Testing AdS/CFT at LHC
William Horowitz
The Ohio State University
February 6, 2009
With many thanks to Yuri Kovchegov and Ulrich Heinz
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High-pT Physics at LHC
William Horowitz
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First, a Perturbative Detour
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pQCD Success in High-pT at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration,
hep-ex/0510008
– Consistency:
RAA(h)~RAA(p)
– Null Control:
RAA(g)~1
– GLV Calculation: Theory~Data for reasonable
fixed L~5 fm and dNg/dy~dNp/dy
• Assuming pQCD E-loss, let’s clear up some myths
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Surface Emission: Red Herring?
• If you believe in pQCD E-loss, observed
jets come from deep in the medium
HT, AMY, ASW
S. A. Bass, et al., arXiv:0808.0908 [nucl-th].
2/7/09
WHDG
S. Wicks, et al., Nucl. Phys. A784,
426 (2007)
High-pT Physics at LHC
BDMPS + Hydro
T. Renk and K. J. Eskola,
PoS LHC07, 032 (2007)
William Horowitz
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Fragility is Fragile
• Linear-linear plot of RAA(qhat) is the
incorrect way to think about the problem
PHENIX,
Phys. Rev. C77, 064907 (2008)
K. J. Eskola, et al., Nucl. Phys. A747, 511 (2005)
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Fragility is Fragile (cont’d)
• If you believe in pQCD E-loss, RAA is
NOT a fragile probe of the medium
– Linear on a log-log plot
– Double => halve RAA
– Similar results for WHDG,
GLV, AMY, ZOWW, etc.
PHENIX,
Phys. Rev. C77, 064907 (2008)
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Quantitative Extraction
PHENIX, PRC77,
064907 (2008)
• Model params to within ~20%
– Experimental error only!!
• Sys. theor. err. could be quite large
– Running coupling uncertainties
» Smaller at LHC?
– Multi-gluon correlations?
» Larger at LHC?
– Handling of geometry
– …
• See also TECHQM wiki:
https://wiki.bnl.gov/TECHQM/index.php/WHDG
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High-pT Physics at LHC
S. Wicks, et al., Nucl. Phys. A783, 493 (2007)
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Trouble for High-pT wQGP Picture
p0 v2
– v2 too small
– NPE supp. too large
M Tannenbaum, High-pT Physics at LHC ‘09
NPE v2
STAR, Phys. Rev. Lett. 98, 192301 (2007)
Pert. at LHC energies?
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
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Back to the Future Fifth Dimension
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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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Strong Coupling Calculation
• The supergravity double conjecture:
QCD  SYM  IIB
– IF super Yang-Mills (SYM) is not too
different from QCD, &
– IF Maldacena conjecture is true
– Then a tool exists to calculate stronglycoupled QCD in SUGRA
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AdS/CFT Energy Loss Models
– 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
– Heavy Quark Drag calculation
• Embed string representing HQ into AdS geometry
• Includes all E-loss modes
• Empty space calculation: Kharzeev, arXiv:0806.0358 [hep-ph]
• Previously: thermalized QGP plasma, temp. T, gcrit<~Mq/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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RAA Approximation
– Above a few GeV, quark production
spectrum is approximately power law:
• dN/dpT ~ 1/pT(n+1), where n(pT) has some
momentum dependence
y=0
RHIC
– We can approximate RAA(pT):
• RAA ~ (1-e(pT))n(pT),
where pf = (1-e)pi (i.e. e = 1-pf/pi)
LHC
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Looking for a Robust, Detectable Signal
– Use LHC’s large pT reach and identification of c
and b to distinguish between pQCD, AdS/CFT
• Asymptotic pQCD momentum loss:
erad ~ as L2 log(pT/Mq)/pT
• String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
– Independent of pT and strongly dependent on Mq!
– T2 dependence in exponent makes for a very sensitive probe
– Expect: epQCD
0 vs. eAdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
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Model Inputs
– AdS/CFT Drag: nontrivial mapping of QCD to SYM
• “Obvious”: as = aSYM = const., TSYM = TQCD
– D 2pT = 3 inspired: as = .05
– pQCD/Hydro inspired: as = .3 (D 2pT ~ 1)
• “Alternative”: l = 5.5, TSYM = TQCD/31/4
• Start loss at thermalization time t0; end loss at Tc
– WHDG convolved radiative and elastic energy loss
• as = .3
– WHDG radiative energy loss (similar to ASW)
•
= 40, 100
– Use realistic, diffuse medium with Bjorken expansion
– PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900)
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LHC c, b RAA pT Dependence
WH and M. Gyulassy,
Phys. Lett. B 666, 320 (2008)
– Significant
NaïvePrediction
LHC
Unfortunately,
Large
suppression
expectations
rise large
inZoo:
Rleads
met
suppression
What
(pTin
to
) for
full
flattening
a Mess!
pQCD
numerical
pQCD
Rad+El
similar
calculation:
to AdS/CFT
AA
– Use
Let’sofgorealistic
through
dRAA
geometry
step
(pT)/dp
by step
> 0 Bjorken
=> pQCD;
expansion
dRAA(pTallows
)/dpT <
saturation
0 => ST below .2
Tand
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An Enhanced Signal
• But what about the interplay between
mass and momentum?
– Take ratio of c to b RAA(pT)
• pQCD: Mass effects die out with increasing pT
RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /pT)
– Ratio starts below 1, asymptotically approaches 1.
Approach is slower for higher quenching
• ST: drag independent of pT, inversely
proportional to mass. Simple analytic approx.
of uniform medium gives
RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27
– Ratio starts below 1; independent of pT
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LHC RcAA(pT)/RbAA(pT) Prediction
• Recall the Zoo:
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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Additional Discerning Power
– Consider ratio for ALICE pT reach
mc = mb = 0
– Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1
» Does not include partonic E-loss, which will be nonnegligable as ratio goes to unity
– Higgs (non)mechanism => Rc/Rb ~ 1 ind. of pT
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Not So Fast!
• Speed limit estimate for
applicability of AdS drag
D7 Probe Brane
Q
Worldsheet boundary
Spacelike if g > gcrit
– g < gcrit = (1 + 2Mq/l1/2 T)2
~ 4Mq2/(l T2)
z
Trailing
String
“Brachistochrone”
• Limited by Mcharm ~ 1.2 GeV
• Similar to BH LPM
– gcrit ~ Mq/(lT)
x
• No single T for QGP
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High-pT Physics at LHC
D3 Black Brane
William Horowitz
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LHC RcAA(pT)/RbAA(pT) Prediction
(with speed limits)
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
– T(t0): (, highest T—corrections unlikely for smaller momenta
– Tc: ], lowest T—corrections likely for higher momenta
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Derivation of BH Speed Limit I
• Constant HQ velocity
– Assume const. v kept by F.v
Minkowski Boundary
z=0
2
½
– Critical field strength Ec = M /l
• E > Ec: Schwinger pair prod. zM =
• Limits g < gc ~ T2/lM2
l½ /
2pM
E
F.v = dp/dt
Q v
D7
dp/dt
J. Casalderrey-Solana and D. Teaney, JHEP 0704, 039 (2007)
– Alleviated by allowing var. v
• Drag similar to const. v
Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013 (2006)
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High-pT Physics at LHC
zh = 1/pT
D3
z=
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Derivation of BH Speed Limit II
• Local speed of light
– BH Metric => varies with depth z
• v(z)2 < 1 – (z/zh)4
l½/2pM
– HQ located at zM =
– Limits g < gc ~ T2/lM2
• Same limit as from const. v
S. S. Gubser, Nucl. Phys. B 790, 175 (2008)
zM =
Minkowski Boundary
z=0
l½ /
2pM
– Mass a strange beast
• Mtherm < Mrest
• Mrest  Mkin
– Note that M >> T
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High-pT Physics at LHC
E
F.v = dp/dt
Q v
D7
dp/dt
zh = 1/pT
D3
z=
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Universality and Applicability
• How universal are drag results?
– Examine different theories
– Investigate alternate geometries
• When does the calculation break down?
– Depends on the geometry used
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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
Albacete, Kovchegov, Taliotis,
JHEP 0807, 074 (2008)
Before
vshock
Q
z
Bjorken-Expanding Medium
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After
x
High-pT Physics at LHC
Q
z
vshock
x
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Shocking Motivation
• Warm-up for full Bjorken metric
R. A. Janik and R. B. Peschanski, Phys. Rev. D 73, 045013 (2006)
• No local speed of light limit!
– Metric yields
-1 < v < 1
– In principle, applicable to all
quark masses for all momenta
– Subtlety in exchange of limits?
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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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Shock Geometry Results
• Three t-ind. solutions (static gauge):
m
X = (t, x(z), 0,0, z)
z=0
– x(z) = c, ± m ½ z3/3
Q
vshock
+ m ½ z3/3
- m ½ z3/3
c
x
z=
2/7/09
• Constant solution unstable
• Time-reversed negative x solution unphysical
• Sim. to x ~ z3/3, z << 1, for const. T BH geom.
High-pT Physics at LHC
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HQ Momentum Loss in the Shock
x(z) = m ½ z3/3 =>
Relate m to nuclear properties
– Use AdS dictionary: m ~ T--/Nc2
– T-- = (boosted den. of scatterers) x (mom.)
– T-- = Nc2 (L3 p+/L) x (p+)
•
•
•
•
2/7/09
Nc2 gluons per nucleon in shock
L is typical mom. scale; L-1 typical dist. scale
p+: mom. of shock gluons as seen by HQ
p: mom. of HQ as seen by shock
=> m = L2p+2
High-pT Physics at LHC
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HQ Drag in the Shock
• HQ Rest Frame
• Shock Rest Frame
Mq
vsh
L
vq = -vsh
1/L
i
vq = 0
i
Mq
vsh = 0
–Recall for BH:
–Shock gives exactly the same drag as BH for L = p T
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Conclusions and Outlook for
• the LHC Experiment:
– Use data to test E-loss mechanism
• RcAA(pT)/RbAA(pT) wonderful tool
– p+Pb and Direct-g Pb+Pb critical null controls
• the AdS Drag:
– Applicability and universality crucial
• Both investigated in shock geom.
– Shock geometry reproduces BH momentum loss
• Unrestricted in momentum reach
• Variable velocity case nontrivial
– Future work
• Time-dependent shock treatment
• AdS E-loss in Bjorken expanding medium
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Backup Slides
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Measurement at RHIC
– Future detector upgrades will allow for identified c
and b quark measurements
– RHIC production spectrum significantly
harder than LHC
•
• NOT slowly varying
y=0
RHIC
– No longer expect
pQCD dRAA/dpT > 0
• Large n requires
corrections to naïve
Rcb ~ Mc/Mb
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High-pT Physics at LHC
LHC
William Horowitz
34
RHIC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
• Large increase in n(pT) overcomes reduction in
E-loss and makes pQCD dRAA/dpT < 0, as well
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RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
• Wider distribution of AdS/CFT curves due to large n:
increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
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Simultaneous p, e- Suppression
• pQCD is not falsified:
Naïve
pQCD => large mass, small loss
–•
Elastic
loss?
-R
•
But
p,
h
R
~
e
– Uncertainty in
AAc, b
AA!
contributions
– In-medium
fragmentation?
– Resonances?
H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006)
A. Adil and I. Vitev, hep-ph/0611109
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
2/7/09
High-pT Physics at LHC
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Zooming In
– Factor ~2-3 increase in ratio for pQCD
– Possible distinction for Rad only vs. Rad+El at low-pT
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Additional Discerning Power
• Consider ratio for ALICE pT reach
– Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1
» Does not include partonic energy loss, which will be nonnegligable as ratio goes to unity
2/7/09
High-pT Physics at LHC
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• Consider ratio for ALICE pT reach
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High-pT Physics at LHC
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LHC p Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic,
in preparation
2/7/09
• Our predictions show a
significant increase in RAA as a
function of pT
• This rise is robust over the
range of predicted dNg/dy for
the LHC that we used
• This should be compared to
the flat in pT curves of AWSbased energy loss (next slide)
• We wish to understand the
origin of this difference
High-pT Physics at LHC
William Horowitz
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Comparison of LHC p Predictions
(a)
(b)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A.
Wiedemann, Nucl. Phys. A747:511:529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461474 (2005)
Curves of ASW-based energy loss are flat in pT
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Why ASW is Flat
• Flat in pT curves result from extreme suppression at the
LHC
– When probability leakage P(e > 1) is large, the (renormalized or not)
distribution becomes insensitive to the details of energy loss
• Enormous suppression due to:
– Already (nonperturbatively) large suppression at RHIC for ASW
– Extrapolation to LHC assumes 7 times RHIC medium densities (using
EKRT)
» Note: even if LHC is only ~ 2-3 times RHIC,
still an immoderate ~ 30-45
• As seen on the previous slide, Vitev predicted a similar
rise in RAA(pT) as we do
– Vitev used only radiative loss, Prad(e), but assumed fixed path
– WHDG similar because elastic and path fluctuations compensate
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Elastic Can’t be Neglected!
M. Mustafa, Phys. Rev. C72:014905 (2005)
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S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
High-pT Physics at LHC
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Elastic Remains Important
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A Closer Look at PQM
– Difficult to draw conclusions on
inherent surface bias in PQM
from this for three reasons:
• No Bjorken expansion
• Glue and light quark contributions
not disentangled
• Plotted against Linput (complicated
mapping from Linput to physical
distance)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
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Direct g: A+A IS Well Understood
PHENIX, Phys. Rev. Lett. 94, 232301 (2005)
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More Geometry
• Nontrivial a posteriori
• pT dependence of
surface bias
fixed length dependence
(not surface emission!)
S. A. Bass, et al., arXiv:0808.0908 [nucl-th].
2/7/09
High-pT Physics at LHC
S. Wicks, WH, M. Djordjevic and M.
Gyulassy, Nucl. Phys. A784, 426 (2007)
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