Jet Energy Loss with pQCD and
AdS/CFT in Heavy Ion Collisions
W. A. Horowitz
The Ohio State University
February 11, 2010
With many thanks to Brian Cole, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov
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HIP Seminar
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QCD: Theory of the Strong Force
• Running as
– -b-fcn
• SU(Nc = 3)
PDG
ALEPH, PLB284, (1992)
• Nf(E)
– Nf(RHIC) ≈ 2.5
Griffiths Particle Physics
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Bulk QCD and Phase Diagram
Long Range Plan, 2008
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Present and Future QGP Experiments
• RHIC
• LHC
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BRAHMS
PHENIX
PHOBOS
STAR
ATLAS
PHENIX
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ALICE
ATLAS
CMS
LHCb
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Evolution of a HI Collision
STAR
T Hirano, Colliding Nuclei from AMeV to ATeV
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Past, Present, and Future Questions
• Bulk properties
–
–
–
–
Deconfinement
Thermalization, density
EOS, h/s
QGP DOF
• Weakly vs. Strongly coupled plasma
– G = U/T: <<1 or >>1?
• Weakly vs. Strongly coupled theories
– as ~ 0.3 << 1?
l = √(gYM2 Nc) ~ 3.5 >> 1?
• New computational techniques
– AdS?
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Methods of QCD Calculation I: Lattice
Long Range Plan, 2008
• All momenta
• Euclidean correlators
Kaczmarek and Zantow, PRD71 (2005)
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Davies et al. (HPQCD), PRL92 (2004)
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Methods of QCD Calculation II: pQCD
d’Enterria, 0902.2011
Jäger et al., PRD67 (2003)
6/30/2016
• Any quantity
• Small coupling (large momenta only)
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Methods of QCD Calculation III: AdS(?)
Maldacena conjecture: SYM in d  IIB in d+1
Gubser, QM09
• All quantities
• Nc → ∞
• SYM, not QCD: b = 0
– Probably not good approx. for p+p; maybe A+A?
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Why High-pT Jets?
• Tomography in medicine
One can learn a lot from a single probe…
and even more with multiple
probes
PET Scan
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http://www.fas.org/irp/imint/docs/rst/Intro/P
art2_26d.html
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SPECT-CT Scan uses
internal g photons and
external X-rays
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Tomography in QGP
• Requires wellcontrolled theory of:
– production of rare, highpT probes
pT
f
, g, e-
• g, u, d, s, c, b
– in-medium E-loss
– hadronization
• Requires precision
measurements of
decay fragments
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Invert attenuation
pattern => measure
medium properties
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QGP Energy Loss
• Learn about E-loss mechanism
– Most direct probe of DOF
pQCD Picture
AdS/CFT
Picture
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Jets in Heavy Ion Collisions
• p+p
Y-S Lai, RHIC & AGS Users’ Meeting, 2009
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• Au+Au
PHENIX
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High-pT Observables
Naively: if medium has no effect, then RAA = 1
Common variables used are transverse
momentum, pT, and angle with respect to the
reaction plane, f
, g, e-
f
Fourier expand RAA:
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pT
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pQCD Rad Picture
• Bremsstrahlung Radiation
– Weakly-coupled plasma
• Medium organizes into Debye-screened centers
– T ~ 250 MeV, g ~ 2
• m ~ gT ~ 0.5 GeV
• lmfp ~ 1/g2T ~ 1 fm
• RAu ~ 6 fm
– 1/m << lmfp << L
Gyulassy, Levai, and Vitev, NPB571 (200)
• mult. coh. em.
– Bethe-Heitler
– LPM
dpT/dt ~ -LT3 log(pT/Mq)
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dpT/dt ~ -(T3/Mq2) pT
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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 Rad E-Loss Picture
• v2
• e-
e-
WAH, Acta Phys.Hung.A27 (2006)
Djordjevic, Gyulassy, Vogt, and Wicks, PLB632 (2006)
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What About Elastic Loss?
• Appreciable!
• Finite time effects small
Adil, Gyulassy, WAH, Wicks, PRC75 (2007)
Mustafa, PRC72 (2005)
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Quantitative Disagreement Remains
p0 v2
– v2 too small
– NPE supp. too large
WHDG
C. Vale, QM09 Plenary (analysis by R. Wei)
NPE v2
Wicks, WAH, Gyulassy, Djordjevic, NPA784 (2007)
Pert. at LHC energies?
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
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Strongly Coupled Qualitative Successes
AdS/CFT
Blaizot et al., JHEP0706
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
PHENIX, PRL98, 172301 (2007)
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Betz, Gyulassy, Noronha, Torrieri, PLB675 (2009)
Jets in AdS/CFT
• Model heavy quark jet energy loss by
embedding string in AdS space
dpT/dt = - m pT
m = pl1/2 T2/2Mq
– Similar to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75 (2007)
– Very different from LPM
dpT/dt ~ -LT3 log(pT/Mq)
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Compared to Data
• String drag: qualitative agreement
WAH, PhD Thesis
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Light Quark and Gluon E-Loss
PHENIX 0-5% p0
WAH, in preparation
Gubser, QM09
DLqtherm ~ E1/3
DLgtherm ~ (2E)1/3
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Baryon to Meson Ratios
STAR
STAR
AdS/CFT
pQCD
AdS/CFT
pQCD
WAH, in preparation
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Quantitative g, q from AdS?
• Highly sensitive to IC
Chesler et al., Phys.Rev.D79:125015,2009
– Distinguishing measurement?
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Looking for a Qualitative, Distinguishing 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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LHC c, b RAA pT Dependence
WAH, M. Gyulassy, PLB666 (2008)
– Unfortunately, large suppression pQCD similar to AdS/CFT
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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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pQCD vs. AdS/CFT at LHC
• Plethora of Predictions:
WAH, M. Gyulassy, PLB666 (2008)
– Taking the ratio cancels most normalization differences
– pQCD ratio asymptotically approaches 1, and more slowly so for increased
quenching (until quenching WAH,
saturates)
M. Gyulassy, PLB666 (2008)
– AdS/CFT ratio is flat and many times smaller than pQCD at only moderate pT
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Not So Fast!
– Speed limit estimate for
applicability of AdS drag
• g < gcrit = (1 + 2Mq/l1/2 T)2
~ 4Mq2/(l T2)
– Limited by Mcharm ~ 1.2 GeV
• Similar to BH
LPM
Q
Worldsheet boundary
Spacelike if g > gcrit
x5
Trailing
String
“Brachistochrone”
– gcrit ~ Mq/(lT)
– No Single T for QGP
• smallest gcrit for largest T
T = T(t0, x=y=0): “(”
• largest gcrit for smallest T
T = Tc: “]”
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D7 Probe Brane
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“z”
D3 Black Brane
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LHC RcAA(pT)/RbAA(pT) Prediction
(with speed limits)
WAH, M. Gyulassy, PLB666 (2008)
– T(t0): “(”, corrections likely small for smaller momenta
– Tc: “]”, corrections likely large for higher momenta
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RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WAH, M. Gyulassy, JPhysG35 (2008)
• 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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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
P Chesler,
Quark Matter 2009
Shock Geometries
Nucleus as Shock
DIS
Embedded String in Shock
Albacete, Kovchegov, Taliotis,
JHEP 0807, 074 (2008)
Before
After
vshock
Q
z
x
Q
z
vshock
x
WAH and Kovchegov, PLB680 (2009)
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Asymptotic Shock 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
L
Mq
vsh
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
• For L typical momentum scale of the
medium
–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
– pQCD and AdS/CFT enjoy qualitative
successes, concerns in high-pT HIC
• RHIC suppression of lights and heavies
• Future LHC measurements
– Quantitative comparisons with rigorous
theoretical uncertainty estimates needed for
falsification/verification
• Theoretical work needed in both in pQCD and AdS
– In AdS, control of jet IC, large pT required
– In pQCD, wide angle radiation very important, not under
theoretical control
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