isolated prompt photons in lead-lead collisions at

ATLAS-CONF-2012-051 28May2012

ATLAS NOTE

ATLAS-CONF-2012-051

May 28, 2012

Measurement of high p

isolated prompt photons in lead-lead collisions at

√ s

= 2.76 TeV with the ATLAS detector at the LHC

The ATLAS Collaboration

Abstract

Prompt photons are a powerful tool in heavy ion collisions. Their production rates pro- vide access to the initial state PDFs, which are expected to be modified by nuclear e

ects.

They also provide a means to calibrate the expected energy of jets that are produced in the medium, and thus are a tool to probe the physics of jet quenching more precisely both through jet spectra and fragmentation properties. The ATLAS detector measures photons with its hermetic, longitudinally segmented calorimeter, which gives excellent spatial and energy resolution, and detailed information about the shower shape of each measured pho- ton. This gives significant rejection against the expected background from neutral pions in jets. Rejection against jet fragmentation products is further enhanced by isolation criteria, which can be based on calorimeter energy or the presence of high

tracks. First results on the spectra of isolated prompt photons from approximately 133

of lead-lead data are shown, as a function of transverse momentum and centrality. The measured spectra are compared to expectations from perturbative QCD calculations.

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 jet quenching at the Large Hadron Collider (LHC) was discovered using di-jet asymmetry dis- tributions [1], the detailed physical mechanism is still not understood. One of the limiting factors in understanding jet quenching is having a proper calibration of the initial jet energy. 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

, they are integrating over a range of initial unquenched jet energies. Replacing one of the jets with a penetrating probe, such as a photon or electroweak boson (W or Z), o

ers 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, it is essential to measure photon rates in heavy ion collisions. 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

or quark-antiquark annihilation

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) the two cannot be unambiguously separated. 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. At high

, photon rates are expected to be modified by nuclear e

ects on the nucleon PDFs, as well as by jet-medium interactions (see e.g. Ref.[5]).

Prompt photon rates have been measured extensively in proton-proton collisions, from the CERN ISR [6, 7] to the CERN SppS [8] and to the Fermilab Tevatron[9, 10]. Both of the large LHC experiments, ATLAS [11, 12] and CMS [13] have measured isolated prompt photons in the early

s =7 TeV proton-

proton data. In nearly all cases, good agreement has been found with perturbative QCD calculations at next to leading order, which are typically calculated using the JETPHOX package [14, 15]. In lower- energy heavy ion collisions, the PHENIX experiment performed measurements of direct photon rates in gold-gold collisions at

s_NN =

200 GeV [16].

Hard process rates in heavy ion collisions generally scale as follows, for any particular process (la- beled “X” here):

NX =L_AAσ^AA_tothN_colliσ^pp_X

σ^pp_tot

(1)

In this equation,

is the heavy ion integrated luminosity,

is the total inelastic lead-lead cross section (calculated to be 7.6 b using Glauber Monte Carlo code [17, 18]),

is the mean number of binary collisions,

is the cross section for subprocess

in proton-proton collisions, and

is the total inelastic proton-proton cross section. Given that

is the number of inelastic events (N

), while

is simply the mean nuclear thickness function

variable as:

R_AA =

(N

)

T_AAσ^pp_X

(2)

This allows the straightforward comparison of yields in heavy ion collisions, normalized by the initial parton flux, to cross sections measured in proton-proton data and calculated using standard event and process generators. CMS performed the first measurement of isolated prompt photon rates in both proton- proton as well as lead-lead collisions, at the nucleon-nucleon CM energy of

s =

2.76 TeV [19]. They

found rates consistent with a scaling with the number of binary collisions, and thus found

values

consistent with unity for all centrality and

ranges considered.

In this work, isolated prompt photons are measured in lead-lead collisions with the ATLAS detector, making use of its large-acceptance, longitudinally segmented calorimeter. Yields per event are measured averaged over

1.3 and as a function of photon

from 45-200 GeV. Comparisons with previous data as well as NLO QCD calculations are also presented.

2 Experimental setup

2.1 ATLAS detector

The ATLAS detector is described in detail in Ref. [20]. 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

out to

2.5. The pixel detector consists 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 detectors at radii ranging from 299 to 514 mm in the barrel region, and 9 disks in the endcap region (of which a typical particle trajectory crosses four). The TRT covers the larger radii from 563 to 1066 mm with 72 layers of straw tubes, of which a particle typically leaves signals in about 40 straws.

The entire detector is immersed in a 2 T axial magnetic field and allows tracking up to

2.5 using the pixel and SCT, and

2.0 using the TRT.

The ATLAS calorimeter is a large-acceptance, longitudinally-segmented sampling calorimeter cov- ering out to

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

1.475, and two endcap regions, covering 1.375

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

0.003− 0.006 (depending on

tion of photons from the two-photon decays of

and

mesons. The second layer is 17 radiation lengths thick, sampling the majority of an electromagnetic shower, and has cells of size

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 energy loss in front of the calorimeter within the region

1.8. In test beam environments and in typical proton-proton 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 [21]. This is a hardware trigger which sums up electromagnetic energy in towers of size

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

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 pseudorapidity is defined in terms of the polar angleθasη=−ln tan(θ/2).

0.1

0.2) exceeding a programmable threshold. The trigger with the lowest

threshold that was not prescaled for the duration of the 2011 heavy ion run had a threshold of 16 GeV, which has been found to be 100% efficient for photons above 20 GeV.

3 Estimation of the underlying 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 recon- struction, as explained in detail in Ref.[22], whose description is closely followed here.

This procedure is done in several iterative steps. A first estimate of the underlying event average transverse energy density,

(η), is evaluated for each calorimeter layer

in intervals of

of width

0.1 using all cells in each calorimeter layer, within the given

interval excluding those within “seed” jets.

In the first subtraction step, the seeds are defined to be jets reconstructed using the anti-k

[23] algorithm with

0.2 which have at least one tower with

3 GeV and which have a ratio of the maximum to the mean tower energy of at least 4. The presence of elliptic flow in lead-lead collisions leads to a 2v

cos 2(φ

)

modulation on the UE, where v

is the second coefficient in a Fourier decomposition of the azimuthal variation of the UE particle or energy density, and the event plane angle,

, points in the direction of the largest upward modulation in the event.

The techniques outlined in [24, 25] are used to measure

on an event-by-event basis, using the event plane defined by the ATLAS forward calorimeter (FCal):

Ψ2 =

1 2 tan















 X

k

wkE_Tk

sin (2φ

)

k

wkE_Tk

cos (2φ

)

















,

(3)

where

runs over cells in the FCal,

represents the cell azimuthal angle, and

represent per-cell weights empirically determined to smooth the

distribution. An

was measured sepa- rately for each calorimeter layer according to

v

j∈i

E_Tj

cos

2

φj−Ψ2

i X

j∈i

E_Tj

,

(4)

where

runs over all cells in layer

(η

)

1

2v

cos

2

φj−Ψ2

i,

(5)

where

,

,

and

represent the cell

,

and

positions, and area, respectively, for cells,

in layer

0.2 jets generated in this first subtraction step were calculated via a four-vector sum of all (assumed massless) cells contained within the jets using the

values obtained from Eq. 5.

The second subtraction step starts with the definition of a new set of seeds using a combination of

0.2 calorimeter jets from the first subtraction step, each with

25 GeV, and jets formed from inner detector tracks, using anti-k

with

0.4, with

10 GeV. Using this new set of seeds, a new estimate of the UE,

(η), is calculated excluding cells within

0.4 of the new seed jets, where

∆R= q

(η

)

(φ

)

. New v

values, v

i

, were also calculated excluding all cells within

∆η=

0.4 of any of the new seed jets. This exclusion largely eliminates distortions of the calorimeter v

measurement in events containing high-

jets.

4 Photon reconstruction

Once the mean energy

and v

values are evaluated in each layer, excluding all seeds from the aver- aging, the background subtraction is then applied to the original cell energies using Eq. 5 but with

and v

replaced by the new values,

(η) and v

. This procedure 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 three sources: jets, photons/electrons, and background fluctuations (possibly including higher order flow harmonics). It should be noted that while it is straightforward to estimate a mean energy as a function of

make further subtraction of more localized structures. Thus, fluctuations are an essential aspect of the photon analysis in the heavy ion data.

Acting upon the subtracted cells, the ATLAS photon reconstruction [26] is seeded by clusters of at least 2.5 GeV found using a sliding window algorithm applied to the second sampling layer of the electromagnetic 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 typically 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

and

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) [26].

This window size is used in the proton-proton analysis 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 used in ATLAS allows detailed characterization of the shape of each photon shower, providing tools to reject jets and hadrons, while maintaining high e

ciency for the photons themselves. In this analysis, nine shower-shape variables are used, all of which have been used extensively in previous ATLAS publications, particularly the measurement of prompt photon spectra as a function of pseudorapidity [11, 12].

The primary shape variables used can be broadly classified by which sampling layer is used.

The second sampling is used to measure

• R_η

, the ratio of energies deposited in a 3

7 (η

7 window, in units of the second layer cell size.

• wη,2

, the root-mean-square width of the energy distribution of the cluster in the second layer in the

direction

• R_φ

, the ratio of energies deposited in a 3

3 (η

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:

• R_had

, the ratio of transverse energy measured in the hadronic calorimeter to the transverse energy of the photon cluster.

• R_had1

, 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

when

0.8 or

1.37 while it is applied to

otherwise.

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

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

• F_side

, 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_ratio

, the asymmetry between the transverse energies in the first and second maxima in the strip layer

• ∆E, the diff

erence 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

er slightly, but significantly, from the Monte Carlo calculations [11]. To account for these differences, a set of correction factors has been developed to account for small shifts in the distributions. This analysis uses the standard shift factors obtained by comparing

simulations 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,

(R

). The isolation energy is the sum of transverse energies in calorimeter cells (including hadronic and electromagnetic sections) in a cone

∆η²+ ∆φ² < R_iso

around 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 pp analyses [11, 12], the cone size was chosen to be

0.4, while in this heavy ion analysis, the cone is chosen to be slightly smaller,

0.3, to reduce the sensitivity to underlying event fluctuations. The analysis presented here also uses a less restrictive isolation criterion

(R

0.3)

6 GeV, as compared to the criterion used in the pp analyses

(R

0.4)

3 GeV [11, 12].

A standard correction based on a fraction of the photon energy is applied to the calculated isolation

energy to remove photon shower leakage into the isolation cone. However, it is found that a small

(approximately 2%) leakage of the photon energy contaminates the isolation cone energy in the most

peripheral events. At present, no correction is applied for this. However, a systematic uncertainty based

on this residual leakage is assigned as a function of centrality (see below).

[TeV]

ET

Σ FCal

0 1 2 3

Counts/Event [1/TeV]

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

, 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 of events that trigger the 16 GeV level 1 trigger, and the solid line shows the distribution for photon candidates with

40 GeV satisfying tight selection cuts (see section 10.3).

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

4.9), at the electromagnetic scale, FCal

. The trigger and event selection were studied in detail in the 2010 data sample [24] 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

distributions in the 2011 data match those measured in 2010 to a high degree of precision, 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

distribution 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

40 GeV, and that satisfy the “tight” selection cuts explained in Section 10.3.

Table 1 collects all of the centrality-related information used in this analysis. It specifies the FCal

ranges 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

. The geometric quantities are calculated as described in Ref. [29] using a Glauber Monte Carlo

calculation, with a simple implementation of the ATLAS FCal response. One finds smaller uncertainties

of the mean nuclear thickness since it is the ratio of

, which scales with

, and

itself.

Bin

range

Error

Error

Error

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 45.9 6% 77.8 9% 1.22 9.4%

Table 1: Centrality bins used in this analysis, tabulating the percentage range, the

range (in 2011), the average number of participants (hN

quantities.

6 Simulation data samples

For the extraction of photon performance parameters (e

ciencies, photon energy scale, isolation prop- erties), a set of 450,000 photon+jet events using the ATLAS MC11 tune of PYTHIA 6.4 at

s =

2.76 TeV, is overlaid on minimum-bias HIJING events, which are referred-to as “HIJING+PYTHIA” sam- ples. The HIJING events are modified after initial generation to include angular modulations as a func- tion of centrality, transverse momentum and pseudorapidity, parametrized from ATLAS measurements of the second through sixth Fourier components of the angular distributions relative to the event plane measured in the FCal [27]. The sample is divided equally into three subsamples based on requiring a minimum transverse momentum for the outgoing primary photon. The first has

17 GeV, the second has

35 GeV and the third

70 GeV. The generated samples are fully simulated using GEANT4 and digitized to produce simulated raw data files, that are reconstructed and analyzed exactly as is done for experimental data.

In the HIJING+PYTHIA sample, the FCal

has been scaled up by 1.081 to best match the measured and simulated distributions. This is to ensure a comparison of equivalent levels of activity in the barrel region where the analysis is performed, and detailed comparisons of fluctuations in small regions have already been performed by ATLAS [28], which validate this procedure.

7 Comparison of photon candidates in data and simulation

7.1 Photon shower shape variables

Comparisons of shower shape variables are used to validate the use of the Monte Carlo for determining

efficiency and background contamination correction factors. Figure 2 shows three typical examples of

shape variables for data from the 0-10% centrality bin, compared with Monte Carlo calculations. In all

cases, photon clusters passing tight cuts with reconstructed transverse energy greater than 40 GeV (after

UE subtraction) and

1.3 are shown. These distributions are all normalized by the number of counts

in each distribution, separately for data and Monte Carlo, and divided by the bin width.

ws,3

0 0.2 0.4 0.6 0.8 1

Normalized counts

10-1

1 10

Preliminary ATLAS Data Simulation Converted Unconverted 0-10% Central

η,2

w

0.005 0.01 0.015

Normalized counts

10 102

103 ATLAS Preliminary

Rhad1

-0.1 -0.05 0 0.05 0.1

Normalized counts

10-1

1 10 102

Preliminary ATLAS

ws,3

0 0.2 0.4 0.6 0.8 1

Normalized counts

10-2

10-1

1

10 ATLAS Preliminary Data

Simulation Converted Unconverted 40-80% Central

η,2

w

0.005 0.01 0.015

Normalized counts

1 10 102

103 ATLAS Preliminary

Rhad1

-0.1 -0.05 0 0.05 0.1

Normalized counts

10-1

1 10 102

Preliminary ATLAS

Figure 2: Comparisons of three photon identification variables from data (black points) with full sim- ulation results. 0-10% central events are shown in the top row, while 40-80% central is shown on the bottom. The simulation is shown both fully integrated (yellow) and broken out into contributions from unconverted photons (red histogram) and converted photons (blue histogram).

8 Theoretical predictions

While the MC11 PYTHIA samples are used for corrections within small phase space bins, they also pro- vide a prediction of the photon spectrum at leading order. For next-to-leading order (NLO) calculations, the JETPHOX package is used [15], which has been successfully compared to data from the Tevatron and LHC. JETPHOX provides access to all modern PDFs and calculates both direct production as well as photons from fragmentation processes, with an implementation of an isolation cut built into the cal- culations. The calculations shown in this work use the CTEQ6.6 PDFs, with no nuclear modification, and require less than 6 GeV isolation energy in a cone of

0.3 relative to the photon direction.

Uncertainties are estimated by simultaneously varying the renormalization and initial and final state fac-

torization scales by a factor of two, relative to the baseline result, assuming

.

This coherent variation of the renormalization and initial and final state factorization scales by a factor

of two varies the JETPHOX yield up and down by about 13%, independent of

within the numerical

accuracy of the calculations.

9 Collision data selection

9.1 Event selection

The data sample analyzed here is from the 2011 LHC heavy ion run, colliding lead nuclei at

s_NN =

2.76 TeV. After requiring the 16 GeV Level 1 electromagnetic cluster trigger, which is sensitive in particular 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. 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, leaving an integrated luminoisty of about

133

for this analysis, after the exclusion of several runs. Both sets of Minimum Bias Trigger Scintillators (covering 2.09

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 vertex is required to be reconstructed in the ATLAS detector, to reject background events from e.g. cosmic rays. While ATLAS recorded about 150 million events out of the nearly one billion delivered minimum bias collisions in the 2011 heavy ion run, the photon sample only contains less than 250k events, and only a fraction of these were photons passing the quality cuts outlined below.

9.2 Estimating number of sampled events

In this measurement, yields are presented per minimum bias collision, which are estimated using the total integrated luminosity, measured using the ATLAS luminosity detectors [30]. The luminosity has been calculated using a coincidence rate of the two LUCID detectors, with special dead-time free elec- tronics, with an algorithm that accounted for accidental rates [31]. Converting the measured luminosity to the total number of minimum bias events requires a measurement of event counts for the minimum bias sample. The conversion factor from measured luminosity to the total number of events has been measured by counting the total number of sampled minimum-bias events of centrality 80% and above, and correcting for prescale factors, with a precision of better than 1%, as established by comparing data taken at widely separated time intervals throughout the heavy ion run. This procedure gives the number of minimum bias events in the most-central 80% events to be

786×10

events, with an uncertainty of less than 1%.

9.3 Isolation energy distributions

As described above, the isolation energy

(R

) is the sum of transverse energies in calorimeter cells in a cone around the photon axis, excluding the photon itself, which is defined as the central core of cells in a region corresponding to 5×7 cells in the second layer of the EM calorimeter. The distance of the outer radius of the cone from the photon axis in the

plane can be anywhere from 0.2 to 0.4. Figure 3 shows the distributions of

(R

0.3) for the data as a function of collision centrality, compared with simulated distributions, normalized in the region

(R

0.3)

0. Both data and MC distributions grow noticeably wider with increasing centrality, as the background subtraction is only able to subtract the mean energy in an

interval, removing reconstructed jets, so local fluctuations are still preserved.

Furthermore, in the data, an enhancement on the

(R

0.3)

0 side of these distributions is expected from di-jet background. Still it is observed that the isolation distributions in data and simulation vary in a similar fashion, especially in the region of negative isolation energy.

Given that the width of the distribution varies with the eventwise FCal

, growing slowly with

centrality, it is important to check the e

ect of the di

ering distributions of

in data and MC, since

the MC is not weighted to resemble the solid curve in Figure 1. The ratio between the minimum bias

distribution and the triggered distribution is approximately linear in

. To assess the effect of this

di

erence, distributions were studied with and without scaling the distributions by

. The largest

=0.3) [GeV]

(Riso

ET

-20 0 20 40 60

Normalized counts

10-4

10-3

10-2

10-1

1

40-80%

Preliminary ATLAS

=2.76 TeV sNN

Pb+Pb b-1

µ = 133 Lint

Data PYTHIA+HIJING

=0.3) [GeV]

(Riso

ET

-20 0 20 40 60

Normalized counts

10-4

10-3

10-2

10-1

1

20-40%

Preliminary ATLAS

=2.76 TeV sNN

Pb+Pb b-1

µ = 133 Lint

Data PYTHIA+HIJING

=0.3) [GeV]

(Riso

ET

-20 0 20 40 60

Normalized counts

10-4

10-3

10-2

10-1

1

10-20%

Preliminary ATLAS

=2.76 TeV sNN

Pb+Pb b-1

µ = 133 Lint

Data PYTHIA+HIJING

=0.3) [GeV]

(Riso

ET

-20 0 20 40 60

Normalized counts

10-4

10-3

10-2

10-1

1

0-10%

Preliminary ATLAS

=2.76 TeV sNN

Pb+Pb b-1

µ = 133 Lint

Data PYTHIA+HIJING

Figure 3: Distributions of photon isolation energy in a

0.3 cone for the four centrality bins in data (black points) and for MC (yellow histogram), normalized for negative

(R

0.3) values. The differences at large values of

(R

0.3) can be attributed to the presence of jet contamination in the data, which is not present in the MC sample.

difference was with the most peripheral bin, where the width (estimated by a Gaussian fit) was 14%

larger in the weighted case. However, the fraction of MC events over a fixed cut of 6 GeV (explained below) is 5% in the unweighted distribution and 6% in the weighted distribution. Given the small e

ect found in these estimates, reweighting is not used in the final analysis, and the expected effects on the extracted yields are far smaller than the final stated systematic uncertainties, discussed below.

10 Photon trigger and reconstruction performance

10.1 Kinematic bins

The kinematic intervals used in this analysis are defined as follows. For each centrality bin, as described above, the photon kinematic phase space is divided into intervals in photon

and

. For the presentation of final yields, photons are integrated over

1.3 but some corrections are made separately in four intervals, [−1.3,

0.0),[0.0, 0.8] and (0.8, 1.3]. Within each

interval, there are eight ranges in

, 45-50 GeV, 50-60 GeV, 60-70 GeV, 70-80 GeV, 80-100 GeV, 100-120 GeV, 120-140 GeV, and 140-200 GeV.

10.2 Photon trigger e ffi ciency

The trigger efficiency has been checked using a sample of minimum bias data, where the primary triggers

did not select on particular high-

activity. In this sample, events were triggered based on either a

coincidence in the zero degree calorimeters (ZDCs), which measure neutral particles with

8.3

or a total of 50 GeV or more deposited in the calorimeter system. Figure 4 shows the probability for

[GeV]

photon pT

0 10 20 30 40

(>16 GeV)∈

0 0.5 1

Preliminary ATLAS

=2.76 TeV sNN

Pb+Pb Tight photons All photons

Figure 4: Trigger e

ciency for events with photon candidates, based on minimum bias data, given as the ratio of the number of “HI tight” photons (points) and all photon candidates (histogram) where an associated 16 GeV electromagnetic energy trigger was satisfied at level 1, relative to all recorded events.

fully identified photons (after background subtraction) (black points) or inclusive photon candidates (histogram) to match to a L1 “region of interest” of 16 GeV or more with a

0.15 between the reconstructed photon and the trigger cluster. It is found that the e

ciency curve in both cases reaches 100% just above photon

20 GeV, similar to that found in pp collisions.

10.3 Photon selection cuts

Photons are selected for this analysis using the “tight” criteria developed for the photon analysis in proton-proton collisions. Cut intervals are defined on all nine shower shape variables defined above, and are implemented in a

-independent, but

tight” cuts, defined as a minimal set of changes to the standard set of tight cuts used for unconverted pho- tons in the proton-proton analysis. These had been optimized in proton-proton collisions as a function of

erent detector geometries and di

erent numbers of radiation lengths in front of the calorimeter. For the heavy ion analysis, as small a set of the cuts as possible were re- laxed to maintain good performance and background rejection, while avoiding too strong of a centrality dependence, which can be induced by the e

ect of fluctuations on several of the variables,

and

in particular. As two examples, the upper cut on

was increased from approximately 100 MeV to 300 MeV, while the minimum cut on

was reduced to 0.7 from approximately 0.9. The admixture of converted photons, which depends on the amount of material in front of the electromagnetic calorimeter, and thus the pseudorapidity of the photon, is not accounted for in the analysis, but is checked by means of comparison of data with Monte Carlo.

After application of “HI tight” cuts to the 0-80% centrality sample, but before applying isolation

requirements, there are 6435 photon candidates with

45 GeV and within

1.3.

photon reco pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

-0.8 η -1.3 <

Preliminary ATLAS

HIJING+PYTHIA

photon reco pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

Preliminary ATLAS

HIJING+PYTHIA

< 0 η -0.8 <

photon reco pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

Preliminary ATLAS

HIJING+PYTHIA

< 0.8 η 0 <

photon reco pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

Preliminary ATLAS

HIJING+PYTHIA

< 1.3 η 0.8 <

Figure 5: Photon energy scale

derived from the HIJING+PYTHIA sample as a function of reconstructed photon

, applied as a correction to the reconstructed photon energy.

10.4 Photon energy scale

While the photon energy calibration is the same as used for

collisions, based on measurements of

bosons decaying into an electron and positron [26], the mixing of converted and unconverted photons leads to a small underestimate of the photon energy on average. This section gives a more detailed look at the photon energy scale, the fractional di

erence between the reconstructed and truth photon transverse energies, (p

)/p

. Reconstructed tight and isolated photons (our nominal signal sample) are matched to primary truth photons when they are within

∆φ²+ ∆η² <

0.2 relative to each other. For these photons, the average correction to the photon energy scale is calculated for the four pseudorapidity bins described above in section 10.1). To illustrate the performance of the reconstruction, Figure 5 shows the dependence of this correction on the truth photon

. Figure 6 shows the dependence of this correction on reconstructed photon

, which is used to apply this correction to the measured photon candidates. It was checked that there are no significant di

erences between peripheral and central events, and so centrality-integrated average corrections are used.

10.5 Energy resolution

The fractional energy resolution determined by Gaussian fits to

in 4 GeV intervals in

is shown in Figure 7 for peripheral (40-80%) and central (0-10%) events, and for two bins in

the form

)/p

p²₀+

(p

p_T

)

(

)

. The sampling term

for central events is found

to be 10-12% in both pseudorapidity bins. While these fits are not used in the analysis, it is useful to get

a sense of the precision of the ATLAS electromagnetic calorimeter for measuring photon energies.

photon truth pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

< -0.8 η -1.3 <

Preliminary ATLAS

HIJING+PYTHIA

photon truth pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

Preliminary ATLAS

HIJING+PYTHIA

< 0 η -0.8 <

photon truth pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

Preliminary ATLAS

HIJING+PYTHIA

< 0.8 η 0 <

photon truth pT

0 50 100 150 200

T/pTp∆

-0.02 -0.015 -0.01 -0.005 0 0.005

Preliminary ATLAS

HIJING+PYTHIA

< 1.3 η 0.8 <

Figure 6: Photon energy scale

derived from the HIJING

PYTHIA sample as a function of reconstructed photon

, applied as a correction to the truth photon energy.

[GeV]

photon truth pT

50 100 150

T)/p T(pσ

0 0.02 0.04 0.06

Preliminary ATLAS

HIJING+PYTHIA

=2.76 TeV sNN

|<0.8 η

| 40-80%

0-10%

|<1.3 η 0.8<|

40-80%

0-10%

Figure 7: Photon resolution

)/

from simulation, for 0-10% central events (closed symbols), 40-

80% peripheral events (open symbols),

0.8 (circles) and 0.8

1.3 (squares).

11 Yield extraction

11.1 Double sideband technique

The main goal of this note is to measure the fully-corrected spectrum of photons for each centrality bin.

This involves removal of background from di-jet events and correction for the photon e

ciency. Correc- tions to the spectral shape from the photon energy resolution are found to be small and are not included in this analysis. The technique used for background subtraction is the so-called “double sideband method”.

In this approach, already used by ATLAS in Refs. [11] and [12], photon candidates are binned on two axes, illustrated in Figure 8. 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. The idea is to find candidates which satisfy most of the criteria for being photons, but which have an enhanced probability of being from jet fragments.

=0.3) [GeV]

(Riso

ET

0 5 10 15 20

HI Tight Non-tight

A B

C D

Figure 8: Illustration of the double sideband approach, showing the two axes for binning photon can- didates: 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.

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 truth photons would appear, after applying a truth-level isolation criterion.

• B: tight, non-isolated photons:

These are photons which happen to be in the vicinity of a jet, or an underlying 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 real

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 narrow photons, nor ones which are in isolated regions.

The non-tight photons are used to estimate the contribution from jets in the signal region A. This works provided there is essentially no correlation between the axes, i.e. that it is not the isolated nature of a cluster which tends to make it pass tight cuts. If this is rigorously the case, and if there is no leakage of signal from region A to the other non-signal regions (B, C and D), then the double sideband approach suggests that one can use the ratio of counts in C to D to extrapolate the measured number of counts in region B to correct the measured number of counts in region A, i.e.

N^sig =N_A^obs−N^obs_B N_C^obs

N_D^obs

(6)

If there is any leakage of signal into the background regions, then these must be removed systematically before attempting to use them to extrapolate into the signal region. A set of “leakage factors”,

, are calculated to extrapolate the number of signal events in region A into the other regions.

N^sig_A =N_A^obs−

N^obs_B −cBN_A^sig

N_C^obs−cCN_A^sig

N^obs_D −c_DN^sig_A

(7) The leakage factors are calculated using the simulated PYTHIA sample as

. In the 40-80%

centrality interval and from

40 to 200 GeV,

ranges from 0.005 to 0.04,

ranges from 0.06 to 0.02, and

is less than 0.003. In the 0-10% centrality interval and over the same

range,

ranges from 0.16 to 0.24,

ranges from 0.06 to 0.01, and

ranges from 0.01 to 0.005. Except for

, which reflects the very different isolation distributions in peripheral and central events, the isolation factors are of similar scale.

In practice, Equation 7 is solved numerically using the Brent root solver implemented into ROOT [32].

In order to calculate the statistical uncertainty for each centrality and

interval, the equation is solved 5000 times, each time sampling the eight parameters (N

,

) from a Poisson distribu- tion with the observed value assumed to be the mean of the distribution. The mean of a Gaussian fit to the distribution of

is taken as the background-corrected yield, while Gaussian standard deviation is taken as the statistical error on the mean.

11.2 Photon e ffi ciencies

The final conversion of the measured yield into a yield per event, and ultimately into

, requires several more factors: the total number of events in each centrality sample, and a reconstruction efficiency including all known e

ects. The e

ciencies are defined for “HI tight”, isolated photons relative to all PYTHIA photons with an isolation energy in a cone of

0.3 around the photon direction of less than 6 GeV. This selection at the truth particle level removes about 1.5% of the photon sample.

Once the truth photons are properly defined, the needed e

ciency corrections are categorized into three broad classes:

• Reconstruction efficiency:

This is the probability that a photon is reconstructed with 90% or more of its truth 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.

[GeV]

photon pT

0 50 100 150 200

Efficiency

0 0.2 0.4 0.6 0.8 1

Preliminary ATLAS

40-80%

∈ Photon ID

20-40%

∈ Photon ID

10-20%

∈ Photon ID

0-10%

∈ Photon ID

40-80%

∈ Total

20-40%

∈ Total

10-20%

∈ Total

0-10%

∈ Total

Figure 9: Photon reconstruction e

ciency as a function of photon

and event centrality averaged over

1.3, based on MC calculations performed in four subintervals in

identification efficiency, without the contribution from the isolation requirement. The solid lines indicate the smoothed total e

ciency used to correct the measured photon yield.

• Isolation efficiency:

This is the probability that a photon which would be reconstructed and pass identification cuts, also passes the chosen isolation cut. While this is not performed the

analysis, where the fluctuations of the isolation energy are well below the chosen isolation cut, the large fluctuations from the underlying event in heavy ion collisions can lead to an individual photon being found in the non-isolated region. While leakage into region B also depends on photon

, the isolation e

ciency primarily reflects the standard deviation of the isolation energy distribution.

These e

ciencies are defined in such a way that the “total e

ciency”

– the probability that a photon would be reconstructed AND identified AND isolated – 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

0.3 around the photon direction. Figure 9 shows the product of the reconstruction and identification efficiency (points) and the total efficiency (solid lines).

12 Photon yields

In this section, the double sideband technique is applied to extract the photon yield per minimum bias event (1/N

)dN/

(

(which scales as the number of binary collisions). The photon yield is defined as

1

dN_γ

d p_T

(p

tot ×N_evt×∆p_T

(8)

where

is the background-subtracted yield in region A,

is the abovementioned total e

ciency,

is the number of events in centrality bin

is the width of the transverse momentum interval,

and

is the average nuclear thickness for that bin. Each bin requires a small correction to account

[GeV]

photon pT

0 100 200 300

1-Purity

-0.5 0 0.5 1

Preliminary ATLAS

= 2.76 TeV sNN

Pb+Pb b-1

µ = 133 Lint

40-80%

20-40%

10-20%

0-10%

Figure 10: The factor 1

extracted from data in each

interval for two centrality bins, using the double sideband method.

for the photon energy resolution but these are found to be small, and well within the stated experimental uncertainties, and are thus not applied in this analysis.

12.1 Choice of analysis parameters

The final photon yields are extracted using “HI tight” cuts, an isolation cone radius of

0.3 and an isolation energy cut of

6 GeV to define region A, a selection of

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

,

,

and

the central 0-10% interval, the 6 GeV isolation selection sits at 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

ciency”

correction described above.

12.2 Measured photon purity

The double sideband method provides an estimate for the purity (P) of the measured sample, which

is defined as

. The correction 1

applied to the measured yield in Region A is shown in

Figure 10 as a function of transverse momentum in the four measured centrality intervals. While the

statistical errors are large, driven both by the low count numbers in both data and some of the MC

intervals, the trend is clear in both centrality ranges: the correction is relatively large at low transverse

momentum, at about 30%, but decreases systematically with

. Values of negative 1

can arise when

the number of events in the background regions is low, but they are all consistent with positive values,

within the large statistical uncertainties.