Heavy Ion Collisions with
pQCD and AdS/CFT
W. A. Horowitz
The Ohio State University
November 24, 2009
With many thanks to Brian Cole, Miklos Gyulassy, Ulrich Heinz, and Yuri Kovchegov
6/30/2016
UW Particle Theory 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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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)
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• 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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Present and Future QGP Experiments
• RHIC
• LHC
–
–
–
–
–
–
–
–
BRAHMS
PHENIX
PHOBOS
STAR
ALICE
ATLAS
CMS
LHCb
ATLAS
PHENIX
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Evolution of a HI Collision
T Hirano, Colliding Nuclei from AMeV to ATeV
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STAR
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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
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Low-pT Measurements
• Viscosity: why the fuss?
– Naive pQCD => h/s ~ 1
– Naive AdS/CFT => h/s ~ 1/4p
Luzum and Romatschke, PRC78 (2008)
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U Heinz, Quark Matter 2009
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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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SPECT-CT Scan uses
internal g photons and
external X-rays
http://www.fas.org/irp/imint/docs/rst/Intro/P
art2_26d.html
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Tomography in QGP
• Requires wellcontrolled theory of:
pT
– production of rare, highpT probes
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
• Au+Au
Y-S Lai, RHIC & AGS Users’ Meeting, 2009
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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
– LPM
dpT/dt ~ -LT3 log(pT/Mq)
– 1/m << lmfp << L
• mult. coh. em.
– Bethe-Heitler
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
Mustafa, PRC72 (2005)
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Adil, Gyulassy, WAH, Wicks, PRC75 (2007)
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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: reasonable agreement
WAH, PhD Thesis
– Distinguishing measurement?
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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
– 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
Q
Worldsheet boundary
Spacelike if g > gcrit
x5
Trailing
String
“Brachistochrone”
“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
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
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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
– Nc2 gluons per nucleon in shock
– L is typical mom. scale; L-1 typical dist. scale
• E-M in shock rest frame: T’00 ~ Nc2 L4
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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 (“lab” 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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Quantitative, Falsifiable pQCD
• Requires rigorous pQCD estimates, limits
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Acronyms, Acronyms
• Four major pQCD formalisms for Rad E-loss
– Opacity expansion: GLV (DGLV), ASW-SH
– Multiple soft scattering: BDMPS (ASW-MS)
– Higher Twist: HT
– Thermal field theory: AMY
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Energy Loss
– RAA ~ ∫(1-ϵ)n P(ϵ) dϵ
• Ef = (1-ϵ)Ei
– Opacity expansions finds single inclusive
gluon emission spectrum
• dNg/dxdkTdqT
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Poisson Convolution
Gyulassy, Levai, and Vitev NPB594 (2001)
• Find P(ϵ) by convolving dNg/dx
– Approximates probabilistic multiple gluon
emission
• assume independent emissions
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Opacity Expansion Calculation
• Want to find dNg/dx
– Make approximations to simplify derivation
• Small angle emission: kT << xE
– Note: ALL current formalisms use collinear approximation
– Derived dNg/dxdkT violates collinear approx
• Both IR and UV safe
• Enforce small angle emission through UV cutoff in kT
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Uncertainty from Collinear Approx
• Derived dNg/dxdkT maximally violates
collinear approximation
– dNg/dx depends
sensitively on kT cutoff
• Despite UV safety
– For effect on extracted
prop., must understand x
• Discovered through
TECHQM Brick Problem
WAH and B Cole, arXiv:0910.1823
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ASW-SH Definition of x
• ASW-SH: xE
– Minkowski coords
P
• Always on-shell
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GLV Definition of x
• GLV: x+
– Light-cone coords
P
• Always on-shell
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Coordinate Transformations
– Same in the limit kT/xE → 0!
• UV cutoff given by restricting maximum
angle of emission
P
q
– Previous comparisons with data took qmax=p/2
– Vary qmax to estimate systematic theoretical
uncertainty
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Jacobians
• ϵ is fraction of longitudinal momentum
– Need dNg/dxE to find P(ϵ)
– A Jacobian is required for x = x+ interpretation
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Rad. Gluon Kin. Sensitivities
• UV
WAH and B Cole, arXiv:0910.1823
• What about IR?
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Collinearity and Gluon Mass
• Massless gluons:
– Large IR cutoff sensitivity
• Gluons with thermal mass
BDMS, JHEP 0109 (2001)
Larger x better respects kT << xE
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WAH and B Cole, arXiv:0910.1823
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Results
• Quantitatively compare to PHENIX data
WAH and B Cole, arXiv:0910.1823
– Assumed infinite Elastic precision
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Parton Energy Dependence
• Dependence on
parton energy
WAH and B Cole, arXiv:0910.1823
6/30/2016
• Uncertainty on qhat
– Assume all formalisms
equally affected
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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)
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Conclusions II
• Generalize AdS/CFT HQ Drag
– Hot and cold nuclear matter
– Gain confidence in universality
• Systematic theoretical uncertainty for pQCD
– Collinear approximation badly violated
• Some effects persist to LHC energies
– Single particle more interesting than full jet reconstruction?
• Extracted medium properties likely consistent w/i unc.
– Effects of running coupling not yet rigorously
investigated
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