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Direct Photon Spectra and Elliptic Flow in 2.76 TeVPb-Pb Collisions from ALICE
Martin Wildeon behalf of the ALICE Collaboration
Westfälische Wilhelms-Universität Münster
December 5, 2012
Helmholtz Research School
H-QM Quark Matter Studies
Martin Wilde 12-5-12 p.1
Table of Contents
1 Direct Photon Production and the ALICE Detector
2 Part I: Direct Photon SpectraAnalysis StrategyDetection of Converted Photons and π0sInclusive Photon Results in pp and Pb-PbDecay Photon Background CalculationDirect Photon Results in pp and Pb-Pb
3 Part II: Direct Photon v2Analysis StrategyInclusive Photon v2 AnalysisDecay Photon v2Direct Photon v2
Martin Wilde 12-5-12 p.2
Direct Photons in pp and Pb-Pb Collisions
(a) Quark-gluon Comptonscattering
(b) Quark-Anti-quark annihilation
(c) Fragmentation photons(bremsstrahlung)
Direct Photons - DefinitionPhotons that are not produced by particle decays
Prompt Photons: In pp and Pb-Pb
Calculable within NLO pQCD
Predominant source in pp
Signal scales with numberof binary collisions in Pb-Pb
Fragmentation photons may be modified byparton energy loss in the medium
Measurement of direct photons in pp is an ideal test for pQCD
Martin Wilde 12-5-12 p.3
Direct Photons in Pb-Pb CollisionsAdditional sources of direct photons in Pb-Pb collisions
Jet-Medium Interactions:
Scattering of hard partons withthermalized partons
In medium (photon) bremsstrahlungemitted by quarks
Thermal Photons:
Scattering of thermalized particles
QGP: qq̄ → gγ and qg → qγ (+NLO)
HHG (hot hadronic gas): Hadronic interactions(e.g. π+π− → γρ0)
Exponentially decreasing but dominant at low pT
Photons leave medium unaffected, an ideal probe to study HI collisions
√sNN
= 5.5TeV,charge particle rapidity density: 3000
2006 J. Phys. G: Nucl. Part. Phys. 32 1295
Martin Wilde 12-5-12 p.4
The ALICE Detector and Data Sample
pp,√s = 7TeV:
Data sample:3.54× 108 events(min. bias)
Monte Carlo:Pythia-Perugia0 and Phojet
Pb-Pb, √sNN
= 2.76TeV:
Data sample: 17× 106 min. bias events
Monte Carlo: Hijing(min. bias plus enriched events with highp
Tπ0s)
Photons are measured via their conversionproducts in ITS and TPC
Martin Wilde Direct Photon Production and the ALICE Detector 12-5-12 p.5
General Strategy of the Analysis
Subtraction Methodγdirect = γinc − γdecay = (1− γdecay
γinc) · γinc
Inclusive photons: measure all photons that are produced
Decay photons: calculated from measured particle spectra with photon decaybranches (π0, η, ...)
Double Ratioγincπ0 /
γdecayπ0
paramu γinc
γdecayif > 1 direct photon signal
→ advantage of ratio method: cancellation of uncertainties
Photons and π0s (and η) are measured via conversion methodπ0 → γγ, γ → e+e−
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.7
Photon Reconstruction with ITS and TPCSecondary Vertex Algorithm - V0 Particles
Charged tracks with large impactparameter are paired
Candidates with a small DCA→ V0 candidate
Most abundant particle species:K 0s , Λ, Λ̄ or γ
Photon conversion probability in|η| < 0.9 up to R = 180 cm at 8.5%
Cuts on the decay topology of photons and electron track properties→ Purity at 90% at 2GeV/c for 0-40% Pb-Pb events
Background is mainly combinatorial - Strange particle contribution negligible
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.8
Photon Corrections and Invariant Cross Section for pp
(GeV/c)T
p1 10
)3 c-2
(pb
GeV
3dp
σ3 dE
410
510
610
710
810
910
1010
1110
1210
3.5%± uncertainty ppσγInclusive
= 7 TeVspp,
Raw γ spectrum in pp and Pb-Pb corrected for:
purity (P)efficiency (E)conversion probability (C)
and secondary photon candidates subtracted
Inclusive photon cross section in pp: E d3σdp3 = 1
2πσMBOR
Nevents
1pT
PCE
Nγprim
∆y∆pT
Main sources of uncertainty:
Material budget of thedetector ∼ 4.5%
Efficiency estimation by cutvariationspT< 5GeV: pp ∼ 3%, Pb-Pb ∼ 6%
pT> 5GeV: pp ∼ 6%, Pb-Pb ∼ 15%
e.g. geometrical cuts, detectorPID, sharing of tracks betweensec. vertices
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.9
Inclusive Photon Invariant Yield in Pb-Pb
(GeV/c)T
p1 10
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-710
-610
-510
-410
-310
-210
-110
1
10
210
310
(0-40%)γInclusive (40-80%)γInclusive
= 2.76 TeVNNs Pb-Pb,
Two centrality selections: 0-40% and 40-80%(central and peripheral)
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.10
π0 and η Reconstruction via Conversion
)2
(GeV/cγγM0.1 0.15 0.2
2E
ve
nts
/2 M
eV
/c0
2
4
6
8
10
310×
PCM
<0.8 GeV/cT
: 0.6<p0π
)2 (GeV/cγγM0.4 0.5 0.6 0.7
2E
ve
nts
/8 M
eV
/c
0
2
4
6
310×
<1.8 GeV/cT
: 1.4<pη
Neutral pion and η (pp only) based on converted photons
Measurement based on identical set of photons as usedfor photon results
Inv. mass calculated for all photon pairs in an event
Combinatorial background obtained via mixed eventtechnique
Raw π0 spectrum obtained by peak integration
Efficiency and acceptance estimated with MCsimulations
For more details see:
pp at TeV: Phys. Lett. B 717, 162 (arXiv:1205.5724)
Pb-Pb and pp at 2.76TeV: published soon, similarmethod
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.11
Cocktail Generator
(GeV/c)T
p0 2 4 6 8 10 12 14 16
0 π /
deca
yγ
-510
-410
-310
-210
-110
1
10
210
310γall decay
)γ-e+ (eγγ → 0π)γγ0π,γ-e+,eγ-π+π (γγ → η
)γη (γ0π → ω)γγ, γω (γρ →’ η)γω, γ0π (γη → φ
)γη, γ0π (γ-π+π → ρ
= 7 TeVspp,
1/08/2012
Decay photon spectra are obtained via calculation
Based on a fit to measured π0 and η (in pp)
Other meson spectra obtained via mT-scaling
Incorporated mesons: π0, η, η′, ω, φ and ρ0
mT-Scaling:
Same shape of cross sections,f (m
T), of various mesons
E d3σm
dp3 = Cm · f (mT
)
Meson (Cm) Mass Decay Branch B. Ratioπ0 134.98 γγ 98.789%
e+e−γ 1.198%η 547.3 γγ 39.21%
π+π−γ 4.77%(0.48) e+e−γ 4.9 · 10−3
ρ0 770.0 π+π−γ 9.9 · 10−3
(1.0) π0γ 7.9 · 10−4
ω 781.9 π0γ 8.5%(0.9) ηγ 6.5 · 10−4
η′ 957.8 ρ0γ 30.2%ωγ 3.01%
(0.25) γγ 2.11%φ 1019.5 ηγ 1.3%
π0γ 1.25 · 10−3(0.35) ωγ < 5%
Phys. Rev. C (arXiv:1110.3929)
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.12
Direct Photons in pp Collisions at 7 TeV
(GeV/c)T
p0 2 4 6 8 10 12
)0 π/de
cay
γ)/
(0 π/
inc
γ(
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Direct photon double ratio)
decayγ/
direct,NLOγNLO prediction: 1 + (
T = 0.5 to 2.0 pµfor
In the ratio uncertaintiesrelated to:
normalization
π0 measurement
rec. efficiency
partially or exactly canceled
The NLO double ratio prediction is plotted as RNLO = 1 +γdirect,NLO
γdecaycocktail
Measurement is consistent with the expected direct photon signal
Direct photon signal in pp at 7TeV is consistent with zero
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.13
Double Ratio - Pb-Pb 2.76 TeV - peripheral
(GeV/c)T
p0 1 2 3 4 5 6 7 8
)0 π/de
cay
γ)/
(0 π/
inc
γ(
0.8
1.0
1.2
1.4
1.6
1.8
Direct photon double ratio)
decayγ/
direct,pp,NLOγ
collNLO prediction: 1 + (N
T = 0.5 to 2.0 pµfor
= 2.76 TeVNNs40-80% Pb-Pb,
Double ratio for peripheral events shows no excess at any value of pT
Measurement is consistent with the expected direct photon signal
pp NLO predictions scaled with Ncoll
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.14
Double Ratio - Pb-Pb 2.76 TeV - central
(GeV/c)T
p0 2 4 6 8 10 12 14
)0 π/de
cay
γ)/
(0 π/
inc
γ(
0.5
1.0
1.5
2.0
2.5
3.0
Direct photon double ratio)
decayγ/
direct,pp,NLOγ
collNLO prediction: 1 + (N
T = 0.5 to 2.0 pµfor
= 2.76 TeVNNs0-40% Pb-Pb,
Clear extra yield of 20% for pT< 2GeV/c
Ncoll scaled pp NLO in agreement with high pTdirect photons
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.15
Double Ratio - Pb-Pb 2.76 TeV - central
[GeV/c]T
p1 1.5 2 2.5 3 3.5 4 4.5 5
0.6
0.8
1
1.2
1.4
1.6
1.8
PHENIX Preliminary
=200GeVNN
sAu+Au
background
0π/γ / measured
0π/γRun4
*γ+1 from incl.γ/directγ
0 - 20%(150 MeV/c shifted)
0 - 10%
[GeV/c]T
p0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
]-2
in
v. y
ield
[(G
eV
/c)
dir
ec
tγ
-610
-510
-410
-310
-210
-110
1
10
incl.*γ/direct
*γ • inclγ = directγ
AB T•pQCD
thermal
pQCD + thermal
Au+Au (0-20%)directγ
PHENIX Preliminary
a) b)
(GeV/c)T
p0 2 4 6 8 10 12 14
)0 π/de
cay
γ)/
(0 π/
inc
γ(
0.5
1.0
1.5
2.0
2.5
3.0
Direct photon double ratio)
decayγ/
direct,pp,NLOγ
collNLO prediction: 1 + (N
T = 0.5 to 2.0 pµfor
= 2.76 TeVNNs0-40% Pb-Pb,
Clear extra yield of 20% for pT< 2GeV/c
Ncoll scaled pp NLO in agreement with high pTdirect photons
Similar to low pTdirect photon observation by PHENIX
arXiv:nucl-ex/0605005
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.16
Results of Pb-Pb Direct Photons at 2.76 TeV
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-710
-610
-510
-410
-310
-210
-110
1
10
210
310
Direct photons
= 2.76 TeVNNs0-40% Pb-Pb,
Direct Photon Spectrumfor central Pb-Pb events
Spectrum derived fromdouble ratio by:
γdirect = (1− γdecay
γinc) · γinc
NLO predictions in agreement with spectrum (pT> 4GeV/c)
At low pT(< 2.2GeV/c) spectrum fitted with an exponential
→ slope parameter T = 304± 51stat+syst MeV
Intermediate region: superposition of low and high pTdirect photons
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-710
-610
-510
-410
-310
-210
-110
1
10
210
310
= 2.76 TeVNNs0-40% Pb-Pb,
Direct photons (scaled pp)
T = 0.5 to 2.0 pµDirect photon NLO for
MeVstat+syst
51±/T), T = 304 T
exp(-p×Exponential fit: A
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.17
Results of Pb-Pb Direct Photons at 2.76 TeV
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-710
-610
-510
-410
-310
-210
-110
1
10
210
310
Direct photons
= 2.76 TeVNNs0-40% Pb-Pb,
Direct Photon Spectrumfor central Pb-Pb events
Spectrum derived fromdouble ratio by:
γdirect = (1− γdecay
γinc) · γinc
NLO predictions in agreement with spectrum (pT> 4GeV/c)
At low pT(< 2.2GeV/c) spectrum fitted with an exponential
→ slope parameter T = 304± 51stat+syst MeV
Intermediate region: superposition of low and high pTdirect photons
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-710
-610
-510
-410
-310
-210
-110
1
10
210
310
= 2.76 TeVNNs0-40% Pb-Pb,
Direct photons (scaled pp)
T = 0.5 to 2.0 pµDirect photon NLO for
MeVstat+syst
51±/T), T = 304 T
exp(-p×Exponential fit: A
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.17
Conclusions I: Direct Photon Spectra
Statistical analysis of direct photons based on converted photons via doubleratio
With current uncertainties no significant direct photon signal in pp andperipheral Pb-Pb
Direct photon signal is consistent with expectation from NLO pQCD
In central Pb-Pb:Low p
Tdirect photon signal, exponential in shape
Similar excess measured at RHIC interpreted as thermal signal
Slope parameter:TALICE = 304± 51stat+syst MeV (0-40%)TPHENIX = 221± 19stat ± 19syst MeV (0-20%)arxiv:0804.4168 PRL 104 (132301) 2010
Martin Wilde Part I: Direct Photon Spectra 12-5-12 p.18
What can we learn from direct photon v2?
0.0 1.0 2.0 3.0 4.0 5.0 6.0pT (GeV/c)
0.00
0.04
0.08
0.12
0.16
0.20
v 2(pT)
1.0 fm/c
0.4 fm/c0.2 fm/c
Au+Au@200 AGeV
0.6fm/c
0.8 fm/c
Thermal Photons
b = 6 fm
QM0.5xHMQM+HM
ideal hydro th. photon v2 for different QGP formation times τ0
arXiv:0809.0548 [nucl-th]
Initial azimuthal asymmetry in coordinate space in non-central A+A⇒ asymmetry in momentum space
dNdφ = 1
2π
(1 + 2
∑n≥1 vn cos(n(φ−ΨRP
n )))
v2: elliptic flow, collectiveexpansion at low pT
v2 at high pT : path lengthdependence of in-medium partonenergy loss
Thermal Photon v2
Constrains onset of direct photonproductionEarly production → small flowLate production → hadron-likeflow
Martin Wilde Part II: Direct Photon v2 12-5-12 p.20
General Strategy of the v2 Analysis
(GeV/c)T
p0 2 4 6 8 10 12 14
)0 π/de
cay
γ)/
(0 π/
inc
γ(
0.5
1.0
1.5
2.0
2.5
3.0
Direct photon double ratio)
decayγ/
direct,pp,NLOγ
collNLO prediction: 1 + (N
T = 0.5 to 2.0 pµfor
= 2.76 TeVNNs0-40% Pb-Pb,
Direct photon v2 obtained via comparison between measured and calculateddecay photon v2
vdirect γ2 =
R·v inc γ2 −vdecay γ
2R−1
Factor R represents the direct photondouble ratio
R · v inc γ2 : weighted inclusive photon v2 due to extra photons compared to
background
vdecay γ2 : calculated decay photon v2 from cocktail calculation
Martin Wilde Part II: Direct Photon v2 12-5-12 p.21
Inclusive Photon v2 Analysis
Centrality (%)0 10 20 30 40 50 60 70 80 90
Re
so
lutio
n
0
0.2
0.4
0.6
0.8
17/07/2012
=2.76 TeVNN
sPbPb,
V0A 3subeventV0C 3subevent
ALI−PERF−31433
ALI-PERF-43616
v2 given by the reaction plane
v2 = 〈cos(2(φ−ΨRP2 ))〉
Extracted via this formula or by a fit
Relation of RP to EP:
v2 =vEP2
〈cos(2ΨEP2 −ΨRP
2 ))〉 =vraw2
resolution
Event Plane angle determined by usingthe VZERO detector
VZEROA: 2.8 < η < 5.1
VZEROC: −3.7 < η < −1.7
Reaction plane resolution obtained by thethree sub-event method
Martin Wilde Part II: Direct Photon v2 12-5-12 p.22
Inclusive Photon v2 Results 0-40%
ALI-PREL-43604 ALI-PREL-43612
Magnitude of v2 increases with decreasing centrality
Similar v2 to hadrons
Expected behavior, main contributions are decay photons
Martin Wilde Part II: Direct Photon v2 12-5-12 p.23
Cocktail Simulation and Decay Photon v2
ALI-PERF-43620
Spectra of other mesons withphoton decay branches obtainedby mT scaling
Assumption: vπ0
2 = vπ±
2
v2 of various mesons (X)calculated via KET (quarknumber) scaling from vπ±
2
Decay photon vX2 obtained by
cocktail calculation
vX2 (pXT ) = vπ±
2
(√(KEX
T+ mπ
±)2 − (mπ
±)2)
with:KET = mT − m =
√p2T
+ m2 − m
Martin Wilde Part II: Direct Photon v2 12-5-12 p.24
Comparison of Inclusive and Decay v2
ALI-PREL-43608
Above 3GeV/c inclusive photonssignificantly smaller than decayphotons
→ Direct photon v2 contributionwith vdirect
2 < v inc2
Below 3GeV/c consistent withinuncertainties
→ Either contribution of directphotons with similar v2 or nodirect photons
Martin Wilde Part II: Direct Photon v2 12-5-12 p.25
Direct Photon v2 0-40% and Conclusions II
ALI-PREL-43588
Significant direct photon v2 forpT < 3GeV/c measured
Magnitude of v2 comparable tohadrons
Result points to late productiontimes of direct photons after flowis established
Large inverse slope parameter oflow pT direct photon spectrumfavours earlier production times
Similar direct photon v2 resultsseen by PHENIX
Martin Wilde Part II: Direct Photon v2 12-5-12 p.26
Denominator Ratio: Cocktail Generator Pb-Pb Results
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-1310
-1110
-910
-710
-510
-310
-110
10
310
510
γall decay )γ-e+ (eγγ → 0π
)γγ0π,γ-e+,eγ-π+π (γγ → η)γη (γ0π → ω
)γγ, γω (γρ →’ η)γω, γ0π (γη → φ
)γη, γ0π (γ-π+π → ρ
= 2.76 TeVNNs0-40% Pb-Pb, 26/07/2012
(GeV/c)T
p0 2 4 6 8 10 12 14
0 π /
deca
yγ
-510
-410
-310
-210
-110
1
10
210
310γall decay
)γ-e+ (eγγ → 0π)γγ0π,γ-e+,eγ-π+π (γγ → η
)γη (γ0π → ω)γγ, γω (γρ →’ η)γω, γ0π (γη → φ
)γη, γ0π (γ-π+π → ρ
= 2.76 TeVNNs0-40% Pb-Pb,
26/07/2012
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-1310
-1110
-910
-710
-510
-310
-110
10
310
510
γall decay )γ-e+ (eγγ → 0π
)γγ0π,γ-e+,eγ-π+π (γγ → η)γη (γ0π → ω
)γγ, γω (γρ →’ η)γω, γ0π (γη → φ
)γη, γ0π (γ-π+π → ρ
= 2.76 TeVNNs40-80% Pb-Pb, 26/07/2012
(GeV/c)T
p0 2 4 6 8 10 12 14
0 π /
deca
yγ
-510
-410
-310
-210
-110
1
10
210
310γall decay
)γ-e+ (eγγ → 0π)γγ0π,γ-e+,eγ-π+π (γγ → η
)γη (γ0π → ω)γγ, γω (γρ →’ η)γω, γ0π (γη → φ
)γη, γ0π (γ-π+π → ρ
= 2.76 TeVNNs40-80% Pb-Pb,
26/07/2012
Martin Wilde Part II: Direct Photon v2 12-5-12 p.28
Combined Fit for Direct Photons
(GeV/c)T
p0 2 4 6 8 10 12 14
)2 c-2
(G
eVdy
Tdp
TpN2 d
ev
. Nπ21
-710
-610
-510
-410
-310
-210
-110
1
10
210
310
Direct photons
Hagedorn
Exponential
Hagedorn+Exponential
/T)T
+ B exp(-pn/nC)T
(1+p1 π2
A = dy
Tdp
Tp
N 2d π21
51 MeV±T = 299
= 2.76 TeVNNs0-40% Pb-Pb,
Combined fit (Hagedorn + Exponential) gives similar result for the inverseslope parameter T as for the exponential only fit
Martin Wilde Part II: Direct Photon v2 12-5-12 p.29
Systematic Cut Studies ppCut Variations for γ and π0:
Cut Name Std. value Variation 1 Variation 2 Variation 3
Electron dEdx -4,5σ -4,4σ -3,4σ -Pion dEdx 1,-10σ 2,1σ 2,0.5σ 2,0.5σ
Min. p e+/e− 0.4 GeV/c 0.4 GeV/c 0.4 GeV/c 0.3 GeV/cFind. Cls. TPC 0.35 0.6 - -Photon χ2 20 30 10 -
qt 0.05 0.07 0.03 -min. pt e+/e− 50MeV/c 75MeV/c 100MeV/c -photon η, π0 y 0.9, 0.8 0.8, 0.7 1.2, 0.9 -
min. R 5 cm - 180 cm 2.8 cm - 180 cm 10 cm - 180 cm -
V0s with shared electrons rejectedPurity for different centralities usedTOF and α cut not used for ppR cut already considered for material budget
π0 yield extraction:
Three different integration windowsDifferent Numbers of mixed events for bg, different mixed event bins(n V0s, n tracks)
Cocktail simulation:
Two different fitsVariation of the mt scaling factors (η measured)
Martin Wilde Part II: Direct Photon v2 12-5-12 p.30
Systematic Cut Studies Pb-PbCut Variations for γ and π0:
Cut Name Std. value Variation 1 Variation 2 Variation 3
Electron dEdx -3,5σ -4,5σ -2.5,4σ -Pion dEdx 3,-10σ 2.5,-10σ 3.5,-10σ 3,-10σ
Min. p e+/e− 0.4 GeV/c 0.4 GeV/c 0.4 GeV/c 0.3 GeV/cFind. Cls. TPC 0.6 0.7 0.35 -Photon χ2 10 5 20 -
qt 0.05 0.03 0.07 -min. pt e+/e− 50MeV/c 75MeV/c 100MeV/c -photon η, π0 y 0.75, 0.7 0.9, 0.8 0.8, 0.7 -
min. R 5 cm - 180 cm 2.8 cm - 180 cm 10 cm - 180 cm -α meson central 0.65 1.00 - -α meson peripheral 0.8 1.00 - -
TOF -5,-5σ -3,-5σ -2,-5σ -
V0s with shared electrons rejectedPurity for different centralities used
π0 yield extraction:
Three different integration windowsDifferent Numbers of mixed events for bg, different mixed event bins(n V0s, n tracks)
Cocktail simulation:
Two different fits, with and without blast waveVariation of the mt scaling factors
Martin Wilde Part II: Direct Photon v2 12-5-12 p.31
PHENIX Direct Photon v2 Results
0 2 4 6 8 10 12
-0.05
0
0.05
0.1
0.15
0.2
0.25
(c)
2 vdir.γ
0 2 4 6 8 10 12
-0.05
0
0.05
0.1
0.15
0.2
0.25
(b)
2 vinc.γ
|=1.0~2.8)η (|RXNE.P.
|=3.1~3.9)η (|BBC
E.P.
0 2 4 6 8 10 12
-0.05
0
0.05
0.1
0.15
0.2
0.25
(a)
2 v0π
2v
[GeV/c]T
p
Martin Wilde Part II: Direct Photon v2 12-5-12 p.32
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