Electromagnetic Emission
(and energy loss) in the QGP
Guy D. Moore (McGill University)
P. Arnold, L. Yaffe, S. Jeon,
P. Aurenche, F. Gelis, H. Zaraket,
and of course many others
1
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Initial heavy ions, made up of primary partons
2
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5
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9
Interesting part: the behavior of secondaries making up the
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But photons are produced at each stage
And almost all photons escape unscathed.
10
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16
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Decay photons: decays in flight of π0 and η
17
Cartoon of yields of each processL
og(N
umbe
r)
Log(Energy)
Prompt
QGPHadronic
Prompt: power law hard
tail
QGP: thermal (exp. tail)
plus small powerlaw tail
Hadronic: like QGP but
softer
18
The bad news isL
og(N
umbe
r)
Log(Energy)
Prompt
QGPHadronic
Decay Photons
Probably more Decay pho-
tons than Direct photons at
every energy!
Why? direct photons have
no αEM suppression
19
Seeing the prompt photons
Prompt photon yield should be calculable
• Perturbative calculation
Not easy: relatively small x, scale dependence
• Measurement in pp collisions
May be visible above the backgrounds!
• Main background: π0 decays
• π0 rate is measurable (with errors)
• π0 production is suppressed (Jet Quenching)
20
Direct photons: Already observed?
(GeV)Tp
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
(GeV)Tp
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
PbGl, peripheral (60-80%)
PHENIX preliminary PHENIX preliminary
= 200 GeV Au+Au NNs
PbGl, central (0-10%)
= 200 GeV Au+Au NNs
(γ / π0) m
easured / (
γ / π0) sim
(γ / π0) m
easured / (
γ / π0) sim
Phenix observation can be interpreted as seeing photon
excess in central collisions at high pT .
At pT ∼ 5 GeV, probably “direct” photons.
21
Direct photons: Already observed!
Eγ(GeV)
QM2004 data, most central bin
22
Thermal Photons: an Interesting Theoretical
Problem
• Approximate/Assume QGP to be in equilibrium
• Compute dNγ(k, T )/d3kd4x by Thermal Field Theory
• Insert into hydrodynamic evolution of the QGP
+
Leading order diagrams.
Parametrically O(αsαEM).
Logarithmically enhanced.
Problem believed solved in
1989
23
That treatment is incomplete!
Aurenche, Gelis, Kobes, Zaraket
and
naively O(α2sαEM)
actually O(αsαEM)
Bremsstrahlung, inelastic annihilation: collinear
enhancements
Thermal QFT diagrams, summing all lines but γ:
24
Treatment STILL incomplete!
Loop diagrams like
corresponding to the interference between diagrams,
are also αsαEM! (Double collinear enhancement)
25
Physical reason
Opening angle ∼ gsT/E ¿ 1, and vquark ' c.
Wave packet transverse size ∼ 1/gsT .
Approaching quark
wide transverseScattering
site
Outgoing quark
Wave packets overlap overa long distance (Formation length)
Outgoing photonwave packet
26
Second scattering while wave packets still overlap:
Approaching quark
Emissions from scatterings overlap and interfere in
amplitude.
For E ∼ T , τ−1form∼ g2sT , and scattering width Γ ∼ g
2sT .
Some–incomplete–interference expected. LPM effect!
27
Diagrammatic Analysis
Lengthy power counting analysis (Arnold, GM, Yaffe)
One must include
diagrams of form
corresponding roughly to
*
But no other diagrams needed
28
Resummation of Diagrams
Diagrams may be resummed by defining a dressed vertex,
+=
+ + . . . =
determined by an integral equation (second line).
29
Emission rate from thermal QGP (3 light flavors) is AMY
dNγd3kd4x
=2αEM4π2k
∫ ∞
−∞
dp
2π
∫ d2p⊥(2π)2
nf (k+p) [1−nf (p)]
2[p (p+k)]2×
×
[
p2 + (p+k)2]
Re{
2p⊥ · f(p⊥; p, k)}
(1)
2p⊥ = iδE f(p⊥; p, k) +2π
3g2s
∫ d2q⊥(2π)2
m2D T
q2⊥(m2D+q
2⊥)×
×
[
f(p⊥; p, k)− f(q+p⊥; p, k)]
, (2)
δE =p2⊥ +m
2∞
2
k
p(k+p)(3)
Note, (2) is implicit and must be solved numerically.
30
Result
Brem/pair type and 2↔ 2 production rates are comparable.
31
Folding into a hydro code:
Hydro model dependence À rate uncertainty!
Ruuskanen et. al.
Thermal γ ∼ γ(π0)/10.
Challenging but not im-
possible experimentally
32
Jet quenching
A few hard partons are produced when the primaries collide.
They must escape through the QGP.
Lose energy on the way, mostly
to gluon brem.
33
Jet quenching, γ production similar: brem, LPM...
Emission rate, per dk of gluon energy and dt of time:
dΓ(p, k)
dkdt=
Csg2s
16πp71
1± e−k/T1
1± e−(p−k)/T×
×
1+(1−x)2
x3(1−x)2q → qg
Nfx2+(1−x)2
x2(1−x)2g → qq
1+x4+(1−x)4
x3(1−x)3g → gg
×
×
∫
d2h
(2π)22h · Re F(h, p, k) ,
(p: parton energy; x ≡ k/p; h: measure of non-collinearity)
34
Here F is given by
2h = iδE(h, p, k)F(h) + g2∫
d2q⊥(2π)2
C(q⊥)×
×
{
(Cs − CA/2)[F(h)− F(h−k q⊥)]
+(CA/2)[F(h)− F(h+pq⊥)]
+(CA/2)[F(h)− F(h−(p−k)q⊥)]}
,
δE(h, p, k) =h2
2pk(p−k)+m2k2k
+m2p−k2(p−k)
−m2p2p
.
with C(q⊥) =m2
D
q2⊥
(q2⊥
+m2D
), m2D =
g2s T2
6 (2Nc+Nf) .
35
Jet quenching has been observed!
0 2 (GeV/c)Tp
4 6 8 100
0.5
1
1.5
2d+Au FTPC-Au 0-20%
d+Au Minimum Bias
pT (GeV/c)
Au+Au Central
RAB (pT)
STAR data: charged yield (scaled to pp), AA vs. DA.
36
A calculation of γ production and jet quenching using the
same formalism and hydro model should inter-relate them.
There are also γ produced as secondaries off the jets as they
quench (the bremsstrahlung is sometimes a γ not a gluon).
Work in progress S. Jeon, GM
preliminary results of γ production from hard jets not
promising: γ yield 10−3 of energetic partons–but see Gale’s
talk.
37
Conclusions• Direct γ’s are intrinsically interesting
• Decay γ’s should outnumber direct γ’s, making
observation of direct γ’s challenging
• Computing γ production from QGP is Challenging
due to LPM, but is nevertheless broadly under control
• uncertainties in QGP γ dominated by Hydro, not QFT
• Connection between γ production and jet quenching
deserves more attention, and may help constrain hydro
(and other) uncertainties.
38
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