FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
FYS453 Relativistic Heavy Ion Collisions Exam Slides
Photons
Motivation
QGP
Plasma
QM11
Backup
Henrik Qvigstad
henrik.qvigstad@fys.uio.no
Compton
Plasma
University of Oslo
June 22, 2011
1 / 44
FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
1 Flow
Motivation
Definitions
Experimental Measurement
Radial Flow
Direct Flow
Elliptic Flow
Variations in Initial Condition and Flow
2 Photons in Relativistic Heavy Ion Collisions
Motivation
Photons as a signature of QGP
Photon production by quark annihilation in QGP
3 Quark Matter 2011
4 Backup slides
Photons through the Compton Process
Photon production by quark annihilation in QGP
2 / 44
FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Flow
Motivation
• An hypothesis of an strongly
interacting nuclear matter, expanding
from an initial state of spatially
anisotropy, predicts anisotropy of the
particle momentum distribution in the
final state.
• The anisotropy develops early in the
expansion, as the spatial asymmetries
decrease rapidly with time, so the
anisotropy is a probe of the early
stage of the collision.
• The anisotropy is sensitive to the
properties of nuclear matter at this
stage. (QGP, sQGP, Hadron Gas)
3 / 44
FYS4530
Definitions
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Parametrization through expansion,
∞
X
d 3N
1 d 2N
=
[1 +
2vn (y , pT ) cos(nϕ)],
d 3p
2π dydpT
(1)
n=1
where
• v1 is referred to as Direct Flow and
• v2 is refereed to as Elliptic Flow.
Backup
Compton
Plasma
4 / 44
FYS4530
Measurement
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
Method: Event Plane Method, event-by-event measure
X
X
Qn,x =
wi cos(nϕn ), Qn,y =
wi sin(nϕn ),
i
(2)
i
QM11
Backup
Compton
Plasma
vnobs = (pT , y ) = hcos[n(ϕi −Φn )]i,
vn =
vnobs
,
Rn
Φn = atan2(Qn,x , Qn,y )/n,
(3)
Rn = hcos[n(Φi − ΦRP )]i
(4)
5 / 44
FYS4530
Measurement
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Method: Particle Correlation, where we observe
∞
X
dN pairs
∝ (1 +
2vn2 cos(n∆φ).
d∆φ
(5)
n=1
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
The parametrization of 5 is called the pair-wise correlation
method. Direct measurement can be done with the two-particle
cumulant method:
∗
i,
vn {2}2 = hcos[n(φ1 − φ2 )]i = hun,1 un,2
(6)
where un ≡ e inφ .
Higher order cumulant methods are also available. It can be
shown that
∗
∗
∗
∗
∗ 2
vn4 {4} ≡ −hhun,1 un,2 un,3
un,4
ii = −hun,1 un,2 un,3
un,4
i+hun,1 un,2
i
(7)
6 / 44
FYS4530
H. Qvigstad
Radial Flow
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Transverse Flow: A+A @ SIS-SPS
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
From the fit to Thermal Model we can extract
inverse slope parameter T
7 / 44
FYS4530
Radial Flow
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
The
TheFireball
Fireballrapidly
rapidlyexpands
expands
note
1 1 dET
π R 2 τ 0 dy
~ 5 - 15
ε Bj =
ε Bjorken
GeV/fm3
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
PHENIX Preliminary
uu==HHrr
HH0==(71
± 7) km/sec/Mpc
0 (71 ± 7) km/sec/Mpc
-18
-1
HH0==(2.3
(2.3±±0.2)x10
0.2)x10-18sec
sec-1
0
-1
HHRHIC ==<u
≅ 4x102222sec
<uT>/R
sec-1
RHIC
T>/R ≅ 4x10
HHRHIC / /H0
 2 x 104040
RHIC H0  2 x 10
PHENIX (nucl-ex/0410012)
Evidence
Evidencefor
foruniversality
universality
ofofHubble
HubbleFlow
Flow!!
R. Lacey, QM’05 talk
8 / 44
FYS4530
H. Qvigstad
Direct Flow
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
• As the two nuclei collide, an hot and dense medium is
created, deflecting the participants and the fringe region.
• This causes direct flow, hv1 (y ) = cos(ϕ)i
9 / 44
FYS4530
H. Qvigstad
Disappearance of Flow
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Transition to
Quark-Gluon
Plasma leads to
decrease in
pressure and,
therefore, to
softening of the
directed flow
10 / 44
FYS4530
H. Qvigstad
Directed flow in microscopic simulations
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Au+Au @ 130 and 200 AGeV
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
11 / 44
FYS4530
H. Qvigstad
Centrality, pT, and η dependence of v1
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
●
Negative slope at midrapidity:
✔
✔
●
●
Same as at RHIC
In contrast to some of the theoretical predictions
Zero crossing around pT ~1.5 GeV
Weak centrality dependence
IlyaSelyuzhenkov 27/05/2011
12 / 44
FYS4530
H. Qvigstad
v1 at forward rapidity
8
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
●
Extended rapidity range with V0s detectors
●
20% offset between results for η <-2 and η >2
✔
V0s systematics is under study
Azimuthal asymmetry with V0s: poster #614 by G. Eyyubova
IlyaSelyuzhenkov 27/05/2011
13 / 44
FYS4530
H. Qvigstad
Longitudinal scaling
10
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
STAR data: PRL 101, 252301 (2008)
PHOBOS data: PRL97, 012301 (2006)
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Universal trend when shifted to beam rapidity
Data follows the longitudinal scaling observed at RHIC
IlyaSelyuzhenkov 27/05/2011
14 / 44
FYS4530
Elliptic Flow
H. Qvigstad
0.08
Flow
0.06
0.04
0.02
v2
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
ALICE
STAR
0
PHOBOS
PHENIX
-0.02
Motivation
QGP
Plasma
NA49
CERES
-0.04
E877
EOS
-0.06
QM11
E895
FOPI
-0.08
1
Backup
10
2
10
3
10
104
sNN (GeV)
Compton
Plasma
Figure: Elliptic
• At low energy, elliptic flow was observed out-of-plane
(negative v2 ), a phenomena called squeeze out.
√
• At mid energy ( s ∼ 2 − 3GeV /A), elliptic flow changes
to in-plane
15 / 44
FYS4530
0.12
H. Qvigstad
0.1
Flow
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
0.08
v2
Motivation
Definitions
Measure
Radial
Direct
Elliptic
0.06
v2{2}
v2{2} (same charge)
v2{4}
v2{4} (same charge)
v2{q-dist}
v2{LYZ}
v2{EP} STAR
v2{LYZ} STAR
0.04
0.02
0
0
10
20
30
40
50
60
70
80
centrality percentile
Figure: Integrated v2, 0.2 < pT < 5.0 GeV /C
• Strong elliptic flow is seen in ALICE data.
• The relative gap between v2 {2} and v2 {4} is interpreted
as being the result of non-flow and flow variations.
16 / 44
FYS4530
Higher Order Coefficients
H. Qvigstad
Initial Condition Variations
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
C(Δφ)
Flow
Centrality 0-1%, |η| < 0.8
1.01
|Δη| > 1
v2,3,4,5{2, |Δη| > 1}
1.008
1.006
1.004
1.002
1
0.998
0.996
2.0 < pt,trig < 3.0
1.0 < pt,assoc < 2.0
0.994
0.992
-1
0
1
2
3
4
Δφ (rad.)
FIG. 4. (color online) T he two-particle azimuthal correlation, measured in 0 < ∆ φ < π and shown symmetrized over
2π, between a trigger particle with 2 < pt < 3 GeV/ c and
an associated particle with 1
2 GeV/ for the 0–1%
centrality class. T he solid red line shows the sum of the measured anisotropic flow Fourier coefficients
17 / 44
FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Photon Production
Motivation
• Photon mean free path length is much
larger then then the size of the system
and thus
• photons escape without post- final
state interaction.
• The Spectra of Photons therefore
contains undisturbed information about
initial, perturbative, stage of the
collision which is sensitive to the
parton distribution function.
Assuming equilibration,
• the Photon Spectrum is sensitive to the equation of
state. If equilibrium is reached, the information about the
temperature.
• The Thermal Photon flow is sensitive of the quark/hadron
flow.
18 / 44
FYS4530
H. Qvigstad
Direct and Inclusive
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
The Inclusive Photon Spectrum includes
• Direct Photons, that is
• Thermal,
• QGP and
• Hadron Gas, and
• Non-Thermal, i.e. Prompt Photon and Pre-Equilibrium
Photon production and
• Decay Photons, the product of resonance decay
(Light Cone)
Figure: Light cone
19 / 44
FYS4530
Direct Photon Extraction
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
The Direct Photon Spectra is difficult to extract, due to
• huge background from decay product, e.g. π 0 → γγ,
• superposition of spectra from the phases of the
evolution of the system
• etc ...
QM11
Backup
Compton
Plasma
20 / 44
FYS4530
Direct Photon Extraction
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
The Direct Photon Spectra is difficult to extract, due to
• huge background from decay product, e.g. π 0 → γγ,
• superposition of spectra from the phases of the
evolution of the system
• etc ...
The spectrum can be extracted by,
1 measuring the production rate of Decay Photon Mothers
by
1.1 extracting signal from background using Event Mixing, and
1.2 apply efficiency correction determined using simulation,
and then
2 subtracting Non-Direct Photon Background determined by
simulation.
21 / 44
FYS4530
H. Qvigstad
Photon Production in the Plasma
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Photons in the plasma can be produced through annihilation,
qq̄ → γg ,
qq̄ → γγ,
(8)
or through “Compton Scattering”,
gq → γq,
g q̄ → γq̄.
(9)
Backup
Compton
Plasma
22 / 44
FYS4530
H. Qvigstad
Photons through annihilation
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
• σ(qq̄ → γg ) can be written in terms of σ(e − e + → γγ) , a
cross section that is worked out in Berestetskii, et. al.
1982, according to Wong.
• Furthermore, The differential cross section contains terms
which vary as (t − m2 )−1 and (u − m2 )−1 .
• For the relativistic case
a 2 o
λij eq 2 4παe αs n s ln
−
1
(10)
σqq̄→γg (s) = 2
e
s
m2
23 / 44
FYS4530
Photon Production in the plasma
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Using the approximation of ~pγ = ~pq , photon production due to
annihilation (qq̄ → γg ) in the plasma is given by
Eγ
dNγann
4Ns2
=
fq (~pγ )
(11)
d~pγ d 4 x
(2π)6
p
XZ
s(s − 4m2 )
3
×
.
d pq̄ fq̄ (~pq̄ )[1 + fg (~pq̄ )]σ̄qf q̄f →γg (s)
2Eq̄
f
Using Fermi-Dirac for fq , Bose-Einstein for fg , the relativistic
approximation, and u & d quarks,
for annihilation
dNγann
4Eγ T
5 αe αs
2
=
fq (~pγ )T ln
Eγ
+ Cann
(12)
d~pγ d 4 x
9 (2π)2
m2
24 / 44
FYS4530
Key Lesson
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
The Key Lessons is:
• The spectrum of photons production in the Plasma is
virtually same (proportional) as/to the spectrum of
momentum for the Plasma
QM11
Backup
Compton
Plasma
• For a thermal QGP, Fermi-Dirac and Bose-Einstein, the
high energy spectrum is
dNγ
∝ e −Eγ /T
dEγ
(13)
25 / 44
FYS4530
H. Qvigstad
Flow
Collision Evolution
Background
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Photons are also produced in the other stages of a HIC,
• the pre-QGP phase:
• Direct Photons, i.e. binary collisions,
• and production in pre-equilibrated Collision Matter,
• and the post-QGP phase:
• production in the Hadron Gas,
• and as decay products of final state produced particles.
26 / 44
FYS4530
H. Qvigstad
Critical d+Au Check
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
8
Photons
Motivation
QGP
Plasma
QM11

New:
 no exponential excessin
d+Au
Backup
Compton
Plasma
Poster: Y. Yamaguchi
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
27 / 44
FYS4530
H. Qvigstad
Confirmation fromd+Au and Cu+Cu
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
51

Fraction of direct photonscompared to pQCD
Photons
Motivation
QGP
Plasma
Noexcessind+Au
(nomedium)
ExcessalsoinCu+Cu
QM11
Backup
Compton
Plasma
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
28 / 44
FYS4530
H. Qvigstad
Direct Photon v2
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
11
preliminary
Au+Au@200GeV
minimumbias

p0 v2

 A:
there are no direct
photons
 B: direct photon v2 similar
to inclusive photon v2
QM11
Backup
Compton
Plasma
p0 v2 similar to inclusive
photon v2
Two possibilities
inclusivephoton v2

Key: precisemeasurement
of direct photon excess
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
29 / 44
FYS4530
H. Qvigstad
Direct Photon v2
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
12
Au+Au@200GeV
minimumbias
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
direct photon v2 large
(~15%) at pT =2.5GeV
 v2  0where prompt
photonsdominate

Direct photon v2
preliminary
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
30 / 44
FYS4530
H. Qvigstad
TheoryComparison: Direct Photon v2
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
13
Theorycalculation:
Holopainen, Räsänen, Eskola
arXiv:1104.5371v1
preliminary


Backup
Compton
Plasma

Modelsunder-predict
direct photon v2
Measurement further
constrains Ti andt i
Challengeto theorists
Plenary: S. Esumi (flow),Tue
Parallel: E. Kistenev(directphotons)Thu
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
31 / 44
FYS4530
H. Qvigstad
All togethernow
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
SummaryofRAA resultsinvariouschannels,withreferences
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
17
Figure: From PHENIX RAA talk by Martin L. Purschke, , QM11
32 / 44
Isolated photon R AA vs NPart
FYS4530
H. Qvigstad
Flow
30-100%
MB 10-30%
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
0-10%
20-25 GeV
Motivation
QGP
Plasma
25-30 GeV
QM11
Backup
Compton
Plasma
30-40 GeV
40-50 GeV
50-80 GeV
No centrality dependence
Yen-J ie Lee(MIT)
Nuclear Modification factors from the CMS experiment
Quark Matter 2011
19
Figure: From CMS Nuclear Modification Factor talk by Yen J Lee,
QM11
33 / 44
FYS4530
H. Qvigstad
Isolated photon R AA in 0-10% PbPb collisions
PbPb 0-10% Photon R AA
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
PbPb(EPS09,nDS,HKN07)/pp(CT10)
Pb+Pb
Photons
Motivation
QGP
Plasma
QM11
E TIso <5 GeV
Backup
Compton
Plasma


CMS measured the isolated photon R AA for the first time
The photon R AA at 0-10% is consistent with unity
Yen-J ie Lee(MIT)
Nuclear Modification factors from the CMS experiment
Quark Matter 2011
18
Figure: From CMS Nuclear Modification Factor talk by Yen J Lee,
QM11
34 / 44
FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
fin
QM11
Backup
Compton
Plasma
35 / 44
FYS4530
H. Qvigstad
Photons through annihilation
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
The gluon vertex is associated with
a
µ λij
g γαβ
2
(14)
The photon vertex(es) are associated with
QM11
Backup
Compton
Plasma
µ
− ieq γαβ
(15)
Thus, the cross sections are related as
a 2
λij αs e 2
dσ
dσ
Eγ
(qq̄ → γg ) = Eγ
(qq̄ → γγ) (16)
d~pγ
2 αe eq
d~pγ
36 / 44
FYS4530
H. Qvigstad
Photons through annihilation
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
The cross-section can be written in terms of
t = (p1 − p3 )2 = (pq − pγ )2 , and it can be shown that
q
s − 4mq2 dσ p · (p + p ) √s dσ
γ
q
q̄
√
Eγ
=
δ
−
.
d~pγ
2π
dt
2
s
(17)
Furthermore, qq̄ → γγ is related to e + e − → γγ such that
e 4 dσ
dσ
q
(qq̄ → γγ) =
(e + e − → γγ)
dt
e
dt
(18)
, a cross section that is worked out in Berestetskii, et. al. 1982,
according to Wong.
37 / 44
FYS4530
H. Qvigstad
Photons through annihilation
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
t − m2 = −2pg · pq = −2Eg (Eq − |~pq | cos θgq ).
(19)
The differential cross section contains terms which vary as
(t − m2 )−1 and (u − m2 )−1 . Thus the cross section is at
maximum when the produced particle momenta is parallel with
the momenta with the initial particles, i.e.
θgq , θγq̄ {0, π}.
m2 )−1
Furthermore, expanding the (t −
the the width of the peak, ∆θgq , is
m
∆θgq =
.
Eq̄
(20)
around θgq show that
(21)
Thus, for the relativistic case,
dσ
1
Eγ
(qq̄ → γγ) = σqq̄→γγ (s) Eg [δ(~pγ − ~pq ) + δ(~pγ − ~pq̄ )].
d~pγ
2
(22)
38 / 44
FYS4530
Photons through annihilation
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
The total cross section for e + e − → γγ is also worked out in
Berestetskii, and by using the previous
σqq̄→γg (s) =
e 2 4πα α
q
e s
(23)
e( s − 4m2
!
√
√
s + s − 4m2
4m2 16m4
√
×
1+
− 2
ln √
s
s
s − s − 4m2
)
r
4m2
4m2
− 1+
1−
.
s
s
Thus, for the relativistic case
a 2 o
λij eq 2 4παe αs n s σqq̄→γg (s) = ln
−
1
2
e
s
m2
(24)
39 / 44
FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
Photons through the Compton
Process
Another source of photons in the plasma are through
gq → γq,
(25)
g q̄ → γq̄.
(26)
QM11
Backup
Compton
Plasma
This process is analogous to the Compton Reaction, where a
photon scatters of a charged particle, and are therefore called
the Compton Process.
As for the case of qq̄ annihilation, we may write
a 2
λij αs e 2
dσ
dσ
Eγ
(g q̄ → γg ) = Eγ
(γq → γq) (27)
d~pγ
2 αe eq
d~pγ
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FYS4530
Photons through the Compton
Process
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Also, as for qq̄,the cross section contains (t − m2 )−1 and
(u − m2 )−1 terms. So, maximum and width is again at
Photons
θgq , θγq̄ {0, π}.
Motivation
QGP
Plasma
QM11
∆θgq =
Backup
Compton
Plasma
m
,
Eq̄
(28)
(29)
and for the relativistic case
Eγ
1
dσ
(gq → γq) = σqq̄→γγ (s) Eγ δ(~pγ − ~pq ).
d~pγ
2
a 2 λij eq 2 4παe αs
s
1
σqq̄→γg (s) = ln
+
2
e
s
m2
2
(30)
(31)
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FYS4530
Photon Production in the plasma
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Using the approximation of ~pγ = ~pq , photon production due to
annihilation (qq̄ → γg ) in the plasma is given by
Eγ
dNγann
4Ns2
=
fq (~pγ )
(32)
4
d~pγ d x
(2π)6
p
XZ
s(s − 4m2 )
3
×
.
d pq̄ fq̄ (~pq̄ )[1 + fg (~pq̄ )]σ̄qf q̄f →γg (s)
2Eq̄
f
Backup
Compton
Plasma
Similarly, production due to Compton Process ((gq → γq)) is
given by
Eγ
dNγcom (gq → γq)
4Ns N
=
fq (~pγ )
(33)
4
d~pγ d x
(2π)6
XZ
s − m2
×
d 3 pg fg (~pg )[1 − fg (~pg )]σ̄gqf →γqf (s)
2Eg
f
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FYS4530
H. Qvigstad
Photon Production in the plasma
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Using Fermi-Dirac for fq , Bose-Einstein for fg , the relativistic
approximation, and u & d quarks,
for annihilation
dNγann
4Eγ T
5 αe αs
2
Eγ
=
fq (~pγ )T ln
+ Cann
(34)
d~pγ d 4 x
9 (2π)2
m2
Backup
Compton
Plasma
The result for Compton scattering is similar, such that the total
for the two is
dNγann
4Eγ T
5 αe αs
2
Eγ
=
fq (~pγ )T 2ln
+ Cann + Ccomp
d~pγ d 4 x
9 (2π)2
m2
(35)
43 / 44
FYS4530
H. Qvigstad
Flow
Motivation
Definitions
Measure
Radial
Direct
Elliptic
Photons
Motivation
QGP
Plasma
QM11
Backup
Compton
Plasma
Photon Production by Hadrons
In addition annihilation and Compton scattering of quarks,
interaction hadrons in the plasma leads to photon production;
i.g. the annihilation
π + + π − → γ + ρ0 ,
π± + π0 → γ + π±,
(36)
π 0 + ρ± → γ + π ±
(37)
and Compton scattering;
π ± + ρ0 → γ + π ± ,
The processes are analogous to the ones previously discussed.
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