Title: 3D Jet Tomography : A Probe of the Hydro Initial State
13D 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, Drescher, Dumitru,
Hayashigaki Nara, PRC 74 (2006) 044905 Adil
Gyulassy, under preparation
2Whats all the fuss about??
3Its the Hydro Stupid
!!
Kolb Heinz
!!
4 or is it ???
5 or is it ? Contd
Statement should be Assuming ?Part initial
state, data is consistent with ideal
hydrodynamics in QGP stage
6Model 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
7CGC Distribution
- Use kT factorization formula, with unintegrated
gluon distributions - Unintegrated distributions depend on QSAT (KLN
Model) - QSAT determined using participant density (not
explicitly factorized!!! See, Drescher Nara
(2006)) - Free parameters are normalizations of xG and
dNg/dy - Set to make dNg/dy 1000 at midrapidity, b 0
- Set to make Q2S,A/B 2 GeV2 at midrapidity, b 0
8Why is the CGC so weird???
More eccentric bulk naturally leads to higher
elliptic flow
9The Upshot
- Before we declare perfection we need to
realize - A CGC initial state needs more viscosity to
explain data - Need independent way to tie down initial state
- Then we can determine how perfect our fluid
really is - We propose as a probe
10Jet 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 eccentricities should
give different high pT v2. - The long range bulk correlations over rapidity y,
will help us differentiate the initial states
11RAA- First at y 0
- Nuclear Modification Factor is used to track
nuclear effects - Calculated using model similar to Drees, Feng,
Jia. - ? 0.06
12RAA for RHIC and LHC
13Measurements of v2 at y 0 probably not
enoughLets extend our reach and go off
midrapidity
14Local Rapidity Triangle
Figure from BGK 1977.
- Get rapidity dependent local participant density
with BGK - Note global multiplicity is boost invariant for A
B but not local density - Binary un-twisted
15How 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.
16Thanks 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.
17Opposite 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
18V1(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
- Sensitive to high x assumptions
19V1(pT,y) Calculations contd
- Can extrapolate energies and nuclei to LHC (5500
GeV and Lb-Lb) - All parameters fit at RHIC, prediction of
multiplicity from CGC/KLN - Multiplicity dN/dy(y0, b0) 2300. Previous
prediction in range 1900-2500 - Counteracting effects of higher multiplicity and
lower gradients give small energy dependence of
effect.
20Conclusions
- Perfection Proclamation a shaky edifice maybe
stringing us along - Need better handle on Initial State input into
Hydro (CGC, BGK) - 3D Jet Tomography provides a way
- CGC (KLN) and BGK have different twist off mid
rapidity - High pT, v1 (pT,y) is the first and simplest
prediction - CGC Initial State has mono-jet implications
- High pT matter is also twisted (pT range to be
determined) - Still significant theoretical input needed
- More sophisticated E-loss (Collisional, pT
dependent, fluctuating) - There is significant dependence on nuclear edge
(subsumed in running of ?s) that needs to be
controlled theoretically (get consistent d-A) - 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
21Acknowledgements
- I would like to thank the following people for
their support and valuable discussions - (in alphabetical order)
- B. Cole, A. Dumitru, H-J. Drescher, M. Gyulassy,
U. Heinz, T. Hirano, W. Horowitz, L. Mclerran, Y.
Nara, I. Vitev, S. Wicks
22Bonus Slides
23The 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.
24Multiplicity and NPart Scaling
25And 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
26Our 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)
27Edge 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
28A 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
29RAA vs. Azimuth and Rapidity
- Nuclear Modification Factor is used to track
nuclear effects - Calculated using Drees, Feng, Jia et al.
- ? 0.25
30What about the Moments?
- Decompose RAA into fourier moments
- Moments increase in magnitude with increasing
asymmetry - Higher moments increase in significance with
larger b and ?
31Bjorken 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
32Opacity 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
33Edge Sensitivity
- Figures show ltxgt in fm as function of pT and y
- 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
34RAA 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
35Octupole 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(?)