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#: 1
... and your jet energy loss calculation?... and your jet energy loss calculation?
What drives you?What drives you?
akaPerturbative jet energy loss mechanisms: Learning from RHIC, extrapolating to LHC
Simon WicksMiklos Gyulassy
Institut für
Theoretische Physik
#: 2
Why does it matter?
If we put the pedal to the metal, how fast will it go?
#: 3
Q: What is / are the dominant energy loss process(es)?
We must model the medium(and the interactions of the jet with it).
No generic energy loss mechanism.
#: 4
An excess of theoretical modelsGLV
GLV + collisionalBDMPS-Z-ASW
Higher Twist – Wang etcAMY
van Hees / RappVA coll dissociation
AdS/CFT – LRWAdS/CFT – TCS
AdS/CFT – Kovtun et alAdS/CFT – Gubser
...STAR Phys. Rev. Lett. 98 (2007) 192301
#: 5
What models are available?
Peshier / Cassing model ...
AdS/CFTAdS/CFT
wQGP
sQGP
ssQGP
On-shell quasiparticlesie width << energy
'Dynamic quasi-particles'ie width ~ energy
No quasi-particles(except jets ...)
Resonance modelseg Rapp & Van Hees,
Shuryak ...
(Parton cascade)
HTLHTL
GW model
#: 6
Why look at collisional processes?
1) Know what are the energy loss mechanisms are.Different energy loss mechanisms scale differently with density and jet energy.
2) Collisions are what induces (causes the medium modification to) the radiative energy loss.
#: 7
A very selective history
1) Bjorken 1982 (FERMILAB-PUB-82-059-THY)Vacuum estimate, cut-off at Debye mass
2) Thoma-Gyulassy 1991 (Nucl.Phys.B351:491-506,1991)Classical EM naturally regulates the infrared (but has little to say about ultra-violet)
3) Braaten-Thoma 1991 (Phys.Rev.D44:2625-2630,1991)HTL for low momentum exchange, vacuum for high momentum exchange, cut-off between the two magically drops out under certain assumptions.
All assume that momentum exchange is small compared to the momenta of the jet & medium particles.
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The Formalism
t-channel exchange
Neglect difference between Q-q and Q-g
(except Casimir)
NOT make assumptions like
ω << T, μ in coefficients.
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Phase space
Massive jet, massless medium
Similar treatment to:Moore & Teaney Phys.Rev.C71:064904,2005
Djordjevic Phys.Rev.C74:064907,2006Arnold, Moore, Yaffe JHEP 0305:051,2003
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The Matrix Element
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The Matrix Element (cont.)
After
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Collisional energy loss (before multiple collision convolution)
(D)GLV radiative energy loss
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Average energy loss
#: 14
Multiple collisions
How to approach multiple collisions?
1) Take the distribution, find average (drag) and width (diffusion), use in Fokker-Planck / Langevin diffusion process.
BUT expect the number of (momentum changing) collisions to be small.(come back to this later ...)
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Multiple Collisions
2) Poisson convolution for multiple independent
collisions
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Multiple Collisions
NOT continuum limit diffusion process
#: 17
Geometry integrals
So far, shown fixed length plots.
For RAA
: all results shown have been averaged over
all production points and jet trajectories.
ρpart
bulk, ρbinary
jets, Bjorken expansion.
#: 18
Results – RHIC - Pions
WHDG α = 0.3
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Results – RHIC - Pions
WHDG α = 0.3
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Results – RHIC - Electrons
WHDG α = 0.3
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Results – RHIC - Electrons
WHDG α = 0.3
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Predicting LHC
RHIC
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Predicting LHC
RHIC LHC
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Predicting LHC
RHIC LHC
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Predicting - LHC
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A closer look ...
... at the collisional distributions.
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A different perspective ...
1) Diffusion process not applicable except for v long distances2) Uncertainty in HTL model ...
#: 28
Why?
1) HTL breaks downg is not << 1
2) High momentum jet
eg ΔE ~ log(E/gT)For log(T/gT) >> log(E/gT)-log(T/gT)=> log(1/g) >> log(E/T)E = 10 GeV, T = 0.25 GeV=> g << 0.025
3) Both
#: 29
ω << T, μassumption /
approximation is NOT ok to calculate
av en loss
Must take into account medium
recoil.
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How can we quantify this uncertainty?
Look at two schemes that are equivalent 'at leading order'
Both agree in limit ω,q << T, μ and in limit ω,q -> ∞ (or μ -> 0)
#: 31
'Equivalent' calculations
1) Simple extrapolation of HTL to large momentum transfer.
2) Prescription found in AMY – only modify infrared divergent part of amplitude.
#: 32HTL extrapolation
HTL-AMY extrapolation
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Result
#: 34
Equivalent at leading order
g = 2, pt = 10GeV: 1.6 or 1.3g = 1, pt = 10GeV: 1.3 or 1.2
g = 0.1, pt = 1GeV: 1.0 or 1.0
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Why are HTL and HTL-AMY so different?
•Redistribution of longitudinal and transverse components.•Longitudinal and transverse components are screened by the medium in different ways.
HTL HTL-AMY
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Longitudinal and transverse m∞
Longitudinal and transverse modes have asymptotic masses that act differently:
L:
T:
Equations from: Pisarski, Physica A158:246-250,1989
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#: 38
What about qperp
distributions?
p = 10 GeV
p=10GeV: <qperp
2> ≈ 0.25 GeV2/fm for T = 0.24GeV
#: 39
The rare, hard collisions contribute most to <qperp
2>
What about qperp
distributions?
#: 40
If radiation is driven by <qperp
2>, thenwe are not in the regime where:
Diagram from Arnold, Moore and Yaffe: JHEP 0206:030,2002
#: 41
ConclusionsCollisional energy loss is of the same order as radiative energy loss.
To calculate collisional loss, cannot make assumptions (or neglect terms of order) ω << T, μ
HTL gives a large uncertainty in the collisional energy loss.
How to 'predict' for LHC with these large uncertainties?