pQCD and AdS/CFT
in Heavy Ion Collisions
W. A. Horowitz
The Ohio State University
September 22, 2009
With many thanks to Yuri Kovchegov, Miklos Gyulassy, and Ulrich Heinz
6/30/2016
INPP Seminar
1
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
6/30/2016
INPP Seminar
2
Bulk QCD and Phase Diagram
Long Range Plan, 2008
6/30/2016
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3
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 ~ .3 << 1? l = √(gYM2 Nc) ~ 5.5 >> 1?
• New strong coupling techniques
– AdS?
6/30/2016
INPP Seminar
4
Methods of QCD Calculation I: Lattice
Long Range Plan, 2008
• All momenta
• Euclidean correlators
Kaczmarek and Zantow, PRD71 (2005)
6/30/2016
Davies et al. (HPQCD), PRL92 (2004)
INPP Seminar
5
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 for p+p; maybe A+A?
6/30/2016
INPP Seminar
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Present and Future QGP Experiments
• RHIC
• LHC
–
–
–
–
–
–
–
–
BRAHMS
PHENIX
PHOBOS
STAR
ATLAS
PHENIX
6/30/2016
ALICE
ATLAS
CMS
LHCb
INPP Seminar
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Evolution of a HI Collision
STAR
T Hirano, Colliding Nuclei from AMeV to ATeV
6/30/2016
INPP Seminar
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Geometry of a HI Collision
M Kaneta, Results from the
Relativistic Heavy Ion Collider (Part II)
T Ludlum and L McLerran, Phys. Today 56N10 (2003)
• Hydro propagates IC
– Results depend strongly on initial conditions
• Viscosity reduces momentum anisotropy
6/30/2016
INPP Seminar
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Low-pT Measurements (I)
LRP 2008
– Partonic DOF at hadronization!
6/30/2016
INPP Seminar
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Low-pT Measurements (II)
• EOS from lattice
• Anisotropy from
(ideal) Hydro + IC
LRP 2008
PHENIX White Paper
6/30/2016
INPP Seminar
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Low-pT Measurements (III)
• Viscosity: why the fuss?
– Naive pQCD => h/s ~ 1
– Naive AdS/CFT => h/s ~ 1/4p
Luzum and Romatschke, PRC78 (2008)
6/30/2016
INPP Seminar
U Heinz, Quark Matter 2009
13
Why High-pT Jets?
• Tomography
One can learn a lot from a single probe…
and even more with multiple
probes
PET Scan
6/30/2016
http://www.fas.org/irp/imint/docs/rst/Intro/P
art2_26d.html
INPP Seminar
SPECT-CT Scan uses
internal g photons and
external X-rays
14
Why High-pT Jets?
• Learn about medium
– Strongly coupled
SYM soup
Gyulassy, Levai, and Vitev, NPB571 (200)
– Weakly coupled,
Debye-screened gaslike plasma
J Friess, et al., PRD75:106003, 2007
6/30/2016
INPP Seminar
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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:
6/30/2016
pT
INPP Seminar
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pQCD Rad E-loss Calculation
• HE Bremsstrahlung
– m ~ 0.5 GeV, lmfp ~ 1 fm, RAu ~ 6 fm
– 1/ m << lmfp << L
Gyulassy, Levai, and Vitev NPB594 (2001)
– Bethe-Heitler
– LPM
dpT/dt ~ -(T3/Mq2) pT
6/30/2016
dpT/dt ~ -LT3 log(pT/Mq)
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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
6/30/2016
INPP Seminar
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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)
6/30/2016
INPP Seminar
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What About Elastic Loss?
• Appreciable!
• Finite time effects small
Adil, Gyulassy, WAH, Wicks, PRC75 (2007)
Mustafa, PRC72 (2005)
6/30/2016
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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)
6/30/2016
INPP Seminar
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Strongly Coupled Qualitative Successes
AdS/CFT
Blaizot et al., JHEP0706
6/30/2016
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
STAR, PRL102 (2009)
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Betz, Gyulassy, Noronha, Torrieri, 0807.4526
AdS/CFT Drag
• 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)
6/30/2016
INPP Seminar
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Compared to Data
• String drag: reasonable agreement
WAH, PhD Thesis
6/30/2016
INPP Seminar
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Light Quark and Gluon E-Loss
PHENIX 0-5% p0
WAH, in preparation
dpq/dt ~ E1/3
dpg/dt ~ (2E)1/3
6/30/2016
INPP Seminar
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Baryon to Meson Ratios
STAR
STAR
AdS/CFT
pQCD
AdS/CFT
pQCD
WAH, in preparation
6/30/2016
INPP Seminar
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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
6/30/2016
INPP Seminar
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LHC c, b RAA pT Dependence
WAH, M. Gyulassy, PLB666 (2008)
– Significant
NaïvePrediction
LHC
Unfortunately,
Large
suppression
expectations
riselarge
in
Zoo:
Rleads
met
suppression
What
(pTin
) to
for
full
aflattening
Mess!
pQCD
numerical
pQCD
Rad+El
similar
calculation:
to AdS/CFT
AA
– Use
Let’sof
gorealistic
through
dRgeometry
step
(pT)/dp
by step
> 0Bjorken
=> pQCD;
expansion
dRAA(pTallows
)/dpT < saturation
0 => ST below .2
AA
Tand
6/30/2016
INPP Seminar
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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
6/30/2016
INPP Seminar
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LHC RcAA(pT)/RbAA(pT) Prediction
• Recall the Zoo:
WAH, M. Gyulassy, PLB666 (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)
WAH, times
M. Gyulassy,
PLB666than
(2008)pQCD at only moderate p
– AdS/CFT ratio is flat and many
smaller
T
6/30/2016
INPP Seminar
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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: “]”
6/30/2016
D7 Probe Brane
INPP Seminar
“z”
D3 Black Brane
31
LHC RcAA(pT)/RbAA(pT) Prediction
(with speed limits)
WAH, M. Gyulassy, PLB666 (2008)
– T(t0): (O), corrections unlikely for smaller momenta
– Tc: (|), corrections likely for higher momenta
6/30/2016
INPP Seminar
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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
6/30/2016
LHC
INPP Seminar
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RHIC c, b RAA pT Dependence
WAH, M. Gyulassy, JPhysG35 (2008)
• Large increase in n(pT) overcomes reduction in
E-loss and makes pQCD dRAA/dpT < 0, as well
6/30/2016
INPP Seminar
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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
6/30/2016
INPP Seminar
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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
6/30/2016
INPP Seminar
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New Geometries
Constant T Thermal Black Brane
Shock Geometries
P Chesler,
Quark Matter 2009
Nucleus as Shock
DIS
Embedded String in Shock
Before
Albacete, Kovchegov, Taliotis,
JHEP 0807, 074 (2008)
After
vshock
Q
z
x
Bjorken-Expanding Medium
6/30/2016
Q
z
vshock
x
WAH and Kovchegov, PLB680 (2009)
INPP Seminar
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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
6/30/2016
INPP Seminar
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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=
6/30/2016
• Constant solution unstable
• Time-reversed negative x solution unphysical
• Sim. to x ~ z3/3, z << 1, for const. T BH geom.
INPP Seminar
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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
6/30/2016
INPP Seminar
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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:
6/30/2016
INPP Seminar
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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
6/30/2016
INPP Seminar
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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
6/30/2016
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Quantitative, Falsifiable pQCD
• Requires rigorous pQCD estimates, limits
6/30/2016
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Multiple Models
Bass et al., Phys.Rev.C79:024901,2009
WHDG, Nucl.Phys.A784:426-442,2007
– Inconsistent medium properties
– Distinguish between models
6/30/2016
INPP Seminar
Bass et al.
45
Quantitative Parameter Extraction
• Vary input param.
• Find “best” value
Need for theoretical error
PHENIX, PRC77:064907,2008
6/30/2016
INPP Seminar
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Effect of Collinear Approximation
• Assume small
angle emission
kT
w
– kT << w
• Affects ALL
current pQCD
models
• Enforce via
kinematic
cutoffs
WAH and B Cole, in preparation
6/30/2016
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Huge Sensitivity
WAH and B Cole, in preparation
6/30/2016
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Conclusions I
• QCD is a theory with rich structure
– Traditional techniques (Lattice, pQCD)
• Qualitatively successeful
– AdS/CFT exciting new tool
• Also qualitatively successful
• Jet observables to disambiguate
– Examine mass, momentum dependence
• Charm and bottom RAA
• Double ratio: RcAA/RbAA(pT)
6/30/2016
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Conclusions II
• Generalize AdS/CFT HQ Drag
– Hot and cold nuclear matter
– Gain confidence in universality
• Systematic theoretical error for pQCD
– Collinear approximation badly violated
• Some effects persist to LHC energies
– Single particle more interesting than full jet reconstruction?
– Effects of running coupling not yet rigorously
investigated
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