ATLAS-CONF-2012-121 15August2012
ATLAS NOTE
ATLAS-CONF-2012-121
August 15, 2012
Measurement of the correlation of jets with high p
Tisolated prompt photons in lead-lead collisions at √
s
NN= 2.76 TeV with the ATLAS detector at the LHC
ATLAS Collaboration
Abstract
Prompt photons produced in heavy ion collisions are an important channel for studying the effects of jet quenching in the hot, dense medium. Photons provide a means to estimate the expected transverse energy of jets which are produced in the medium, and thus are a tool to probe the physics of jet quenching more precisely both through jet spectra and fragmen- tation properties. The ATLAS detector measures photons with its hermetic, longitudinally segmented calorimeter, which gives excellent spatial and energy resolution, and detailed in- formation about the shower shape of each measured photon. This gives significant rejection against the expected background from neutral pions in jets. Rejection against jet fragmen- tation products is further enhanced by isolation criteria, which can be based on calorimeter energy or the presence of high
pTtracks. Jets are measured with the anti-k
talgorithm for three different radii and their performance in photon-jet events been assessed quantitatively.
First results on the correlation of back-to-back isolated prompt photons with jets from ap- proximately 0.13 nb
−1of lead-lead data are shown, as a function of transverse momentum and centrality. The photons are selected to have 60
< pγT <90 GeV and
|η| <1.3. The jets have
pjetT >25 GeV and
|ηjet|<2.1. The measured spectra are corrected to remove the effect of detector acceptance and resolution compared to expectations from PYTHIA. Centrality- dependent shifts in the mean fractional energy carried by the jet (x
Jγ) and the per-photon jet yield (R
Jγ) are observed. No corresponding changes are seen in the
∆φJγdistributions.
c
Copyright 2012 CERN for the benefit of the ATLAS Collaboration.
Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.
1 Introduction
While one of the first results from lead-lead collisions at the Large Hadron Collider (LHC) was the observation of strongly modified di-jet asymmetry distributions [1], the detailed physical mechanism is still not understood in detail. One of the limiting factors in achieving this is having a proper calibration of the initial energy of the jets. Di-jet measurements are limited by the fact that one does not know whether or not the leading jet was itself quenched. Single jet measurements [2, 3] are themselves limited by the fact that, at a given measured jet
pT, they are integrating over a range of initial jet energies. Replacing one of the jets with a penetrating probe, such as a photon or weak boson (W or
Z), offers the possibility of calibrating the energy of the initial jet. This was first proposed by Wang and collaborators in Ref. [4].
As an important prerequisite to making photon-jet measurements, a preliminary measurement of photon yields per collision in heavy ion collisions has been performed by ATLAS using the lead-lead data [7]. In general, “prompt” photons are those that do not arise from hadron decays. Prompt photons are themselves expected to have two primary sources. The first is direct emission, which proceeds via quark-gluon Compton scattering
qg →qγor quark-antiquark annihilation
qq →gγ. The second is the
“fragmentation” contribution, from the production of a single hard photon during parton fragmentation.
At leading order, there is a meaningful distinction between the two processes, but at next-to-leading-order (NLO) and beyond the two cannot be unambiguously separated. In general, it is desirable to remove the fragmentation photons, as their transverse momentum does not balance against a recoiling jet to the same extent as direct photons. In order to remove QCD background events from di-jet processes, as well as fragmentation photons an “isolation” criterion is typically applied within a cone of a well-defined radius relative to the photon direction. The isolation energy requirement can be applied as a fraction of the photon energy, or as a constant energy threshold. In either case, these can be applied consistently to a QCD calculation such that prompt photon rates can be calculated [5, 6].
After the first measurements of prompt isolated photons in lead-lead collisions by ATLAS [7], this note presents the ongoing work toward first measurements of the correlation of photons with jets in heavy ion collisions as a function of collision centrality. In heavy ion collisions, prior to the turn-on of the LHC, there have been photon-hadron correlation measurements from PHENIX [8] and STAR [9] to probe energy loss, but no correlations with jets. Photon-jet correlations have been measured in lead-lead collisions already by the CMS collaboration [11], who found both a reduction of rates of jets associated with photons, and a decreasing transverse energy fraction
pjetT/
pγT, with increasing collision centrality.
In this work, isolated prompt photons are measured in lead-lead collisions with the ATLAS detec- tor, making use of its large-acceptance, longitudinally segmented calorimeter. They are correlated with measured jets both by looking at the distribution of the ratio of jet transverse energy to photon transverse energy
xJγ, as well as the distributions of their opening angle
∆φ
Jγ, as a function of collision centrality.
The photon performance in this note follows closely the analysis in Ref. [7]. The jet performance utilizes many of the performance and analysis techniques used in the first ATLAS jet yield measurement [14].
2 Experimental setup
2.1 ATLAS detector
The ATLAS detector is described in detail in Ref. [12]. The ATLAS inner detector is comprised of three major subsystems: the pixel detector, the semiconductor detector (SCT) and the transition radiation tracker (TRT), which cover full azimuth and pseudorapidity
1out to
|η|=2.5. The pixel detector consists
1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and thez-axis along the beam pipe. Thex-axis points from the IP to the centre of the LHC ring, and theyaxis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane,φbeing the azimuthal angle around the beam pipe. The
of three layers, at radii of 50.5, 88.5 and 122.5 mm, arranged in cylindrical layers in the barrel region (|η| < 2) and three disks in the endcap region. The SCT is comprised of four cylindrical layers of double- sided silicon strip detectors at radii ranging from 299 to 514 mm in the barrel region, and 9 disks in the endcap region. At larger radii, covering radii from 563 to 1066 mm and
|η|< 2, the transition radiation tracker (TRT) is divided into a 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). A typical track trajectory crosses more than 30 straws. The entire detector is immersed in a 2 T axial magnetic field and allows tracking up to
|η|=
2.5 using the pixel and SCT, and
|η|=2.0 using the TRT.
The ATLAS calorimeter is a large-acceptance, longitudinally-segmented sampling calorimeter cov- ering out to
|η| =4.9 with electromagnetic and hadronic sections. The electromagnetic section is a lead-liquid argon sampling calorimeter with an accordion geometry. It is divided into the barrel region, covering
|η|< 1.475, and two endcap regions, covering 1.375 <
|η|< 3.2. The calorimeter has three pri- mary longitudinal sections, called “layers”. The first sampling layer is 3 to 5 radiation lengths deep and is segmented into fine “strips” of size
∆η
=0.003
−0.006 (depending on η), which allows the discrimi- nation of photons from the two-photon decays of light mesons. The second layer is 17 radiation lengths thick, sampling the majority of an electromagnetic shower, and has cells of size
∆η
×∆φ
=0.025
×0.025.
The third layer has a material depth ranging from 4 to 15 radiation lengths and is used to catch the tails of high energy electromagnetic showers. In front of the strip layer, a presampler is used to correct for en- ergy loss in front of the calorimeter within the region
|η|< 1.8. In test beam environments and in typical proton-proton (
pp) collisions, the calorimeter is found to have a sampling term of 10-17%/√E[GeV].
The total material in front of the electromagnetic calorimeter ranges from 2.5 to 6 radiation lengths as a function of pseudorapidity, except the transition region between the barrel and endcap regions, in which the material is up to 11.5 radiation lengths.
The hadronic calorimeter section is located radially just after the electromagnetic calorimeter. Within
|η|
< 1.7, it is a sampling calorimeter of steel and scintillator tiles, with a depth of 7.4 hadronic interaction lengths. In the endcap region it is copper and liquid argon with a depth of 9 interaction lengths.
2.2 Photon trigger
The sample of events used in this analysis was collected using the first level calorimeter trigger of the ATLAS experiment [13]. This is a hardware trigger which sums up electromagnetic energy in towers of size
∆η
×∆φ
=0.1
×0.1, which is substantially coarser than the electromagnetic calorimeter. A sliding window of size 0.2
×0.2 was used to find electromagnetic clusters by looking for local maxima and keeping only those with energy in two adjacent cells (i.e. regions with a size of either 0.2
×0.1 or 0.1
×0.2) exceeding a programmable threshold. The trigger threshold was chosen to be 16 GeV, which was measured using minimum bias data to be 100% e
fficient for photons above 20 GeV [7].
3 Jet reconstruction in heavy ion collisions and estimation of the under- lying event
A hard process in a heavy ion collision occurs within the overlap region of the two colliding nuclei, which leads to a substantial “underlying event” of particles emitted from the other nucleon-nucleon collisions within the same event. In order to reconstruct photons in the context of a heavy ion collision, the large background from the underlying event (UE) is subtracted from each event. This is performed during the heavy ion jet reconstruction, as explained in detail in Ref.[14], whose description is closely followed here.
pseudorapidity is defined in terms of the polar angleθasη=−ln tan(θ/2).
Calorimeter jets were reconstructed from
∆η
×∆φ
=0.1
×0.1 towers using the anti-k
talgorithm [15]. This algorithm is a well-known jet clustering procedure, which groups calorimeter towers into jets with a well-defined radius, similar to older “cone” algorithms but in a way that is infrared and collinear safe. It was run in four-vector recombination mode with anti-k
tdistance parameters
R=0.2, 0.3, 0.4 and 0.5. The tower energies were obtained by summing energies, calibrated at the electromagnetic energy scale [16], of all cells in all layers within the η and φ boundaries of the towers. Cells that span tower boundaries have their energy apportioned by the fraction of the cell contained within a given tower.
The jet measurements presented here were obtained by performing the anti-k
treconstruction on the towers prior to underlying event subtraction and then evaluating and subtracting the UE from each jet at the calorimeter cell level. The subtraction procedure calculates a per-event average UE energy density excluding contributions from jets and accounting for e
ffects of elliptic flow modulation on the UE [18].
The UE estimation and subtraction was performed using a two-step procedure that was identical for all jet radii.
This procedure is done in several iterative steps. A first estimate of the underlying event average transverse energy density, ρ
i(η), is evaluated for each calorimeter layer
iin intervals of η of width
∆η
=0.1 using all cells in each calorimeter layer, within the given η interval excluding those within “seed” jets.
In the first subtraction step, the seeds are defined to be jets reconstructed using the anti-k
t[15] algorithm with
R=0.2 which have at least one tower with
ET> 3 GeV and which have a ratio of the maximum to the mean tower energy of at least four.
The presence of elliptic flow in lead-lead collisions leads to a 2v
2cos 2(φ
−Ψ2)
modulation on the UE, where v
2is the second coe
fficient in a Fourier decomposition of the azimuthal variation of the UE particle or energy density, and the event plane angle,
Ψ2, points in the direction of the largest upward modulation in the event. The
Ψ2angle is measured event-by-event with the forward calorimeter (FCal), using the technique outlined in [17, 18]:
Ψ2 =
1 2 tan
−1
X
k
w
kETksin (2φ
k)
Xk
w
kETkcos (2φ
k)
, (1)
where
kruns over cells in the FCal, φ
krepresents the cell azimuthal angle, and w
krepresent per-cell weights empirically determined to smooth the
Ψ2distribution. An η-averaged v
2was measured sepa- rately for each calorimeter layer according to
v
2i= Xj∈i
ETj
cos
h2
φ
j−Ψ2i X
j∈i
ETj
, (2)
where
jruns over all cells in layer
i. The UE-subtracted cell energies were calculated according to ETsubj = ETj−Ajρ
i(η
j)
1
+2v
2icos
h2
φ
j−Ψ2i
, (3)
where
ETj, η
j, φ
jand
Ajrepresent the cell
ET, η and φ positions, and area, respectively, for cells,
j,in layer
i. The kinematics for theR =0.2 jets generated in this first subtraction step were calculated via a four-vector sum of all cells (assumed to be massless) contained within the jets using the
ETvalues obtained from Eq. 3.
The second subtraction step starts with the definition of a new set of seeds using a combination
of
R =0.2 calorimeter jets from the first subtraction step, each with
ET> 25 GeV, and jets formed
from inner detector tracks, using anti-k
Twith
R =0.4, with
pT> 10 GeV. Using these seeds, a new
estimate of the UE, ρ
0i(η), is calculated excluding cells within
∆R< 0.4 of the new seed jets, where
∆R= q
(η
cell−η
jet)
2+(φ
cell−φ
jet)
2. New v
2ivalues, v
20i
, were also calculated excluding all cells within
∆
η
=0.4 of any of the new seed jets.
Once the mean energy ρ
iand v
2ivalues are evaluated in each layer, excluding all seeds from the averaging, the background subtraction is then applied to the original cell energies using Eq. 3 but with ρ
iand v
2ireplaced by the new values, ρ
0i(η) and v
20i. After this the kinematics of all jets is recalculated as a four-momentum sum of the new cell energies. This procedure also provides a new set of “subtracted”
cells, from which the mean underlying event has been removed, as well as the large-scale modulation of elliptic flow. The residual deposited energies stem primarily from several sources: jets, photons, electrons, and background fluctuations (possibly including higher order flow harmonics). It should be noted that the procedure outlined here has been used to estimate the mean UE energy density as a function of η. It is at present not possible to make further subtraction of more localized structures.
4 Photon reconstruction
Acting upon the subtracted cells, the ATLAS photon reconstruction [19] is seeded by clusters of at least 2.5 GeV found using a sliding window algorithm applied to the second sampling layer of the electro- magnetic calorimeter, which typically samples over 50% of the deposited photon energy. In the dense environment of the heavy ion collision, the photon conversion recovery procedure is not performed, due to the overwhelming number of combinatoric pairs in more central collisions. However, a substantial fraction of converted photons are still reconstructed by the photon algorithm, as at these high energies, the electron and positron are typically close together as they reach the calorimeter, while their tracks typi- cally originate at a radius too large to be well-reconstructed by the tracking algorithm which is optimized for heavy ion collisions. Thus, the photon sample analyzed here is a mix of converted and unconverted photons, as will be directly illustrated below.
The energy measurement is made using all three layers of the electromagnetic calorimeter and the presampler, with a size corresponding to 3
×5 (in η and φ) cells in the second layer (each being 0.025
×0.025). An energy calibration is applied to each shower to account for both its lateral leakage (outside the nominal window) and longitudinal leakage (into the cryostat and hadronic calorimeter) [19]. This window size is used in the analysis of the
ppcollision data for unconverted photons, while it is used for all photons in this analysis of heavy ion data, leading to a slight degradation in performance when applied to converted photons.
4.1 Photon shower shape variables
The fine-grained, longitudinally segmented calorimeter allows detailed characterization of the shape of each photon shower, providing tools to reject jets and hadrons, while maintaining high efficiency for the photons themselves. In this analysis, nine shower-shape variables are used, all of which have been used extensively in previous publications, particularly the measurement of prompt photon spectra as a function of pseudorapidity [20, 21]. The primary shape variables used can be broadly classified by which sampling layer is used.
The second sampling is used to measure
• Rη
, the ratio of energies deposited in a 3
×7 (η
×φ) window to that deposited in a 7
×7 window, in units of the second layer cell size.
•
w
η,2, the root-mean-square width of the energy distribution of the cluster in the second layer in the
η direction
• Rφ
, the ratio of energies deposited in a 3
×3 (η
×φ) window in the second layer to that deposited in a 3
×7 window, in units of the second layer cell size.
The hadronic calorimeter is used to measure the fraction of shower energy that reaches the hadronic calorimeter:
• Rhad
, the ratio of transverse energy measured in the hadronic calorimeter to the transverse energy of the photon cluster.
• Rhad1
, the ratio of transverse energy measured in the first sampling layer of the hadronic calorimeter to the transverse energy of the photon cluster.
The cut is applied on
Rhad1when
|η|< 0.8 or
|η|> 1.37 while it is applied to
Rhadotherwise.
Finally, cuts are applied in five other quantities measured in the high granularity strip layer, to reject neutral meson decays from jets. In this finely-segmented layer a search is applied for multiple maxima from neutral hadron electromagnetic decays:
•
w
s,tot, the total RMS of the transverse energy distribution in the η direction in the first sampling
“strip” layer
•
w
s,3, the RMS width of the three “core” strips including and surrounding the cluster maximum in the strip layer
• Fside
, the fraction of transverse energy in seven first-layer strips surrounding the cluster maximum, not contained in the three core strips (i.e. (E(±3)
−E(±1))/E(±1))• Eratio
, the asymmetry between the transverse energies in the first and second maxima in the strip layer
• ∆E, the difference between the transverse energy of the first maximum, and the minimum cell
transverse energy between the first two maxima.
In general, it has been found in ATLAS that the shower shape variables measured in data di
ffer slightly from the Monte Carlo calculations [20]. To account for these differences, a set of additive correction factors has been developed to account for small shifts in the distributions. This analysis uses the standard shift factors obtained by comparing simulations of
ppcollisions to the same quantities in the data, with no modification for the heavy ion environment. It is found that the broad features of the distributions agree quite well between data and simulation, except in the regions where di-jet background is expected.
4.2 Photon isolation energy
In order to further reject clusters arising from hadronic fragments of jets, particularly neutral mesons, the calorimeter is also used to measure an isolation energy for each photon candidate,
ET(R
iso). The isolation energy is the sum of transverse energies in calorimeter cells (including hadronic and electromagnetic sections) in a cone
R = p∆
η
2+ ∆φ
2<
Risoaround the photon axis. The photon energy is removed
by excluding a central core of cells in a region corresponding to 5×7 cells in the second layer of the
EM calorimeter. In previous ATLAS analyses of
ppcollision data [20, 21], the cone size was chosen
to be
Riso =0.4, while in this heavy ion analysis, the cone is chosen to be slightly smaller,
Riso =0.3,
to reduce the sensitivity to underlying event fluctuations. The analysis presented here also uses a less
restrictive isolation criterion
ET(R
iso =0.3) < 6 GeV, as compared to the criterion used in the
ppanalyses,
ET(R
iso =0.4) < 3 GeV [20, 21]. Relative to the previous lead-lead analysis [7], a small
correction is applied to the isolation energy using scale factors derived from simulations, to remove the
leakage of the shower into the isolation cone. This correction is typically less than 2% of the measured
photon transverse momentum.
[TeV]
ET
Σ FCal
0 1 2 3
[1/TeV]TEΣ/d evt) dN evt(1/N
10-7
10-5
10-3
10-1
10
40-80% 20-40% 10-20% 0-10%
Preliminary ATLAS
=2.76 TeV sNN
Pb+Pb Minimum bias 16 GeV trigger 40 GeV tight photons
Figure 1: Distribution of FCal
ΣET, at the 2011 energy scale, with centrality bins indicated. The dotted line shows the distribution for minimum bias data, the dashed line shows the distribution for events that satisfy the 16 GeV level 1 electromagnetic cluster trigger, and the solid line shows the distribution for photon candidates with
ET> 40 GeV satisfying tight selection cuts (see section 8.1). All distributions are normalized per minimum bias event.
5 Centrality selection
The centrality of each heavy ion collision is determined using the sum of the transverse energy in all cells in the forward calorimeter (3.1 <
|η|< 4.9), at the electromagnetic scale, FCal
ΣET. The trigger and event selection were studied in detail in the 2010 data sample [17] and it was found that it kept 98
±2% of the total inelastic cross section. The increased luminosity of the 2011 heavy ion run necessitated a more sophisticated trigger strategy, including more restrictive triggers in the most peripheral events. However, it was found that the FCal
ΣETdistributions in the 2011 data match those measured in 2010 to within statistical uncertainties, after accounting for a 4.1% scaling applied to the new data reflecting improved understanding of the energy calibrations. For this analysis, the data have been divided into 4 centrality intervals, covering the 0-10%, 10-20%, 20-40% and 40-80% most central events. In this convention, the 0-10% interval has the highest multiplicities, and the 40-80% the lowest. These bins are shown in Figure 1.
The FCal
ΣETdistribution is shown for three types of events. The top distribution (dotted line) is for the recorded minimum bias events. The dashed line shows the distribution for events that satisfy the 16 GeV level 1 electromagnetic cluster trigger. It is evident that these events are biased toward more central events, as might be expected from the scaling with the number of binary collisions. Finally, the solid line shows the distributions for photon candidates with
ET> 40 GeV, and that satisfy the “tight” selection cuts explained in Section 8.1.
Table 1 collects the centrality-related information used in many ATLAS heavy ion physics analyses.
It specifies the FCal
ΣETranges for each bin, the mean number of participants per bin with its total
systematic uncertainty, the mean number of binary collisions with its total uncertainty, and finally the
mean nuclear thickness
hTAAi. The geometric quantities are calculated as described in Ref. [22] using aGlauber Monte Carlo calculation [23, 24], with a simple implementation of the FCal response.
Bin
ΣETrange
hNpartiError
hNcolliError
hTAAiError
0-10% 2.31-4 TeV 356 0.7% 1500 8% 23.4 3.0%
10-20% 1.57-2.31 TeV 261 1.4% 923 7% 15.1 3.1%
20-40% 0.66-1.57 TeV 158 2.5% 441 7% 6.88 5.2%
40-80% 0.044-0.66 TeV 46 6% 78 9% 1.22 9.4%
Table 1: Centrality bins used in this analysis, tabulating the percentage range, the
ΣETrange (in 2011), the average number of participants (hN
parti), binary collisions (hNcolli),TAA, and the relative error on these quantities.
6 Simulation samples
For the extraction of photon performance parameters (e
fficiencies, photon energy scale, isolation prop- erties), a set of approximately 2 million photon+jet events produced in
ppcollisions using the ATLAS MC11 tune of PYTHIA 6.4 at
√s =
2.76 TeV with MRST PDFs, is overlaid on minimum-bias data, triggered with the ATLAS zero-degree calorimeter (ZDC), which are referred-to as “PYTHIA
+Data”
samples. The data is from the same running period as that being analyzed here, and detector conditions are carefully matched between the simulated event and each data event.
The PYTHIA sample is divided into four subsamples based on requiring a minimum transverse momentum for the outgoing primary photon, at 17, 35, 70 and 140 GeV, after applying a slightly lower cut on ˆ
pT, the transverse momentum of the hard process evaluated in the rest frame of the interaction.
In the data overlay procedure, each PYTHIA event is fully simulated with an event vertex corre- sponding to the vertex measured in the real event. The event data are essentially untouched, but are merged with each simulated event at the raw data sample level. After this, the full merged event is reconstructed by the standard ATLAS reconstruction framework.
7 Collision data selection
The data sample analyzed here is from the 2011 LHC heavy ion run, colliding lead nuclei at
√ sNN =2.76 TeV. After requiring the 16 GeV Level 1 electromagnetic cluster trigger, which is sensitive to both electrons and photons, events were selected which contained a reconstructed photon or electron object with a cluster transverse energy of at least 40 GeV, and which matched to a Level 1 Region of Interest (ROI) with at least 16 GeV, measured at the trigger energy scale. Events were then further analyzed if they satisfied a set of quality cuts: The event had to be taken during a period when the detector was found to be working properly. Both sets of minimum-bias trigger scintillators (MBTS, covering 2.09 <
|η|< 3.84) have to have a well reconstructed time signal, and a relative time between the two counters of less than 5 ns. Finally, a good collision vertex is required to be reconstructed in the inner detector, to reject background events from, e.g., cosmic rays. After all selections, a total integrated luminosity of approximately
Lint=0.13 nb
−1was used for this analysis.
8 Photon reconstruction performance
8.1 Photon selection cuts
Photons are selected for this analysis using the “tight” criteria developed for the analysis of
ppcollision
data. Cut intervals are defined on all nine shower shape variables defined above, and are implemented
in a
pγT-independent, but η-dependent scheme. The cuts used in this analysis are “HI tight” cuts, defined
as a minimal set of changes to the standard set of tight cuts used for unconverted photons in the
ppanalysis. The latter had been optimized in the
ppenvironment as a function of η, reflecting the presence of different detector geometries and different numbers of radiation lengths in front of the calorimeter. For the heavy ion analysis, as small a set of the cuts as possible were relaxed to maintain good performance and background rejection, while avoiding too strong a centrality dependence. After application of “HI tight” cuts to the 0-80% centrality sample, but before applying isolation requirements, there are 2248 photon candidates with
pγT> 60 GeV and within
|η|< 1.3. The lower bound on
pγThas been chosen to provide a large range in jet
pTbelow the photon
pT, and the
|η|range has been chosen to stay within the barrel region of the electromagnetic calorimeter.
The photon transverse energy scale has been measured in the PYTHIA+Data sample and is found to be reconstructed within 1% of the true energy over the energy range considered in this analysis. No fine energy correction is applied in this note, but a conservative uncertainty is assigned to the overall photon energy scale, discussed below.
8.2 Double sideband technique
The estimates of photon purity used for this analysis are derived from the “double sideband” method used to extract photon yields. In this approach, already used by ATLAS in the analysis of
ppcollision data, Refs. [20] and [21], and for lead-lead data in Ref. [7], photon candidates are binned on two axes, illustrated in Figure 2. The horizontal axis is the isolation energy within a chosen isolation cone size.
The vertical axis is essentially a two-valued one, where the first bin is for photons that pass the “tight”
cuts outlined above, while the other bin is for “non-tight” candidates, photons that fail at least one of the more stringent cuts but pass the others, and which tend to be from the decays of light neutral mesons from hard-fragmenting jets.
The four regions are labelled A,B,C and D and correspond to four well-defined categories:
• A: tight, isolated photons:
This is the primary signal region where a well-defined fraction of all true, isolated photons would appear.
• B: tight, non-isolated photons:
These are photons which are in the vicinity of a jet, or an under- lying event fluctuation in the case of a heavy ion collision
• C: non-tight, isolated photons:
These are a combination of isolated jet fragments, as well as true photons which have a shower shape fluctuation that fails the tight cuts. The contribution from the latter increases with increasing collision centrality.
• D: non-tight, non-isolated photons:
This region should primarily be background, since they are candidates which are neither tight photons, nor ones which are in isolated regions.
Regions A and B, and C and D are separated by a 2 GeV-wide window, indicated by dotted lines, to reduce correlations between them. For a chosen photon kinematic range (we use the intervals defined in Ref. [7]) the four measured counts in each region and “leakage factors” derived from simulated photon- jet events give a data-driven estimate for the actual signal yield in the observed signal region.
NsigA =NAobs−
NobsB −cBNAsig
NCobs−cCNAsig
NobsD −cDNsigA
(4)
The leakage factors are calculated using the simulated PYTHIA+Data sample as
ci = Nisig/N
Asig. In the
40-80% centrality interval and from
pT =40 to 200 GeV,
cBis consistently less than 0.01,
cCranges
from 0.06 to 0.03, and
cDis less than 0.001. In the 0-10% centrality interval and over the same
pTrange,
=0.3) [GeV]
(Riso
ET
0 5 10 15 20
HI Tight Non-tight
A B
C D
Figure 2: Illustration of the double sideband region, showing the two axes for binning photon candidates:
region A is the “signal region” (tight and isolated photons) for which efficiencies are defined, region B contains tight, non-isolated photons, region C contains non-tight isolated photons, and region D contains non-tight and non-isolated photons. Regions A and B, and C and D are separated by a 2 GeV-wide window, indicated by dotted lines.
cB
ranges from 0.07 to 0.14,
cCranges from 0.06 to 0.03,
cDranges from 0.01 to 0.005. Except for
cB, which reflects the very different isolation distributions in peripheral and central events, the leakage factors are of similar scale.
In practice, Equation 4 is solved numerically using the Brent root solver implemented into ROOT [25].
In order to calculate the statistical uncertainty for each centrality and
pTinterval, the equation is solved 5000 times, each time sampling the eight parameters (N
Aobs−NobsD,
NAsig−NDsig) from a Poisson distribution with the observed value assumed to be the mean of the distribution. The mean of a Gaussian fit to the distribution of
Nsigis taken as the background-corrected yield, while the Gaussian standard deviation is taken as the statistical error on the mean.
8.3 Photon purity
The final photon performance parameters are extracted using “HI tight” cuts, an isolation cone radius of
Riso =0.3 and an isolation energy cut of
ET(R
iso =0.3) < 6 GeV to define Region A, a selection of
ET(R
iso=0.3) > 8 GeV to define Region B. Regions C and D are defined using the same isolation energy selections, but for photon candidates that satisfy the “non-tight” selections with any of four reversed conditions (w
s,3,
Fside,
Eratioand
∆E). For the central 0-10% interval, the 6 GeV isolation selection sitsat approximately one standard deviation from the peak in the Monte Carlo isolation energy distribution.
This implies that, for this centrality bin, only about 85% of the photon sample should fall within region A, necessitating the “isolation e
fficiency” correction described above.
The double sideband method provides an estimate of the purity (P) of the measured sample, which is
defined as
NAsig/N
Aobs. The correction 1
−Papplied to the measured yield in Region A has been calculated
using the PYTHIA
+Data sample and similar results have been found as in Ref. [7]. A fit to a constant in
Centrality 1-P
0-10% 16
±6%
10-20% 21
±9%
20-40% 23
±8%
40-80% 25
±12%
Table 2: Values for 1
−Pextracted using the double sideband method, along with 1σ uncertainties, as a function of centrality and photon 60 <
pγT< 90 GeV.
the transverse energy interval used in this analysis, 60 <
pγT< 90 GeV, is used to extract values of 1
−Palong with their statistical errors, as presented in Table 2.
8.4 Photon e ffi ciencies
Photon efficiencies are defined for “HI tight” and isolated (i.e. Region A) photons relative to all PYTHIA photons with a true isolation energy in a cone of
Riso=0.3 around the photon direction of less than 6 GeV, defined using the sum of energies from the PYTHIA generator-level particles. This selection removes about 1.5% of the PYTHIA photon sample.
The efficiencies can be factorized into three contributions:
• Reconstruction efficiency:
This is the probability that a photon is reconstructed with 90% or more of its true energy. In the heavy ion reconstruction, the losses primarily stem from a subset of photon conversions, in which the energy of the electron and positron is not contained within a region small enough to be reconstructed by the standard algorithms. This factor is typically around 95% and is found to be constant as a function of transverse momentum for the range measured here.
• Identification efficiency:
This is the probability that a reconstructed photon (according to the previous definition) passes “tight” identification cuts.
• Isolation efficiency:
This is the probability that a photon which is reconstructed and passes iden- tification cuts, also passes the chosen isolation cut. In lead-lead collisions, where the average background is already subtracted, the isolation e
fficiency for photons primarily reflects the stan- dard deviation of the residual background fluctuations.
These efficiencies are defined in such a way that the “total efficiency”
tot– the probability that a photon would be reconstructed
andidentified
andisolated – is simply the product of these three factors. These are assessed using the standard “HI tight” definitions and an isolation cut of 6 GeV within
Riso =0.3 around the photon direction. They have been calculated using the PYTHIA
+Data sample and the results are very similar to earlier results using PYTHIA+HIJING [7]. The total efficiencies are found to be about 83-87% in peripheral events for 60 <
pγT< 90 GeV and 64-70% in the same range in 0-10%
central events, the centrality dependence driven primarily by the fixed isolation energy cut.
9 Photon-jet analysis
In order to probe the physics of energy loss using photon-jet correlations, the measured quantities are
chosen to be sensitive to the modification of jet properties and appropriate to the photon-jet system. The
variables used in this analysis for studying the correlation between photons and jets in experimental data,
and comparing to Monte Carlo simulations, are:
•
The energy fraction
xJγ= pjetT/
pγT.
•
The opening angle between the reconstructed photon and jet,
∆φ
Jγ =|φjet−φ
γ|.In the PYTHIA
+Data simulations,
xJγis found to be peaked near unity, with the position of the peak decreasing with decreasing jet radius, as the same jet reconstructed with a smaller radius is found to have a smaller energy in the jet cone. Experimental e
ffects, especially the jet energy resolution, tend to smear out the peak but do not tend to shift it substantially. And while at leading order, the photon and jet should be back to back in their rest frame, simulations show that, just as for di-jets, the opening angle for jets and photons is generally peaked at
∆φ
Jγ =π, but with a fallo
ffunderstood to be sensitive to multiple jet emission [26].
9.1 Photon and jet selection
In this analysis, only tight, isolated leading photon candidates with 60 <
pT< 90 GeV and
|η|< 1.3 are considered.
All jets for this analysis are required to pass either or both of two selections, which were found in Ref. [14] to substantially reduce the rate of fake jets:
•
a “track jet” reconstructed using selected tracks with
pT> 4 GeV, with an anti-k
tradius of
R=0.4
•
an electron or photon object (i.e. an electromagnetic cluster) with 7 GeV or more after background subtraction.
A jet is accepted if either or both of these objects is found within
∆R< 0.2 with respect to the jet direction.
To account for the acceptance of the ATLAS inner detector (|η| < 2.5), reconstructed jets are only accepted into the analysis if they are within
|ηjet|< 2.1. Events with photon candidates are considered good photon-jet events if the leading jet in the event after fake rejection has
pT>
pTjet,min=25 GeV and
|ηjet|
< 2.1.
To prevent the appearance of low-lying tails at very small values of
xJγ, only photon-jet pairs with
xJγ>
xJγmin=25/60 are accepted into the analysis.
Another selection used in this analysis when measuring the distribution of
xJγ, is to accept events with the relative azimuthal angle between the photon and jet
|∆φ| >
∆φ
min =7π/8. This restricts the photon-jet events to those with a back-to-back topology. This both suppresses events with additional hard radiation beyond the primary 2
→2 hard process, but also suppresses correlations of the photon with a jet from an unrelated hard-process, or from a large fluctuation of the underlying event. The choice of
∆φ
minfollows the convention set by the earlier CMS publication [11].
9.2 Jet performance in photon-jet events
The performance of jets within
|ηjet|< 2.1 in photon-jet events has been studied using the PYTHIA
+Data simulation samples, for photons with 60 <
pγT< 90 GeV. The limited range in photon
pThas been chosen to limit the range of recoil jet energies, which facilitates unfolding the jet spectrum, as discussed below.
The reference set of “truth jets” for subsequent performance studies is created by running the anti-k
talgorithm on the final state hadrons in PYTHIA (without data overlay), for radii
R=0.2 and 0.3. Truth jets are considered “matched” to reconstructed jets if a reconstructed jet passing all analysis selections is found within
∆R= p∆
η
2+ ∆φ
2< 0.4 of the truth jet.
The jet energy scale (h
∆pT/
pTi = h(pjet,recT − pjet,trueT)/p
jet,trueT i) was measured for matched recon-structed jets using the standard jet reconstruction on photon-jet events. It was found to have a value of
about 5% in PYTHIA photon-jet events for jets with transverse energy above 50 GeV, decreasing with
increasing
pjet,trueT. Conversely, it is found to be less than 1% for PYTHIA di-jet events. This can be
[GeV]
jet pT
0 50 100 150 200 250
T)/p T(pσ
0 0.1 0.2 0.3 0.4 0.5
> 20 GeV Photon pT
R=0.3 0-10%
R=0.2 0-10%
R=0.3 40-80%
R=0.2 40-80%
PYTHIA+Data
=2.76 TeV sNN
Pb+Pb
Preliminary ATLAS
[GeV]
jet pT
0 50 100 150 200 250
T)/pT(pσ
0 0.1 0.2 0.3 0.4 0.5
> 60 GeV Photon pT
R=0.3 0-10%
R=0.2 0-10%
R=0.3 40-80%
R=0.2 40-80%
PYTHIA+Data
=2.76 TeV sNN
Pb+Pb
Preliminary ATLAS
Figure 3: Jet energy resolution for reconstructed
R=0.2 and
R=0.3 jets produced in PYTHIA gamma- jet events with photon
pT> 20 GeV (to give access to low energy jets) and for peripheral 40-80% and central 0-10% events, and for photon
pT> 60 GeV, close to the actual kinematics used in this note.
attributed to the very di
fferent fraction of gluon jets between di-jet events, used for the calibrations, and photon-jet events. From the PYTHIA photon-jet samples, the fraction of gluons recoiling against pho- tons of
pγT =25 GeV is about 8%, increasing to 20% by
pγT =200 GeV. This is very different than the same fraction in di-jet events, where typically O(60%) of the jets are initiated by gluons. Gluons have a larger color charge than quarks, so they radiate more during the fragmentation process, with a softer fragmentation function and a wider jet profile than quark jets [27]. Calibrations based on the higher frac- tion of gluon jets produced in di-jet events will typically over-correct the energy of the primarily quark jets produced in photon-jet processes.
In order to provide a correct energy balance between the photon and jet in gamma-jet events, a small energy correction has been applied to each jet, which is O(5%) at
pT =65 GeV, increases at lower jet transverse energy, and decreases slowly out to much higher jet transverse energies.
The jet energy resolution is determined by the standard deviation of the difference between the trans- verse energy of a truth jet and a matched reconstructed jet σ(∆
pT/p
T). It is shown in Fig. 3 for photon energies above 20 GeV and 60 GeV, and is found to be comparable to that extracted from di-jet events embedded into simulated heavy ion events [14]. It has the characteristic
pTdependence found there, dominated by underlying event fluctuations at lower
pTand fluctuations intrinsic to the calorimetric measurement itself (shower sampling and electronic noise) at higher
pT.
After the jet energy scale correction, the jet reconstruction efficiency is determined from simulations as the probability of matching a true jet with a reconstructed jet of
pjet,recT> 25 GeV, the minimum allowed into the data analysis described below. Fig. 4 shows the e
fficiency for
R=0.2 and
R =0.3 jets emitted within
|ηjet|< 2.1 associated with a tight, isolated reconstructed photon with 60 <
pγT< 90 GeV and
∆
φ
Jγ> 7π/8, as a function of collision centrality. It shows a rapid turn-on, reaching approximately 50%
at 30 GeV for all centralities. To incorporate the e
fficiency measurements into the photon-jet analysis, the measured points have been fit with a Fermi distribution 1/(1
+exp(α(
pjetT −β))), where α and β are free parameters.
9.3 Unfolding detector response
In order to correct the measured distribution of
xJγfor the jet energy resolution, the distributions are
unfolded using a similar approach as was applied in Ref. [14]. The procedure uses the singular-value
decomposition (SVD) unfolding approach [28] as implemented in the RooUnfold package in ROOT [25].
[GeV]
T
True pjet
50 100 150 200
Efficiency
0 0.2 0.4 0.6 0.8 1
40-80% Centrality 20-40% Centrality 10-20% Centrality 0-10% Centrality
>25 GeV
T
|<2.1, pjet
ηjet
R=0.2, |
<90 GeV
T
|< 1.3, 60<pγ
ηγ
| π/8
>7
γ
φJ
∆
=2.76 TeV sNN
Pb+Pb PYTHIA+Data
Preliminary ATLAS
[GeV]
T
True pjet
50 100 150 200
Efficiency
0 0.2 0.4 0.6 0.8 1
40-80% Centrality 20-40% Centrality 10-20% Centrality 0-10% Centrality
>25 GeV
T
|<2.1, pjet
ηjet
R=0.3, |
<90 GeV
T
|< 1.3, 60<pγ
ηγ
| π/8
>7
γ
φJ
∆
=2.76 TeV sNN
Pb+Pb PYTHIA+Data
Preliminary ATLAS
Figure 4: Jet reconstruction efficiency in photon-jet events, as a function of truth jet
pjetT, for jet radii
R=0.2 and
R=0.3, for 60 <
pγT< 90 GeV and
∆φ
Jγ> 7π/8.
Response matrices, which contain the correlation of true and reconstructed jet transverse energies, are produced separately for each centrality bin and jet radius for the photon selection and
∆φ
Jγselection used in this analysis, using photons over the full range of simulated
pγT. The input reconstructed
pjetTspectrum has 20 bins, 7.5 GeV wide, ranging from 25 to 175 GeV. The true
pjetTspectrum is divided into 20 bins 10 GeV wide, ranging from 10 to 210 GeV.
Due to the limited statistics of the total sample and that the jet scale changes for every event depend- ing on the photon
pγT, the unfolding technique described below is used:
•
First unfold the
inclusivejet
pTspectrum from each selection of data and MC
•
Then use the same unfolding matrix obtained by this procedure to unfold
single eventsand combine this information with the photon energy to fill the
xJγdistribution.
For each event, where a photon and jet are both selected according to the selections described in subsec- tion 9.1, the input bin corresponding to the reconstructed
pjetTis unfolded into a set of weights in the true
pjetTbins. This vector of weights (each of which corresponds to a di
fferent
pjet,trueTinterval) is then mapped into a
xJγdistribution for each event. This is done by mapping each interval in
xJγonto the
pTintervals, assigning the
xJγinterval the sum of weights in the overlap region. The weight from partial
pTintervals is given by the geometric overlap with the
xJγinterval. By construction, this procedure is designed to preserve the sum of weights, unless a
pTbin maps to an
xJγregion outside the fiducial acceptance of the data analysis. The regularization process inherent in the SVD approach can also lead to some events having a total weight of less than one.
The jet e
fficiencies are defined as a function of the true transverse momentum scale, so they can only be used to correct the
xJγdistributions after unfolding. This is done during the mapping of the
pTweights into
xJγbins by dividing each weight filled into the
xJγdistribution by the centrality- and
pjetT-dependent efficiency
jet(
pjetT,
C) corresponding to the pTvalue in the center of each
pTinterval. In addition, the photon efficiencies described in Section 8.4, which depend on the collision centrality and the photon
pT,
γ(p
γT,
C), are also applied (as 1/γ) to all weights for each event.
The performance of the SVD procedure is optimized by providing an approximation of the input
Monte Carlo spectrum, called
xini[28]. Choosing this spectrum properly reduces the number of orthog-
onal functions needed for the unfolding. For the application to the experimental data,
xiniwas chosen to
be the true jet transverse momentum spectrum obtained in PYTHIA for the selected photon transverse
γ
XJ
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Counts / bin
0 2 4 6 8 10 12 14 16 18 20
Region C 0-10% Central Pb+Pb
=2.76 TeV sNN
=0.13 nb-1
Lint
ATLAS Preliminary
γ
XJ
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Counts / bin
0 2 4 6 8 10 12 14 16 18 20
Region D 0-10% Central Pb+Pb
=2.76 TeV sNN
=0.13 nb-1
Lint
ATLAS Preliminary
γ
XJ
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Counts / bin
0 5 10 15 20 25 30 35 40 45 50
Region A 0-10% Central Pb+Pb
=2.76 TeV sNN
=0.13 nb-1
Lint
ATLAS Preliminary
γ
XJ
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Counts / bin
0 2 4 6 8 10 12 14 16 18 20
Region B 0-10% Central Pb+Pb
=2.76 TeV sNN
=0.13 nb-1
Lint
ATLAS Preliminary
Figure 5: Example of raw
xJγdistributions for regions ABCD, for 0-10% central,
R =0.2 jets, photon transverse momenta 60 <
pγT< 90 GeV and
∆φ
Jγ> 7π/8. Please note the much larger vertical scale in Region A, relative to the other regions.
momentum, centrality and angular range. The
xiniwas then used to reweight the response matrix appro- priately. As a systematic check, the analysis was run assuming
xinito be a flat distribution in
pjetTfrom 20-120 GeV for 60 <
pγT< 90 GeV.
9.4 Background determination
As discussed above in Section 8.3, the signal sample defined by the the tight shower shape selections and isolation energy is not guaranteed to be a fully-pure photon sample. To account for the di-jet backgrounds in the photon-jet signal region, the sum of events in regions C and D, which satisfy the “non-tight” cuts designed to enhance the presence of hard-fragmenting di-jets, are used as an estimate of the background distribution. An example of the raw
xJγdistributions in all four regions is shown in Fig.5. The histograms show the unnormalized counts per
xJγbin for each region. Region B can contain a fraction of photons that fail the isolation cut merely from underlying event fluctuations, so it was excluded from the background distributions.
To make sure the background distributions approximate the residual background in Region A, the
sum of the non-tight distributions (Regions C and D) are unfolded and efficiency corrected exactly as
with the signal distributions, using the same unfolding matrix as is used on the signal region. After this
procedure, the distribution is normalized to an integral equal to a fraction 1
−Pof the distribution in
Region A, and subtracted, propagating the statistical uncertainties.
γ
xJ
0.5 1 1.5 2
γJdx/γJdN) γN(1/
0 0.5 1 1.5 2
Reconstructed MC Unfolded MC R=0.3 40-80%
= 0.13 nb-1
Lint
=2.76 TeV sNN
Pb+Pb Preliminary ATLAS
γ
xJ
0.5 1 1.5 2
γJ/dxγJdN) γN(1/
0 0.5 1 1.5 2
Reconstructed MC Unfolded MC R=0.3 0-10%
= 0.13 nb-1
Lint
=2.76 TeV sNN
Pb+Pb Preliminary ATLAS
γ
xJ
0.5 1 1.5 2
γJdx/γJdN) γN(1/
0 0.5 1 1.5 2
Subtracted Data Unfolded Data R=0.3 40-80%
= 0.13 nb-1
Lint
=2.76 TeV sNN
Pb+Pb Preliminary ATLAS
γ
xJ
0.5 1 1.5 2
γJdx/γJdN) γN(1/
0 0.5 1 1.5 2
Subtracted Data Unfolded Data R=0.3 0-10%
= 0.13 nb-1
Lint
=2.76 TeV sNN
Pb+Pb Preliminary ATLAS
Figure 6: Demonstration of the effect of unfolding on measured distributions. The top two panels com- pare reconstructed PYTHIA
+Data events with fully unfolded and e
fficiency corrected distributions, for
R=0.3 jets and for peripheral and central events. The kinematic cuts here are photon 60 <
pγT< 90 GeV,
|ηγ|