Post on 26-Jan-2021
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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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