3D Jet Tomography : A Probe of the Hydro Initial State

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3D Jet Tomography A Probe of the Hydro Initial
State

• Azfar Adil
• Nuclear Theory Group
• Columbia University

Adil Gyulassy, Phys. Rev. C 72 (2005)
034907 Adil, Gyulassy Hirano , Phys. Rev. D 73
(2006) 074006 Adil Gyulassy, under preparation
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Whats all the fuss about??
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Its the Hydro Stupid Or is It?
Statement should be Assuming ?Part initial
state, data is consistent with ideal
hydrodynamics in QGP stage
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Model for ?Part

• The Participant density is determined by the
  normal Glauber Wounded Nucleons
• The factors TA/B are just the Glauber thickness
  functions of a nucleus
• We use Wood-Saxon nuclear density profiles

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CGC Distribution

• Use kT factorization formula, with CGC inspired
  unintegrated distributions
• Unintegrated distributions depend on QSAT (KLN
  Model)
• QSAT determined using participant density
• Free parameters are normalizations of xG and
  dNg/dy
• Set to make dNg/dy 1000 at midrapidity, b 0
• Set to make Q2SAT,A/B 2 GeV2 at midrapidity, b
  0

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NPart Scaling of Multiplicity
Adil et al. arXivnucl-th/0605012
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Why is the CGC so weird???
More eccentric bulk naturally leads to higher
elliptic flow
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The Upshot

• Before we declare perfection we need to
  realize
• A CGC type initial state needs more viscous
  hydro to
• be consistent with data
• Need independent way to tie down initial state
• We can determine how perfect our fluid really
  is
• after this determination
• We propose as a probe

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Jet Tomography - Now in 3D

• The two kinds of initial bulk matter we need to
  differentiate are CGC type and NPart type.
• They have similar gross properties but different
  Local densities ?Part(xT,yb) and ?CGC(xT,yb)
• We propose detailed Jet Tomography RAA(pT,y,?) in
  order to probe the initial state
• The differences in bulk eccentricites should give
  different high pT v2.
• The long range bulk correlations over rapidity y,
  will help us differentiate the initial states

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RAA- First at y 0

• Nuclear Modification Factor is used to track
  nuclear effects
• Calculated using model similar to Drees, Feng,
  Jia.
• ? 0.06

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RAA for RHIC and LHC
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Measurements of v2 at y 0 probably not
enoughLets extend our reach and go off
midrapidity
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The p-A Triangle- BGK Model

• Low pT particles are produced in y space as a
  triangle
• Height ? ?A A1/3
• Nucleon excitation at yi, uniform
• Slope ? O(A1/3/log(s))
• RHIC ? 0.45, LHC ? 0.28

Figure from Brodsky, Gunion, Kuhn 1977.
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And It Exists!!!

• Monte Carlo event generators such as HIJING have
  QCD dynamics built in

• The multiplicity seen in the RHIC d-A experiment
  has just this triangle/trapezoid
• The shape is apparent if we look at it as a ratio

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Implementation for AB
INTRINSIC LOCAL BJORKEN SCALING VIOLATION
O(A1/3/log(s))

• Approximate local participant density with BGK
• Can get global multiplicity
• Note global multiplicity is boost invariant for A
  B but not local density
• Binary un-twisted

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Our Participant Model

• Distribution inspired by BGK model
• Exponential envelope inserted to model RHIC
  multiplicity
• Parameters set to RHIC central A-A

BRAHMS charged data PRL 88 202301 (2002)
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How to use Tomography
xT

• Different rapidity regions effected by different
  initial nuclei (as seen from BGK model)
• Asymmetry apparent in Participant density
  (rotation around y-axis)
• Binary density unaffected (symmetric)
• Asymmetry can be probed via jet quenching
• Long range rapidity anti correlations can be
  recorded.
• Note The RAA v1 as a function of pT, ? and y is
  a good probe.

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Thanks for all the fish
Dashed Lines Positive Rapidity
Solid Lines Negative Rapidity
CGC

• Figures show ltxgt in fm as function of pT and y
• CGC affects the high pT part as well (unlike
  BGK), generates fish diagrams.
• Note Fish falls off the edge.

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Edge Dependence

• flow and fhigh are the leading Qsat (and thus
  transverse coordinate) dependence of the
  production formula
• Qsat drops to zero sharper for regulated ?s ,
  affects high pT since the Qsat already low
  everywhere at high pT

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Opposite Tomographic Twist
xT

• Use v1(pT,y) to probe higher twist for higher
  pT
• v1(pT,y) changes sign both as a function of pT
  and y

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V1(pT,y) Calculations

• CGC generally gives smaller v1 values than
  participant density
• For monojets, there is a finite rapidity at which
  the v1 flips sign lower rapidity for higher pT
• Sensitive to nuclear edge effects
• Rapidity gap at LHC dilutes gradients

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Conclusions

• Perfection Proclamation under threat
• Need better handle on Initial State (CGC, BGK)
• Once that is done, we can see how low a viscosity
  we need
• 3D Jet Tomography provides a way
• CGC (KLN) and BGK have different twist off mid
  rapidity
• Can differentiate this using RAA(pT,y,?)
• v1 (pT,y) is the first and simplest prediction
  (can check more detail)
• CGC Initial State has monojet Implications that
  can be tested
• High pT matter is also twisted
• Still significant theoretical input needed
• There is significant dependence on nuclear edge
  (subsumed in running of ?s) that needs to be
  controlled theoretically
• The prediction is also dependent on how exactly
  high x degrees of freedom are handled
• Will need to incorporate more effects e.g.
  geometric scaling, anomalous dimension which will
  change high pT parts

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Acknowledgements

• I would like to thank the following people for
  their support and valuable discussions
• (in alphabetical order)
• B. Cole, A. Dumitru, M. Gyulassy, U. Heinz, T.
  Hirano, W. Horowitz, Y. Nara, S. Wicks
• Also, Ivan Vitev and Los Alamos National Lab

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Bonus Slides
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The Local CGC Distribution

• Figures show ltxgt in fm as function of pT and ?
• CGC affects the high pT part as well, generates
  fish diagrams
• The tail of the diagram signifies higher pT
  getting more twisted after a threshold, probe of
  edge effects

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A Closer Look at Local Density

• Contour Plots show particular properties of the
  local density
• Rotation around y - axis
• Zero effect for zero impact parameter
• More quantitatively shown in second figure
• Shift can be clearly seen
• Drop due to overall exponential envelope is
  visible
• Similar geometries studied by Hirano Heinz
  (dynamical firestreak)

Green - 10 , Blue - 50 , Red - 90
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RAA vs. Azimuth and Rapidity

• Nuclear Modification Factor is used to track
  nuclear effects
• Calculated using Drees, Feng, Jia et al.
• ? 0.25

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What about the Moments?

• Decompose RAA into fourier moments
• Moments increase in magnitude with increasing
  asymmetry
• Higher moments increase in significance with
  larger b and ?

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Bjorken NON Scaling at RHIC
From hep-th/0410017

• Bjorken Scaling only good when parameter
  A1/3/log(s) ? ?? 1
• At RHIC ? 0.45, even at LHC will be 0.28
• Something not right in theory vs. data for v2 off
  mid rapidity
• Lets to look at whether any of this violation is
  from geometry

Details and future of hydro at RHIC Tetsufumi
Hirano
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Opacity Line Integral

• Opacity defined as a line integral over local
  participant density
• (x0,y0) origination point
• ? -1,0,1
• We can average over geometrical fluctuations

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RAA from Another Perspective
b 6 Fm
b 6 Fm
? -2
? 2

• Try to track asymmetry in Polar Plots
• Measure using Octupole Twist ?3
• Long range anti-correlation over rapidity
• Dynamic effect due to long range
  anti-correlations in geometry

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Octupole Twist Evolution

• Evolution with rapidity and impact parameter true
  prediction
• As one increases rapidity there is an increasing
  Octupole Twist
• Dynamic effect of a larger transverse
  displacement due to rotation around y-axis
• A simpler observable is ?RAA RAA(0)-RAA(?)