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... 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

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Why does it matter?

If we put the pedal to the metal, how fast will it go?

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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.

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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

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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

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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.

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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

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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

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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.

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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 ...

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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

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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)

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'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

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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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What about qperp

distributions?

p = 10 GeV

p=10GeV: <qperp

2> ≈ 0.25 GeV2/fm for T = 0.24GeV

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The rare, hard collisions contribute most to <qperp

2>

What about qperp

distributions?

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If radiation is driven by <qperp

2>, thenwe are not in the regime where:

Diagram from Arnold, Moore and Yaffe: JHEP 0206:030,2002

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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?