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
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Outline
• Introduction
• pQCD
• AdS/CFT
• Conclusions
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Introduction
Heavy ion jet physics
pT
Heavy ion collision
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f
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Why High-pT Jets?
• Compare unmodified p+p collisions to
A+A:
pT
pT
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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High-pT Observables
Naïvely: if medium has no effect, then RAA = 1
Common variables used are transverse
momentum, pT, and angle with respect to the
reaction plane, f
f
Fourier expand RAA:
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pT
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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:
RAA(h)~RAA(p)
– Null Control:
RAA(g)~1
– GLV Prediction: Theory~Data for reasonable
fixed L~5 fm and dNg/dy~dNp/dy
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Trouble for High-pT wQGP Picture
p0 v2
– v2 too small
– NPE supp. too large
WHDG
C. Vale, QM09 Plenary (analysis by R. Wei)
NPE v2
STAR, Phys. Rev. Lett. 98, 192301 (2007)
Pert. at LHC energies?
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
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Multiple Models
WHDG, Nucl.Phys.A784:426-442,2007
Bass et al., Phys.Rev.C79:024901,2009
– Inconsistent medium properties
– Distinguish between models
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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 RAA
– Many assumptions
• Prod. spectra, FF, geometry, etc.
• Focus on “Brick”
– Fixed L, T, Ejet
• Compare WHDG Rad to ASW-SH
– WHDG Rad: DGLV opacity expansion
• GLV + massive quarks, gluons
– ASW-SH: opacity expansion
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Why WHDG Rad vs. ASW-SH?
• Examine ASW-SH = GLV claim
• Warm-up for WHDG Rad vs. ASW-MS
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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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Compared Quantities
• dNg/dx
– Single inclusive radiated gluon spectrum
• P(e)
– Poisson convolution
– Model multiple emission
• Additional assumptions
– Convolve dNg/dx to find P(e)
• Ef = (1 – e)Ei
• pdf
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Conclusions
• ASW-SH code no good for RAA
– To be fair, hasn’t been used
• RAA cutoff dep. likely => large th. err.
– Must be overcome for tomography
– Strong as dependence, too
• Large gluon mass effect
– Higher order diagrams likely important
• Not to be confused with higher orders of opacity
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Part II: AdS/CFT
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Motivation for High-pT AdS
• 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 as
• Use data to learn about E-loss
mechanism, plasma properties
– Domains of self-consistency crucial for
understanding
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AdS/CFT Energy Loss Models I
– Langevin Diffusion
• Collisional energy loss for heavy quarks
• Restricted to low pT
• 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
– 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)
Gulotta, Pufu, Rocha, JHEP 0810:052, 2008
Gluons and light quarks Gubser,
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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Energy Loss Comparison
D7 Probe Brane
t
z=0
– AdS/CFT Drag:
Q, m
zm = l1/2/2pm
dpT/dt ~ -(T2/Mq) pT
zh = 1/pT
v
x
3+1D Brane
Boundary
D3 Black Brane
(horizon)
Black Hole
z=
– Similar to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
– Very different from LPM
dpT/dt ~ -LT3 log(pT/Mq)
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LHC RcAA(pT)/RbAA(pT) Prediction
• Individual c and b RAA(pT) predictions:
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
– 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 pT
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
– Distinguish rad and el contributions?
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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
Shock Geometries
J Friess, et al., PRD75:106003, 2007
Nucleus as Shock
DIS
Embedded String in Shock
Before
Albacete, Kovchegov, Taliotis,
JHEP 0807, 074 (2008)
vshock
Q
z
Bjorken-Expanding Medium
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After
x
Energy Loss at RHIC and LHC
Q
z
vshock
x
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Standard Method of Attack
• Parameterize string worldsheet
m
– X (t, s)
• Plug into Nambu-Goto action
m
• Varying SNG yields EOM for X
• Canonical momentum flow (in t, s)
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New in the Shock
• Find string solutions in HQ rest frame
– vHQ = 0
• Assume static case (not new)
– Shock wave exists for all time
– String dragged for all time
m
• X = (t, x(z), 0,0, z)
• Simple analytic solutions:
– x(z) = x0, x0 ± m ½ z3/3
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Shock Geometry Results
• Three t-ind. solutions (static gauge):
m
X = (t, x(z), 0,0, z)
– x(z) = x0, x0 ± m ½ z3/3
Q
z=0
vshock
x0 + m ½ z3/3
x0 - m ½ z3/3
x0
x
z=
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• Constant solution unstable
• Time-reversed negative x solution unphysical
• Sim. to x ~ z3/3, z << 1, for const. T BH geom.
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HQ Momentum Loss
x(z) = m ½ z3/3 =>
Relate m to nuclear properties
– Use AdS dictionary
• Metric in Fefferman-Graham form: m ~ T--/Nc2
– T’00 ~ Nc2 L4
• Nc2 gluons per nucleon in shock
• L is typical mom. scale; L-1 typical dist. scale
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Frame Dragging
• HQ Rest Frame
• Shock Rest Frame
Mq
vsh
L
vq = -vsh
1/L
i
vq = 0
i
Mq
vsh = 0
– Change coords, boost Tmn into HQ rest frame:
• T-- ~ Nc2 L4 g2 ~ Nc2 L4 (p’/M)2
• p’ ~ gM: HQ mom. in rest frame of shock
– Boost mom. loss into shock rest frame
– p0t = 0:
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Putting It All Together
• This leads to
–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
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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 = zM = l½/2pMq
– Same speed limit as for BH metric when L = pT
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Conclusions and Outlook
– Use data to test E-loss mechanism
• RcAA(pT)/RbAA(pT) 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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