Theoretical Thoughts on Energy Loss at RHIC and LHC

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Theoretical Thoughts on Energy

Loss at RHIC and LHC

William Horowitz

The Ohio State University

May 21, 2009

With many thanks to Brian Cole, Yuri Kovchegov, and Ulrich Heinz

5/21/09 Energy Loss at RHIC and LHC

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• Introduction

Outline

• pQCD

• AdS/CFT

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• Conclusions

Energy Loss at RHIC and LHC

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Introduction

Heavy ion collision

Heavy ion jet physics p

T f

William Horowitz

3 Energy Loss at RHIC and LHC

Why High-p

T

Jets?

• Compare unmodified p+p collisions to

A+A: p

T p

T

2D Transverse direction

Longitudinal

(beam pipe) direction

Figures from http://www.star.bnl.gov/central/focus/highPt/

• Use suppression pattern to either:

– Learn about medium (requires detailed understanding of energy loss): jet tomography

– Learn about energy loss

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4 5/21/09 Energy Loss at RHIC and LHC

High-p

T

Observables

Naïvely: if medium has no effect, then R

AA

= 1

Common variables used are transverse momentum, p

T

, and angle with respect to the reaction plane, f

Fourier expand R

AA

: f p

T

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Part I: pQCD Eloss

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pQCD Success at RHIC:

(circa 2005)

Y. Akiba for the PHENIX collaboration, hep-ex/0510008

– Consistency:

R

AA

( h )~R

AA

( p )

– Null Control:

R

AA

( g )~1

– GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g

/dy~dN p

/dy

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7 5/21/09 Energy Loss at RHIC and LHC

Trouble for High-p

T

– v

2 too small p 0 v

2

wQGP Picture

– NPE supp. too large

WHDG

NPE v

2

C. Vale, QM09 Plenary (analysis by R. Wei)

STAR, Phys. Rev. Lett. 98, 192301 (2007)

Pert. at LHC energies?

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PHENIX, Phys. Rev. Lett. 98, 172301 (2007)

Energy Loss at RHIC and LHC

William Horowitz

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Multiple Models

WHDG, Nucl.Phys.A784:426-442,2007 Bass et al., Phys.Rev.C79:024901,2009

– Inconsistent medium properties

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– Distinguish between models

Energy Loss at RHIC and LHC

Bass et al.

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Quantitative Parameter Extraction

• Vary input param.

• Find “best” value

Need for theoretical error

PHENIX, PRC77:064907,2008

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Comparing Models

• Difficult at R

AA

– Many assumptions

• Prod. spectra, FF, geometry, etc.

• Focus on “Brick”

– Fixed L, T, E jet

• Compare WHDG Rad to ASW-SH

– WHDG Rad: DGLV opacity expansion

• GLV + massive quarks, gluons

– ASW-SH: opacity expansion

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11 Energy Loss at RHIC and LHC

Why WHDG Rad vs. ASW-SH?

• Examine ASW-SH = GLV claim

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• Warm-up for WHDG Rad vs. ASW-MS

Energy Loss at RHIC and LHC

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Main Results

• Implemented formulae very different

– But, massless DGLV integrand same form

(Modulo detail of scattering center distribution)

But, var. have very diff. physical meaning (!)

• Strong cutoff dependence (!)

• Massive gluon effect (!)

– Pun intended

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13 Energy Loss at RHIC and LHC

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Compared Quantities

• dN g

/dx

– Single inclusive radiated gluon spectrum

• P( e )

– Poisson convolution

– Model multiple emission

• Additional assumptions

– Convolve dN g

• E f

= (1 – e )E i

/dx to find P( e )

• pdf

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14 Energy Loss at RHIC and LHC

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Conclusions

• ASW-SH code no good for R

AA

– To be fair, hasn’t been used

R

AA cutoff dep. likely => large th. err.

– Must be overcome for tomography

– Strong a s dependence, too

• Large gluon mass effect

– Higher order diagrams likely important

• Not to be confused with higher orders of opacity

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15 Energy Loss at RHIC and LHC

Part II: AdS/CFT

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Motivation for High-p

T

AdS

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• Why study AdS E-loss models?

– Many calculations vastly simpler

• Complicated in unusual ways

– Data difficult to reconcile with pQCD

– pQCD quasiparticle picture leads to dominant q ~ m ~ .5 GeV mom. transfers

=> Nonperturbatively large a s

• Use data to learn about E-loss mechanism, plasma properties

– Domains of self-consistency crucial for understanding

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Energy Loss at RHIC and LHC 17

AdS/CFT Energy Loss Models I

– Langevin Diffusion

• Collisional energy loss for heavy quarks

• Restricted to low p

T

• pQCD vs. AdS/CFT computation of D, the diffusion coefficient

Moore and Teaney, Phys.Rev.C71:064904,2005

Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007

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– ASW/LRW model

• Radiative energy loss model for all parton species

• pQCD vs. AdS/CFT computation of

• Debate over its predicted magnitude

BDMPS, Nucl.Phys.B484:265-282,1997

Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) 114003

Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007

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AdS/CFT Energy Loss Models II

String Drag calculation

– Embed string rep. quark/gluon in AdS geom.

– Includes all E-loss modes (difficult to interpret)

– Gluons and light quarks

Gubser, Gulotta, Pufu, Rocha, JHEP 0810:052, 2008

Chesler, Jensen, Karch, Yaffe, arXiv:0810.1985 [hep-th]

– Empty space HQ calculation

Kharzeev, arXiv:0806.0358 [hep-ph]

– Previous HQ: thermalized QGP plasma, temp. T,

Gubser, Phys.Rev.D74:126005,2006

Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013, 2006

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19 Energy Loss at RHIC and LHC

Energy Loss Comparison

D7 Probe Brane t v x z = 0

– AdS/CFT Drag: dp

T

/dt ~ -(T 2 /M q

) p

T z m

= l

1/2 /2 p m z h

= 1/ p

T z = 

Q, m

3+1D Brane

Boundary

D3 Black Brane

(horizon)

Black Hole

– Similar to Bethe-Heitler dp

T

/dt ~ -(T 3 /M q

2 ) p

T

– Very different from LPM dp

T

/dt ~ -LT 3 log(p

T

/M q

)

Energy Loss at RHIC and LHC

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LHC R

c

AA

(p

T

)/R

b

AA

(p

T

) Prediction

• Individual c and b R

AA

(p

T

) predictions:

WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)

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– Taking the ratio cancels most normalization differences seen previously

– pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates)

– AdS/CFT ratio is flat and many times smaller than pQCD at only moderate p

– Distinguish rad and el contributions?

T

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Energy Loss at RHIC and LHC 21

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Universality and Applicability

• How universal are th. HQ drag results?

– Examine different theories

– Investigate alternate geometries

• Other AdS geometries

– Bjorken expanding hydro

– Shock metric

• Warm-up to Bj. hydro

• Can represent both hot and cold nuclear matter

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New Geometries

Constant T Thermal Black Brane

DIS

Shock Geometries

Nucleus as Shock

Embedded String in Shock

J Friess, et al., PRD75:106003, 2007

Albacete, Kovchegov, Taliotis,

JHEP 0807, 074 (2008)

Bjorken-Expanding Medium

Before z x v shock

Q

After z x

Q v shock

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Standard Method of Attack

• Parameterize string worldsheet

– X m

( t , s )

• Plug into Nambu-Goto action

• Varying S

NG yields EOM for X m

• Canonical momentum flow (in t , s )

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New in the Shock

• Find string solutions in HQ rest frame

– v

HQ

= 0

• Assume static case (not new)

– Shock wave exists for all time

– String dragged for all time

• X m

= (t, x(z), 0,0, z)

• Simple analytic solutions:

– x(z) = x

0

, x

0

± m ½ z 3 /3

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25 Energy Loss at RHIC and LHC

Shock Geometry Results

z = 0

• Three t-ind. solutions (static gauge):

X m

= (t, x(z), 0,0, z)

– x(z) = x

0

, x

0

± m ½ z 3 /3

Q z =  v shock x

0

- m ½ z 3 /3 x

0

+ m ½ z 3 /3 x

0 x

• Constant solution unstable

• Time-reversed negative x solution unphysical

• Sim. to x ~ z 3 /3, z << 1, for const. T BH geom.

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HQ Momentum Loss

x(z) = m ½ z 3 /3 =>

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Relate m to nuclear properties

– Use AdS dictionary

• Metric in Fefferman-Graham form: m ~ T

--

/N c

2

– T’

00

~ N c

2 L 4

• N c

2 gluons per nucleon in shock

• L is typical mom. scale; L -1 typical dist. scale

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27 Energy Loss at RHIC and LHC

1/

L

Frame Dragging

• HQ Rest Frame • Shock Rest Frame

L v sh

M q v q

= -v sh i v q

= 0 i v sh

= 0

– Change coords, boost T mn into HQ rest frame:

• T

--

~ N c

2 L 4 g 2 ~ N c

2 L 4 (p’/M) 2

• p’ ~ g M: HQ mom. in rest frame of shock

M q

– Boost mom. loss into shock rest frame

– p 0 t

= 0:

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Putting It All Together

• This leads to

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–Recall for BH:

–Shock gives exactly the same drag as BH for L = p T

• We’ve generalized the BH solution to both cold and hot nuclear matter E-loss

Energy Loss at RHIC and LHC

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Shock Metric Speed Limit

• Local speed of light (in HQ rest frame)

– Demand reality of point-particle action

• Solve for v = 0 for finite mass HQ

– z = z

M

= l ½ /2 p M q

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– Same speed limit as for BH metric when L = p T

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Conclusions and Outlook

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– Use data to test E-loss mechanism

• R c

AA

(p

T

)/R b

AA

(p

T

) wonderful tool

– Calculated HQ drag in shock geometry

• For L = p T, drag and speed limit identical to BH

• Generalizes HQ drag to hot and cold nuclear matter

– Unlike BH, quark mass unaffected by shock

• Quark always heavy from strong coupling dressing?

• BH thermal adjustment from plasma screening IR?

– Future work:

• Time-dependent shock treatment

• AdS E-loss in Bjorken expanding medium

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