ± 4.6
93.9 ± 3.6
94.2 ± 2.9
As a cross-check, photon identification efficiencies are
also inferred from the efficiencies of the same identifica-
tion criteria applied to electrons selected in data from W
decays. Events containing W → eν candidates are se-
lected by requiring: a missing transverse energy greater
than 25 GeV (corresponding to the undetected neutrino);
an opening azimuthal angle larger than 2.5 radians be-
tween the missing transverse energy vector and any en-
ergetic jets (ET > 15 GeV) in the event; an electron
transverse isolation energy in a cone of radius 0.4 in the
η−φ space smaller than 0.3 times the electron transverse
momentum; and a track, associated to the electron, that
passes track-quality cuts, such as a large amount of tran-
sition radiation produced in the TRT and the presence
Identification efficiency
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
Identification efficiency
= 7 TeVsSimulation,
systematic uncertainty
ATLAS
|<0.6
< 3 GeV
γ
η |
E
iso
T
Identification efficiency
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
Identification efficiency
|<1.37
γ
η | ≤
< 3 GeV
0.6
iso
T
E
[GeV] [GeV]
TT
γγ
EE
20203030404050506060707080809090100100
Identification efficiency
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
Identification efficiency
|<1.81
γ
η | ≤
< 3 GeV
1.52
iso
T
E
FIG. 3. Efficiency of the tight identification criteria as a func-
tion of the reconstructed photon transverse energy for prompt
isolated photons. Systematic uncertainties are included.
of hits in the silicon trackers. These selection criteria,
which do not rely on the shape of the electron shower
in the calorimeter, are sufficient to select a W → eν
sample with a purity greater than 95%. The identifi-
cation efficiency of converted photons is taken from the
efficiency for selected electrons to pass the tight photon
selection criteria. This approximation is expected to hold
to within 3% from studies of simulated samples of con-
verted isolated prompt photons and of isolated electrons
from W decays. For unconverted photons, the electrons
in data are used to infer shower-shape corrections. These
corrections are then applied to unconverted photons in
simulation, in order to calculate the unconverted photon
efficiency from Monte Carlo. The results from the elec-
tron extrapolation method are consistent with those from
the simulation, with worse precision due to the limited
statistics of the selected electron sample.
C.Trigger efficiency
The efficiency of the calorimeter trigger, relative to the
photon reconstruction and identification selection, is de-
fined as the probability for a true prompt photon, passing
the tight photon identification criteria and with Eiso
GeV, to pass the trigger selection. It is estimated in two
steps. First, using a prescaled sample of minimum bias
triggers, the efficiency of a lower threshold (≈ 3.5 GeV)
level-1 calorimeter trigger is determined. The measured
efficiency of this trigger is 100% for all photon candidates
with reconstructed Eγ
T> 15 GeV passing tight identifi-
cation criteria. Then, the efficiency of the high-level trig-
T< 3

Page 8

8
[GeV]
T
E
γ
02468 1012141618 20
trigger efficiency
0
0.2
0.4
0.6
0.8
1
-1
Ldt = 880 nb
∫
Data 2010,
Minimum Bias MC
ATLAS
= 7 TeVs
FIG. 4.
structed isolated photon passing the tight identification crite-
ria, as measured in data (circles) and simulated background
events (triangles).
Photon trigger efficiency, with respect to recon-
ger is measured using the sample of events that pass the
level-1 calorimeter trigger with the 3.5 GeV threshold.
The trigger efficiency for reconstructed photon candi-
dates passing tight selection criteria, isolated and with
Eγ
stant within uncertainties over the full ETand η ranges
under study. The quoted uncertainty is obtained from
the estimation of the possible bias introduced by using
photon candidates from data, which are a mixture of sig-
nal and background photon candidates.
Carlo samples the absolute difference of the trigger effi-
ciency for a pure signal sample and for a pure background
sample is found to be smaller than 0.5% for isolated tight
photon candidates with Eγ
T> 15 GeV.
A comparison between the high-level trigger efficiency
in data and in the background predicted by the simula-
tion is shown in Fig. 4.
T> 15 GeV is found to be εtrig= (99.5 ± 0.5)%, con-
Using Monte
VII.BACKGROUND SUBTRACTION AND
SIGNAL YIELD DETERMINATION
A non-negligible residual contribution of background
candidates is expected in the selected photon sample,
even after the application of the tight identification and
isolation requirements. Two methods are used to esti-
mate the background contribution from data and to mea-
sure the prompt photon signal yield. The first one is used
for the final cross section measurement, while the second
one is used as a cross check of the former. All estimates
are made separately for each region of pseudorapidity and
transverse energy.
A.Isolation vs. identification sideband counting
method
The first technique for measuring the prompt photon
yield uses the number of photon candidates observed in
the sidebands of a two-dimensional distribution to esti-
mate the amount of background in the signal region. The
two dimensions are defined by the transverse isolation en-
ergy Eiso
Ton one axis, and the photon identification (γID)
of the photon candidate on the other axis. On the iso-
lation axis, the signal region contains photon candidates
with Eiso
T
< 3 GeV, while the sideband contains pho-
ton candidates with Eiso
T
> 5 GeV. On the other axis,
photon candidates passing the tight identification crite-
ria (“tight” candidates) belong to the γIDsignal region,
while those that fail the tight identification criteria but
pass a background-enriching selection (“non-tight” can-
didates) belong to the γID sideband. The non-tight se-
lection requires photon candidates to fail at least one of
a subset of the photon tight identification criteria, but to
pass all criteria not in that subset. All the shower shape
variables based on the energy measurement in the first
layer of the electromagnetic calorimeter are used to define
the background enriching selection, with the exception
of ws,tot, since it is found to be significantly correlated
with the Eiso
T
of background photon candidates, while
the photon yield measurement relies on the assumption
of negligible (or small) correlations between the trans-
verse isolation energy and the shower shape quantities
used to define the background enriching selection.
The signal region (region “A”) is therefore defined by
photon candidates passing the tight photon identifica-
tion criteria and having experimental Eiso
three background control regions consist of photon can-
didates either:
T< 3 GeV. The
• passing the tight photon identification criteria but
having experimental Eiso
T> 5 GeV (region “B”)
• having Eiso
enriching identification criteria (region “C”)
T< 3 GeV and passing the background-
• having Eiso
enriching identification criteria (region “D”).
T> 5 GeV and passing the background-
A sketch of the two dimensional plane and of the sig-
nal and background control region definitions is shown
in Fig. 5.
The method assumes that the signal contamination in
the three background control regions is small, and that
the isolation profile in the non-tight regions is the same
as that of the background in the tight regions. If these
assumptions hold, then the number of background can-
didates in the signal region can be calculated by tak-
ing the ratio of candidates in the two non-tight regions
(NC/ND), and multiplying it by the number of candi-
dates in the tight, non-isolated region (NB). The number
of isolated prompt photons passing the tight identifica-

Page 9

9
[GeV]
iso
T
E
-505101520253035
ID
γ
pass tight cuts
fail tight cuts
A
C
B
D
FIG. 5. Illustration of the two-dimensional plane, defined by
means of the transverse isolation energy and a subset of the
photon identification (ID) variables, used for estimating, from
the observed yields in the three control regions (B,C,D), the
background yield in the signal region (A).
tion criteria is therefore:
Nsig
A= NA− NBNC
ND
,(1)
where NAis the observed number of photon candidates
in the signal region.
The assumption that the signal contamination in the
background control regions is small is checked using
prompt photon MC samples. As the number of signal
events in the background control regions is always pos-
itive and non-zero, corrections are applied to limit the
effects on the final result.
modified in the following way:
For this purpose, Eq. 1 is
Nsig
A= NA− (NB− cBNsig
A)(NC− cCNsig
(ND− cDNsig
A)
A)
,(2)
where cK≡
age fractions extracted from simulation. Typical values
for cBare between 3% and 17%, increasing with the pho-
ton candidate transverse energy; for cC, between 2% and
14%, decreasing with Eγ
T. cD is always less than 2%.
The total effect of these corrections on the measured sig-
nal photon purities is typically less than 5%.
Nsig
K
Nsig
A
(for K ∈ {B,C,D}) are the signal leak-
The isolated prompt photon fraction measured with
this method, as a function of the photon reconstructed
transverse energy, is shown in Fig. 6.
of isolated prompt photon candidates measured in each
pseudorapidity and transverse energy interval are also re-
ported in Table II. The systematic uncertainties on the
measured prompt photon yield and fraction in the se-
lected sample are described in Section IXB.
The numbers
Photon fraction
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
Photon fraction
-1
Ldt = 880 nb
∫
= 7 TeV, s
Data 2010,
systematic uncertainty
ATLAS
|<0.6
< 3 GeV
γ
η |
E
iso
T
Photon fraction
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
Photon fraction
|<1.37
γ
η | ≤
< 3 GeV
0.6
iso
T
E
[GeV] [GeV]
γ
TT
EE
20203030404050506060707080809090100100
Photon fraction
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
γ
Photon fraction
|<1.81
γ
η | ≤
< 3 GeV
1.52
iso
T
E
FIG. 6. Fraction of isolated prompt photons as a function
of the photon transverse energy, as obtained with the two-
dimensional sideband method.
B.Isolation template fit method
The second method relies on a binned maximum likeli-
hood fit to the Eiso
Tdistribution of photon candidates se-
lected in data which pass the tight identification criteria.
The distribution is fit to the sum of a signal template and
a background template, determined from control samples
extracted from data. This is similar to the technique
employed in [22], but relies less on simulation for signal
and background templates. The signal template is de-
termined from the Eiso
Tdistribution of electrons from W
and Z decays, selected using the criteria described in [50].
Electrons from W decays are required to fulfill tight selec-
tion criteria on the shapes of their showers in the electro-
magnetic calorimeter and to pass track-quality require-
ments, including the presence of transition-radiation hits.
They must also be accompanied by Emiss
and the electron–Emiss
T
system must have a transverse
mass larger than 40 GeV. Electrons from Z decays are
selected with looser criteria, but the pair must have an
invariant mass close to the Z mass. A single signal tem-
plate is constructed for each region in |η|, exploiting the
independence of Eiso
T
from the transverse energy of the
object (after applying the corrections described in Sec-
tion VC) to maximize the available statistics. A small
bias is expected due to differences between the electron
and photon Eiso
Tdistributions, especially in regions where
there is significant material upstream of the calorimeter.
A shift of the signal template is applied to the electron
distributions extracted from data to compensate for the
differences between electrons and photons seen in simu-
lation. This shift, computed using simulated photon and
T
> 25 GeV,

Page 10

10
TABLE II. Observed number of isolated prompt photons in the photon transverse energy and pseudorapidity intervals under
study. The first uncertainty is statistical, the second is the systematic uncertainty, evaluated as described in Section IXB.
Isolated prompt photon yield
Eγ
T[GeV]0.00 ≤ |ηγ| < 0.600.60 ≤ |ηγ| < 1.371.52 ≤ |ηγ| < 1.81
[15,20)(119±3+12
−20) × 102(130±4
+40
−11) × 102
(72±2
+20
−7) × 102
[20,25)(501 ±12
+47
−53) × 101(578 ±18
+125
−45) × 101(304 ±10+40
−23) × 101
±6+16
−10) × 101
[25,30)(260±7
+20
−21) × 101(306 ±10
+46
−18) × 101(135
[30,35)(146±5
+9
−6) × 101(160±6
+19
−9) × 101
(73±4
+8
−5) × 101
[35,40) (82±4
+5
−4) × 101(102±4
+9
−6) × 101
(44±3
+5
−3) × 101
[40,50)(77±3
+5
−4) × 101
(98±4
+9
−7) × 101
(38±2
+3
−2) × 101
[50,60)(329 ±20+17
−14) × 100(420 ±20 ±30) × 100(147 ±16+16
−17) × 100
[60,100)(329 ±20
+19
−15) × 100(370 ±20
+30
−20) × 100(154 ±12
+12
−8) × 100
electron samples, increases from 100 MeV to 600 MeV
with increasing |ηγ|.
tracted from data for each (ET, |η|) bin, using the same
reverse-cuts procedure as in the two-dimensional side-
band technique. A simulation-based correction, typically
of the order of 3-4%, is applied to the final photon frac-
tion to account for signal which leaks into the background
template. The fit is performed in each region of |ηγ| for
the individual bins in transverse energy, and the signal
yield and fraction are extracted. An example of such
a fit is shown in Fig. 7. The results from this alterna-
tive technique are in good agreement with those from the
simpler counting method described in the previous sub-
section, with differences typically smaller than 2% and
within the systematic uncertainties that are uncorrelated
between the two methods.
The background template is ex-
C.Electron background subtraction
The background of prompt electrons misidentified as
photons needs also to be considered.
electron production mechanisms are semileptonic hadron
decays (mostly from hadrons containing heavy flavor
quarks) and decays of electroweak bosons (the largest
contribution being from W decays). Electrons from the
former are often produced in association with jets, and
have Eiso
T
profiles similar to the dominant backgrounds
from light mesons. They are therefore taken into account
and subtracted using the two-dimensional sideband tech-
nique described in Section VIIA. Conversely, electrons
from W and Z decays have Eiso
lar to those of signal photons. The contribution of this
background to the signal yield computed in Section VIIA
needs therefore to be removed before the final measure-
ment of the cross section.
The fraction of electrons reconstructed as photon can-
didates is estimated from the data, as a function of the
electron transverse energy and pseudorapidity, using a
control sample of Z → e+e−decays. The average elec-
tron misidentification probability is around 8%. Using
The dominant
T
profiles that are simi-
iso
TT
E [GeV]E [GeV]
-5-500551010151520202525
Entries / GeV
00
5050
100100
150150
200200
250250
300300
iso
Entries / GeV
< 40 GeV
| < 0.6
ATLAS
∫
γ
T
E
≤
35
η |
γ
= 7 TeVs2010 Data,
Signal Template
Background Template
Fit Result
-1
L dt = 880 nb
FIG. 7. Example of a fit to extract the fraction of prompt
photons using the isolation template technique in the region
0 ≤ |η| < 0.6 and 35 ≤ Eγ
is derived from electrons selected from W or Z decays, and
is shown with a dashed line. The background template is de-
rived from a background-enriched sample, and is represented
by a dotted line. The estimated photon fraction is 0.85 and
its statistical uncertainty is 0.01.
T< 40 GeV. The signal template
the W → eν and Z → ee cross section times branch-
ing ratio measured by ATLAS in pp collisions at√s = 7
TeV [50], the estimated fraction of photon candidates due
to isolated electrons is found to be on average ∼ 0.5%,
varying significantly with transverse energy. A maximum
contamination of (2.5% ± 0.8%) is estimated for trans-
verse energies between 40 and 50 GeV, due to the kine-
matic distribution of electrons from W and Z decays.
The uncertainties on these estimates are less than 1% of
the photon yield.

Page 11

11
VIII.CROSS SECTION MEASUREMENT
The differential cross section is measured by comput-
ing:
dσ
dEγ
T
=
NyieldU
∆Eγ
TεtriggerεrecoεID
??Ldt?
.(3)
The observed signal yield (Nyield) is divided by the
widths of the ET-intervals (∆Eγ
the photon identification efficiency (εID, determined in
Section VIB) and of the trigger efficiency relative to pho-
ton candidates passing the identification criteria (εtrigger,
determined in Section VIC). The spectrum obtained this
way, which depends on the reconstructed transverse en-
ergy of the photon candidates, is then corrected for detec-
tor energy resolution and energy scale effects using bin-
by-bin correction factors (the “unfolding coefficients” U)
evaluated using simulated samples. The corrected spec-
trum, which is then a function of the true photon energy,
is divided by the photon reconstruction efficiency εreco
(Section VIA) and by the integrated luminosity of the
data sample,?Ldt.
of the true to reconstructed ET distributions of photon
candidates, using PYTHIA isolated prompt photon simu-
lated samples. This procedure is justified by the small
bin-to-bin migrations (typically of the order of a few
%) that are expected, given the good electromagnetic
calorimeter energy resolution compared to the width of
the transverse energy intervals used in this analysis (be-
tween 5 and 40 GeV). The values of the unfolding coeffi-
cients are slightly higher than 1 and decrease as a func-
tion of ET, approaching 1. They differ from 1 by less
then 2% in the |ηγ| region between 0.0 and 0.6, and by
less than 5-7% in the other two |ηγ| regions, where more
material upstream of the electromagnetic calorimeter is
present.
T) and by the product of
The unfolding coefficients are evaluated from the ratio
IX.SYSTEMATIC UNCERTAINTIES
Several sources of systematic uncertainties on the cross
section are identified and evaluated as described in the
following sections. The total systematic uncertainty is
obtained by combining the various contributions, taking
into account their correlations: uncorrelated uncertain-
ties are summed in quadrature while a linear sum of cor-
related uncertainties is performed.
A.Reconstruction, identification, trigger
efficiencies
The systematic uncertainty on the reconstruction ef-
ficiency from the experimental isolation requirement is
evaluated from the prompt photon simulation varying the
value of the isolation criterion by the average difference
(of the order of 500 MeV) observed for electrons between
simulation and data control samples. It is 2.5% in the
pseudorapidity regions covered by the barrel calorimeter
and 4.5% in the end-caps.
The systematic uncertainty on the identification effi-
ciency due to the photon shower-shape corrections is di-
vided into two parts. The first term evaluates the impact
of treating the differences between the distributions of the
shower shape variables in data and simulation as an av-
erage shift. This uncertainty is evaluated in the following
way:
• A modified description of the detector material
is used to produce a second sample of simulated
photon candidates. These candidates have differ-
ent shower-shape distributions, due to the differ-
ent amount of material upstream of and within the
calorimeter. This alternative model contains an ad-
ditional 10% of material in the inactive volumes
of the inner detector and 10% of radiation length
in front of the electromagnetic calorimeter. This
model is estimated to represent a conservative up-
per limit of the additional detector material that is
not accounted for by the nominal simulation.
• The correction procedure is applied to the nomi-
nal simulation to estimate the differences between
the nominal and the alternative simulation. The
shifts between the discriminating variable distribu-
tions in the nominal and the alternative simulation
are evaluated, and are used to correct the shower
shape variable distributions of the nominal simula-
tion.
• The photon efficiency from the nominal simulation
is recomputed after applying these corrections, and
compared with the efficiency obtained from the al-
ternative simulation.
The difference between the efficiency estimated from the
nominal simulation (after applying the corrections) and
the efficiency measured directly in the alternative sample
(with no corrections) ranges from 3% at Eγ
to less than 1% at Eγ
T∼ 80 GeV.
The second part of the systematic uncertainty on the
identification efficiency accounts for the uncertainty on
the extracted shower-shape correction factors. The cor-
rection factors were extracted by comparing tight pho-
tons in data and simulation; to evaluate the uncertainty
associated with this choice, the same correction factors
are extracted using loose photons. The difference in the
final efficiency when applying the tight corrections and
the loose corrections is then taken as the uncertainty.
This uncertainty drops from 4% to 1% with increasing
Eγ
T.
Additional systematic uncertainties that may affect
both the reconstruction and the identification efficien-
cies are evaluated simultaneously for the product of the
two, to take into account possible correlations. These
T∼ 20 GeV

Page 12

12
sources of uncertainty include the amount of material
upstream of the calorimeter; the impact of pile-up; the
relative fraction of direct and fragmentation photons in
data with respect to simulation; the misidentification of a
converted photon as unconverted; the difference between
the PYTHIA and HERWIG simulation models; the impact
of a sporadic faulty calibration of the cell energies in the
electromagnetic calorimeter; and the imperfect simula-
tion of acceptance losses due to inoperative readout links
in the calorimeter.
Of all the uncertainties which contribute to this mea-
surement, the largest ones come from the uncertainty on
the amount of material upstream of the calorimeter (ab-
solute uncertainties ranging between 1% and 8% and are
larger at low Eγ
T), and from the uncertainty on the identi-
fication efficiency due to the photon shower-shape correc-
tions (the absolute uncertainties are in the range 1-5%,
and are larger at low Eγ
T).
The uncertainty on the trigger efficiency, evaluated as
described in Section VIC, is 0.5% and is nearly negligible
compared to all other sources.
B.Signal yield estimates
The following sources of systematic uncertainties af-
fecting the accuracy of the signal yield measurement us-
ing the two-dimensional sideband technique are consid-
ered.
1. Background isolation control region definition
The signal yield is evaluated after changing the iso-
lation control region definition. The minimum value of
Eiso
T
required for candidates in the non-isolated control
regions, which is set to 5 GeV in the nominal measure-
ment, is changed to 4 and 6 GeV. This check is sensitive
to uncertainties in the contribution of prompt photons
from QED radiation from quarks: these photons are less
isolated than those originating from the hard process. Al-
ternative measurements are also performed where a max-
imum value of Eiso
Tis set to 10 or 15 GeV for candidates
in the non-isolated control regions, in order to reduce the
correlation between the isolation variable and the shower
shape distributions seen in simulated events for candi-
dates belonging to the upper tail of the isolation distribu-
tion. The largest positive and negative variations of the
signal yield with respect to the nominal result are taken
as systematic uncertainties. The signal photon fraction
changes by at most ±2% in all the transverse energy and
pseudorapidity intervals.
2.Background photon identification control region
definition
The measurement is repeated reversing the tight iden-
tification criteria on a number of strip variables rang-
ing between two (only Fside and ws3) and five (all the
variables based on the first layer of the electromagnetic
calorimeter). The largest positive and negative variations
of the signal yield (with respect to the nominal result)
from these three alternative measurements are taken as
systematic uncertainties. The effect on the signal pho-
ton fraction decreases with increasing photon transverse
energy, and is around 10% for Eγ
GeV.
Tbetween 15 and 20
3.Signal leakage into the photon identification background
control region
From the photon identification efficiency studies, an
upper limit of 5% is set on the uncertainty on the fraction
cC of signal photons passing all the tight photon identi-
fication criteria except those used to define the photon
identification control region. The signal yields in each
Eγ
the estimated signal contamination in the photon iden-
tification control regions (cC and cD/cB) by this uncer-
tainty, and the difference with the nominal result is taken
as a systematic uncertainty. The signal fraction varia-
tions are always below 6%.
T,|ηγ| interval are thus measured again after varying
4.Signal leakage into the isolation background control
region
The fractions cBand cDof signal photons contaminat-
ing the isolation control regions depend on the relative
amount of direct and fragmentation photons in the sig-
nal selected in a certain Eγ
are characterized by larger nearby activity, and therefore
usually have slightly larger transverse isolation energies.
In the nominal measurement, the values of cBand cDare
computed with the relative fractions of direct and frag-
mentation photons predicted by PYTHIA. A systematic
uncertainty is assigned by repeating the measurement af-
ter varying these fractions between 0% and 100%. The
measured signal photon fraction varies by less than 5%.
T,|ηγ| interval, since the latter
5.Signal photon simulation
The signal yield is estimated using samples of prompt
photons simulated with HERWIG instead of PYTHIA to de-
termine the fraction of signal leaking into the three back-
ground control regions. The variations of the signal pho-
ton fractions in each Eγ
T,|ηγ| interval are below 2%.

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13
6.Correlations between the isolation and the photon
identification variables for background candidates
Non-negligible correlations between the isolation vari-
able and the photon identification quantities would affect
Eq. 2: the true number of isolated tight prompt photon
candidates would be
Nsig
A=NA−Rbkg(NB−cBNsig
A)(NC−cCNsig
(ND−cDNsig
A)
A)
(4)
where Rbkg≡
unity.
small but non-negligible correlation between the isolation
and the discriminating shower shape variables used to de-
fine the photon identification signal and background con-
trol regions. The signal yields are therefore recomputed
with the formula in Eq. 4, using for Rbkgthe value pre-
dicted by the PYTHIA background simulation, and com-
pared with the nominal results.
than 0.6% in the |ηγ| < 1.37 intervals and around 3.6%
for 1.52 ≤ |ηγ| < 1.81.
Nbkg
A
Nbkg
B
Nbkg
D
Nbkg
C
would then be different from
The simulation of background events shows a
The effect is smaller
7. Transverse isolation energy corrections
The effects of the Eiso
event on the estimated signal yield are also investigated.
As this is an event-by-event correction, it cannot be un-
folded from the observed cross section. The impact of
this correction is evaluated by estimating the signal yield,
with and without the correction applied, for events with
only one reconstructed primary vertex (to eliminate any
effects of pileup). The estimated signal yields using the
uncorrected values of Eiso
T, normalized to the yields de-
rived using the corrected values, show no trend in Eγ
or η. Furthermore, the impact on the cross section of
the event-by-event corrections is equivalent to that of an
average correction of 540 MeV applied to the transverse
isolation energies of all photon candidates. Similar stud-
ies in PYTHIA and HERWIG MC yield identical results.
T
correction for the underlying
T
C. Unfolding coefficients
The unfolding coefficients used to correct the measured
cross section for ETbin-by-bin migrations are computed
using simulated samples. There are three sources of un-
certainties on these coefficients.
1.Energy scale uncertainty
The uncertainty on the energy scale was estimated to
be ±3% in test beam studies [51], and is confirmed to be
below this value from the comparison of the Z → e+e−
invariant mass peak in data and Monte Carlo. The un-
folding coefficients are thus recomputed using simulated
signal events where the true photon energy is shifted by
±3%. The coefficients change by ±10%. This uncer-
tainty introduces a relative uncertainty of about 10% on
the measured cross section which is fully correlated be-
tween the different Eγ
Tintervals within each pseudora-
pidity range.
2.Energy resolution uncertainty
The uncertainty on the energy resolution may affect
bin-by-bin migrations between adjacent ET bins. Test
beam studies indicate agreement between the sampling
term of the resolution between data simulation within
20% relative. Furthermore, studies of the Z → e+e−in-
variant mass distribution in data indicate that the con-
stant term of the calorimeter energy resolution is below
1.5% in the barrel and 3.0% in the end-cap (it is 0.7%
in the simulation). The unfolding coefficients are thus
recomputed after the reconstructed energy of simulated
photons smearing to take into account a 20% relative in-
crease of the sampling term and a constant term of 1.5%
in the barrel and 3.0% in the end-cap. The resulting vari-
ation of the unfolding coefficients is always less than 1%.
The uncertainty arising from non-gaussian tails of the
energy resolution function is estimated by recomputing
the coefficients using a prompt photon simulation where
a significant amount of material is added to the detector
model. The variations of the unfolding coefficients are
smaller than 1% in all the pseudorapidity and transverse
energy intervals under study.
3.Simulated photon transverse energy distribution
The unfolding coefficients, computed in Eγ
of non-negligible size, depend on the initial Eγ
tion predicted by PYTHIA. An alternative unfolding tech-
nique [52] is therefore used, which relies on the repeated
application of Bayes’ theorem to iteratively obtain an
improved estimate of the unfolded spectrum. This tech-
nique relies less on the simulated original ET distribu-
tion of the prompt photons. The differences between the
cross-sections estimated using the bin-by-bin unfolding
and the iterative Bayesian unfolding are within 2%, and
are taken into account as an additional systematic uncer-
tainty.
Tintervals
Tdistribu-
D.Luminosity
The integrated luminosity is determined for each run
by measuring interaction rates using several ATLAS sub-
detectors at small angles to the beam line, with the abso-
lute calibration obtained from beam position scans [53].
The relative systematic uncertainty on the luminosity

Page 14

14
measurement is estimated to be 11% and translates di-
rectly into a 11% relative uncertainty on the cross section.
X.RESULTS AND DISCUSSION
The measured inclusive isolated prompt photon pro-
duction cross sections dσ/dEγ
and 10. They are presented as a function of the photon
transverse energy, for each of the three considered pseu-
dorapidity intervals. They are also presented in tabular
form in Appendix B. The measurements extend from
Eγ
T= 100 GeV spanning almost three
orders of magnitude. The data are compared to NLO
pQCD calculations, obtained with the JETPHOX program
as described in Section IV. The error bars on the data
points represent the combination of the statistical and
systematic uncertainties (summed in quadrature): sys-
tematic uncertainties dominate over the whole considered
kinematic range. The contribution from the luminosity
uncertainty (11%) is shown separately (dotted bands) as
it represents a possible global offset of all the measure-
ments. The total systematic uncertainties on the theoret-
ical predictions are represented with a solid band. They
are obtained by summing in quadrature the contributions
from the scale uncertainty, the PDF uncertainty (at 68%
C.L.) and the uncertainty associated with the choice of
the parton-level isolation criterion. The same quantities
are also shown, in the bottom panels of Fig. 8, 9, and
10, after having been normalized to the expected NLO
pQCD cross sections.
In general, the theoretical predictions agree with the
measured cross sections for Eγ
and in the two pseudorapidity regions |ηγ| < 0.6 and
0.6 ≤ |ηγ| < 1.37, the cross section predicted by JETPHOX
is larger than that measured in data. Such low transverse
energies at the LHC correspond to extremely small val-
ues of xT= 2Eγ
are less accurate. In such a regime the appropriate values
of the different scales are not clearly defined, and the un-
certainties associated with these scales in the theoretical
predictions may not be well modeled by simple varia-
tions of any one scale about the default value of Eγ
As the low-Eγ
Tregion is where the fragmentation com-
ponent has the most significant contribution to the total
cross section, the total uncertainty associated with the
NLO predictions at low Eγ
Tmay be underestimated.
Tare shown in Fig. 8, 9,
T= 15 GeV to Eγ
T> 25 GeV. For lower ET
T/√s, where NLO theoretical predictions
T[54].
XI.CONCLUSION
The inclusive isolated prompt photon production cross
section in pp collisions at a center-of-mass energy√s = 7
TeV has been measured using 880 nb−1of pp colli-
sion data collected by the ATLAS detector at the Large
Hadron Collider.
The differential cross section has been measured as a
function of the prompt photon transverse energy between
]
-1
[pb GeV
γ
/dE
σ
d
σ
d
TT
11
1010
22
1010
33
1010
44
1010
]
-1
[pb GeV
γ
/dE
-1
Ldt = 880 nb
∫
Data 2010,
luminosity uncertainty
JETPHOX NLO pQCD
γ
T
=E
R
µ
=
F
µ
=
f
µ
CTEQ 6.6,
JETPHOX systematic uncertainty
= 7 TeVs
|<0.6
γ
η |
< 3 GeV
iso
T
E
ATLAS
[GeV] [GeV]
γ
TT
EE
20203030404050506060707080809090100100
data/theory
0.60.6
0.80.8
11
1.21.2
1.41.4
γ
data/theory
FIG. 8. Measured (dots) and expected (full line) inclusive
prompt photon production cross sections, as a function of the
photon transverse energies above 15 GeV and in the pseudo-
rapidity range |ηγ| < 0.6. The bottom panel shows the ratio
between the measurement and the theoretical prediction.
]
-1
[pb GeV
γ
/dE
σ
d
σ
d
TT
11
1010
22
1010
33
1010
44
1010
]
-1
[pb GeV
γ
/dE
-1
Ldt = 880 nb
∫
Data 2010,
luminosity uncertainty
JETPHOX NLO pQCD
γ
T
=E
R
µ
=
F
µ
=
f
µ
CTEQ 6.6,
JETPHOX systematic uncertainty
= 7 TeVs
γ
η | ≤
0.6|<1.37
< 3 GeV
iso
T
E
ATLAS
[GeV] [GeV]
γ
TT
EE
20203030404050506060707080809090100100
data/theory
0.60.6
0.80.8
11
1.21.2
1.41.4
γ
data/theory
FIG. 9. Measured (dots) and expected (full line) inclusive
prompt photon production cross sections, as a function of the
photon transverse energies above 15 GeV and in the pseudo-
rapidity range 0.6 ≤ |ηγ| < 1.37. The bottom panel shows
the ratio between the measurement and the theoretical pre-
diction.

Page 15

15
]
-1
[pb GeV
γ
/dE
σ
d
σ
d
TT
11
1010
22
1010
33
10 10
44
1010
]
-1
[pb GeV
γ
/dE
-1
Ldt = 880 nb
∫
Data 2010,
luminosity uncertainty
JETPHOX NLO pQCD
γ
T
=E
R
µ
=
F
µ
=
f
µ
CTEQ 6.6,
JETPHOX systematic uncertainty
= 7 TeVs
|<1.81
γ
η | ≤
1.52
< 3 GeV
iso
T
E
ATLAS
[GeV] [GeV]
γ
TT
EE
2020 3030 4040505060607070808090 90100100
data/theory
0.60.6
0.80.8
11
1.21.2
1.41.4
γ
data/theory
FIG. 10. Measured (dots) and expected (full line) inclusive
prompt photon production cross sections, as a function of the
photon transverse energies above 15 GeV and in the pseudo-
rapidity range 1.52 ≤ |ηγ| < 1.81. The bottom panel shows
the ratio between the measurement and the theoretical pre-
diction.
15 and 100 GeV, in the three pseudorapidity intervals
|ηγ| < 0.6, 0.6 ≤ |ηγ| < 1.37 and 1.52 ≤ |ηγ| < 1.81, esti-
mating the background from the selected photon sample
and using the photon identification efficiency measure-
ment described in this paper. The photon identification
using the fine granularity of the calorimeters. A photon
isolation criterion is used, after an in situ subtraction
of the effects of the underlying event that may also be
applied to theoretical predictions.
The observed cross sections rapidly decrease as a func-
tion of the increasing photon transverse energy, span-
ning almost three orders of magnitude. The precision of
the measurement is limited by its systematic uncertainty,
which receives important contributions from the energy
scale uncertainty, the luminosity, the photon identifica-
tion efficiency, and the uncertainty on the residual back-
ground contamination in the selected photon sample.
The NLO pQCD predictions agree with the observed
cross sections for transverse energies greater than 25
GeV, while for transverseenergies below 25 GeV the cross
sections predicted by JETPHOX are higher than measured.
However, the precision of this comparison below 25 GeV
is limited by large systematic uncertainties on the mea-
surement and on the theoretical predictions at such low
values of xT= 2Eγ
The measured prompt photon production cross section
is more than a factor of thirty larger than that measured
at the Tevatron, and a factor of 104larger than for photo-
production at HERA, assuming a similar kinematic range
in transverse energy and pseudorapidity. This will allow
the extension of the measurement up to energies in the
TeV range after only a few years of data taking at the
LHC.
T/√s.
XII.ACKNOWLEDGEMENTS
We wish to thank CERN for the efficient commission-
ing and operation of the LHC during this initial high-
energy data-taking period as well as the support staff
from our institutions without whom ATLAS could not
be operated efficiently.
We acknowledge the support of ANPCyT, Argentina;
YerPhI, Armenia; ARC, Australia; BMWF, Austria;
ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP,
Brazil; NSERC, NRC and CFI, Canada; CERN; CON-
ICYT, Chile; CAS, MOST and NSFC, China; COL-
CIENCIAS, Colombia; MSMT CR, MPO CR and VSC
CR, Czech Republic; DNRF, DNSRC and Lundbeck
Foundation, Denmark; ARTEMIS, European Union;
IN2P3-CNRS, CEA-DSM/IRFU, France; GNAS, Geor-
gia; BMBF, DFG, HGF, MPG and AvH Foundation,
Germany; GSRT, Greece; ISF, MINERVA, GIF, DIP and
Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS,
Japan; CNRST, Morocco; FOM and NWO, Netherlands;
RCN, Norway; MNiSW, Poland; GRICES and FCT,
Portugal; MERYS (MECTS), Romania; MES of Rus-
sia and ROSATOM, Russian Federation; JINR; MSTD,
Serbia; MSSR, Slovakia; ARRS and MVZT, Slovenia;
DST/NRF, South Africa; MICINN, Spain; SRC and
Wallenberg Foundation, Sweden; SER, SNSF and Can-
tons of Bern and Geneva, Switzerland; NSC, Taiwan;
TAEK, Turkey; STFC, the Royal Society and Lever-
hulme Trust, United Kingdom; DOE and NSF, United
States of America.
The crucial computing support from all WLCG part-
ners is acknowledged gratefully, in particular from
CERN and the ATLAS Tier-1 facilities at TRIUMF
(Canada), NDGF (Denmark, Norway, Sweden), CC-
IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF
(Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Tai-
wan), RAL (UK) and BNL (USA) and in the Tier-2 fa-
cilities worldwide.
[1] A. L.
Rockefeller), Phys. Lett. B94, 106 (1980).
S. Angelis
et al.
(CERN-Columbia-Oxford-[2] P. Aurenche, R. Baier, M. Fontannaz, and D. Schiff,
Nucl. Phys. B297, 661 (1988).