Testing AdSCFT Drag and pQCD Heavy Quark Energy Loss

1
Testing AdS/CFT Drag and pQCD Heavy Quark Energy
Loss
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Motivation

• Many heavy quark energy loss models
• Hope to distinguish between two broad classes
• Standard Model pQCD
• AdS/CFT Drag
• Comparison difficult
• nontrivial mapping of AdS/CFT to QCD
• predictions for LHC
• Look for robust signal

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pQCD Success at RHIC
(circa 2005)

• Consistency RAA(h)RAA(p)

• Null Control RAA(g)1

• GLV Prediction TheoryData for reasonable fixed
  L5 fm and dNg/dydNp/dy

4
Trouble for wQGP Picture

• wQGP not ruled out, but what if we try strong
  coupling?

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Intro to AdS/CFT

• Large Nc limit of d-dimensional conformal field
  theory dual to string theory on the product of
  d1-dimensional Anti-de Sitter space with a
  compact manifold

31 SYM
z 0
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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 strongly-coupled
  QCD in classical SUGRA

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Qualitative AdS/CFT Successes

• Mach wave-like structures

• sstrong(3/4) sweak, similar to Lattice

• h/sAdS/CFT 1/4p ltlt 1 h/spQCD

• e- RAA p, h RAA e- RAA(f)

T. Hirano and M. Gyulassy, Nucl. Phys. A6971-94
(2006)
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AdS/CFT Energy Loss Models

• Langevin model
• Collisional energy loss for heavy quarks
• Restricted to low pT
• pQCD vs. AdS/CFT computation of D, the diffusion
  coefficient
• ASW model
• Radiative energy loss model for all parton
  species
• pQCD vs. AdS/CFT computation of
• Debate over its predicted magnitude
• ST drag calculation
• Drag coefficient for a massive quark moving
  through a strongly coupled SYM plasma at uniform
  T
• not yet used to calculate observables lets do
  it!

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AdS/CFT Drag

• Model heavy quark jet energy loss by embedding
  string in AdS space
• dpT/dt - m pT
• m pl1/2 T2/2Mq

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Energy Loss Comparison

• AdS/CFT Drag
• dpT/dt -(T2/Mq) pT

• 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(n1), where n(pT) has some momentum
  dependence
• We can approximate RAA(pT)
• RAA (1-e(pT))n(pT),
• where pf (1-e)pi (i.e. e 1-pf/pi)

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Looking for a Robust, Detectable Signal

• Use LHCs large pT reach and identification of c
  and b to distinguish between pQCD, AdS/CFT
• Asymptotic pQCD momentum loss
• String theory drag momentum loss
• 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 gt 0 gt pQCD dRAA(pT)/dpT lt 0 gt ST

eST 1 - Exp(-m L), m pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74126005 (2006) C. Herzog
et al. JHEP 0607013,2006
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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, M. Gyulassy, arXiv0706.2336

• LHC Prediction Zoo What a Mess!
• Lets go through step by step

• Unfortunately, large suppression pQCD similar to
  AdS/CFT

• Large suppression leads to flattening
• Use of realistic geometry and Bjorken expansion
  allows saturation below .2

• Significant rise in RAA(pT) for pQCD RadEl

• Naïve expectations met in full numerical
  calculation
• dRAA(pT)/dpT gt 0 gt
  pQCD dRAA(pT)/dpT lt 0 gt ST

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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
• 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

RcbpQCD(pT) 1 - as n(pT) L2 log(Mb/Mc) ( /pT)
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LHC RcAA(pT)/RbAA(pT) Prediction

• Recall the Zoo

WH, M. Gyulassy, arXiv0706.2336 nucl-th

• 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, M. Gyulassy, arXiv0706.2336 nucl-th
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Not So Fast!

• Speed limit estimate for applicability of AdS
  drag
• g lt 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, xy0) (
• largest gcrit for smallest T
• T Tc

D7 Probe Brane
Q
Worldsheet boundary Spacelike if g gt gcrit
Trailing String Brachistochrone
D3 Black Brane
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LHC RcAA(pT)/RbAA(pT) Prediction(with speed
limits)
WH, M. Gyulassy, arXiv0706.2336 nucl-th

• T(t0) (O), corrections unlikely for smaller
  momenta
• Tc (), corrections likely for higher momenta

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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
• No longer expect
• pQCD dRAA/dpT gt 0
• Large n requires corrections to naïve
• Rcb Mc/Mb

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RHIC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv0710.0703 nucl-th

• Large increase in n(pT) overcomes reduction in
  E-loss and makes pQCD dRAA/dpT lt 0, as well

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RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, arXiv0710.0703 nucl-th

• Wider distribution of AdS/CFT curves due to large
  n increased sensitivity to input parameters
• Advantage of RHIC lower T gt higher AdS speed
  limits

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Conclusions

• AdS/CFT Drag observables calculated
• Generic differences (pQCD vs. AdS/CFT Drag) seen
  in RAA
• Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
• Discovery potential in Year 1 LHC Run
• Understanding regions of self-consistency crucial
• RHIC measurement possible

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Conclusions

• Year 1 of LHC could show qualitative differences
  between energy loss mechanisms
• dRAA(pT)/dpT gt 0 gt pQCD dRAA(pT)/dpT lt 0 gt ST
• Ratio of charm to bottom RAA, Rcb, will be an
  important observable
• Ratio is flat in ST approaches 1 from below in
  pQCD E-loss
• A measurement of this ratio NOT going to 1 will
  be a clear sign of new physics pQCD predicts
  2-3 times increase in Rcb by 30 GeVthis can be
  observed in year 1 at LHC
• Measurement at RHIC will be possible
• AdS/CFT calculations applicable to higher momenta
  than at LHC due to lower medium temperature

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Backups
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Geometry of a HI Collision

• Medium density and jet production are wide,
  smooth distributions
• Use of unrealistic geometries strongly bias
  results

S. Wicks, WH, M. Djordjevic, M. Gyulassy,
Nucl.Phys.A784426-442,2007
1D Hubble flow gt r(t) 1/t gt T(t) 1/t1/3
M. Gyulassy and L. McLerran, Nucl.Phys.A75030-63,
2005
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Langevin Model

• Langevin equations (assumes gv 1 to neglect
  radiative effects)
• Relate drag coef. to diffusion coef.
• IIB Calculation
• Use of Langevin requires relaxation time be large
  compared to the inverse temperature

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But Theres a Catch (II)

• Limited experimental pT reach?
• ATLAS and CMS do not seem to be limited in this
  way (claims of year 1 pT reach of 100 GeV) but
  systematic studies have not yet been performed

ALICE Physics Performance Report, Vol. II
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LHC p Predictions

• 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 AWS-based energy loss (next slide)
• We wish to understand the origin of this
  difference

WH, S. Wicks, M. Gyulassy, M. Djordjevic, in
preparation
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Asymptopia at the LHC
Asymptotic pocket formulae DErad/E a3
Log(E/m2L)/E DEel/E a2 Log((E T)1/2/mg)/E
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in
preparation
30
K. J. Eskola, H. Honkanen, C. A. Salgado, and U.
A. Wiedemann, Nucl. Phys. A747511529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J.
C38461-474 (2005)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U.
A. Wiedemann, Nucl. Phys. A747511529 (2005)
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Pion RAA

• Is it a good measurement for tomography?
• Yes small experimental error
• Claim we should not be so immediately
  dis-missive of the pion RAA as a tomographic tool

• Maybe not some models appear fragile

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Fragility A Poor Descriptor

• All energy loss models with a formation time
  saturate at some RminAA gt 0
• The questions asked should be quantitative
• Where is RdataAA compared to RminAA?
• How much can one change a models controlling
  parameter so that it still agrees with a
  measurement within error?
• Define sensitivity, s min. param/max. param
  that is consistent with data within error

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Different Models have Different Sensitivities to
the Pion RAA

• GLV
• s lt 2
• Higher Twist
• s lt 2
• DGLVElGeom
• s lt 2
• AWS
• s 3

WH, S. Wicks, M. Gyulassy, M. Djordjevic, in
preparation
34
T Renk and K Eskola, Phys. Rev. C 75, 054910
(2007)
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in
preparation
35
A Closer Look at ASW
The lack of sensitivity needs to be more closely
examined because (a) unrealistic geometry (hard
cylinders) and no expansion and (b) no expansion
shown against older data (whose error bars have
subsequently shrunk
(a)
(b)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U.
A. Wiedemann, Nucl. Phys. A747511529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J.
C38461-474 (2005)
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Surface Bias vs. Surface Emission

• Surface Emission one phrase explanation of
  fragility
• All models become surface emitting with infinite
  E loss
• Surface Bias occurs in all energy loss models
• Expansion Realistic geometry gt model probes a
  large portion of medium

A. Majumder, HP2006
S. Wicks, WH, M. Gyulassy, and M. Djordjevic,
nucl-th/0512076
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A Closer Look at ASW

• Difficult to draw conclusions on inherent surface
  bias in AWS 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.
C38461-474 (2005)