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Initial Conditions from
Shadowed Glauber Model
Sushant K. Singh
Variable Energy Cyclotron Centre, Kolkata
CNT QGP Meet 2015 (16-20 Nov 2015)
Variable Energy Cyclotron Centre, Kolkata
Based on arXiv:1510.01311
In collaboration with :
S. Chaterjee, Md Hasanujjaman, S. Ghosh, J. Alam, S. Sarkar
1
Plan of Talk
Review of Glauber Model
 Definition of shMCGM
 Results
 Summary

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Freeze Out
Initial
Condition
Relativistic
Hydro
3
Initial Conditions





Relativistic hydrodynamic equations being
nonlinear, are sensitive to initial conditions.
In absence of a microscopic theory for initial
conditions, several models have been proposed
with adjusting parameters.
In boost invariant expansion, specification of
energy density profiles in transverse plane is
sufficient.
Recently CGC based models are being favored
over Glauber models.
Glauber model still stands to be a powerful way
of explaining many observations in simple and
intuitive way
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Glauber Model

Connects initial geometry to experimental
observables.
N part 

d N ch
 n0  f N coll  (1  f )

d
2


where f is hardness factor
Npart = Number of participants
Ncoll = Number of binary collisions
 Treats nucleus-nucleus collision as a
superposition of nucleon-nucleon collision
process.
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Glauber Model
Assumptions in Glauber model
1. Nucleons within colliding nuclei travel in a
straight line trajectory
2. The nucleon-nucleon cross section is constant
(independent of prior collisions)
After including shadowing
The strength of a source for particle production depends
on the location of the nucleons within the nucleus. A
nucleon deep inside will deposit less energy compared to
the nucleons in front.
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Glauber Model
Two methods of implementation
Optical Model
•Numerical computation of
integrals is time consuming
•Only ε2 ≠ 0. Higher
harmonics can’t be
determined (for spherical
nuclei).
•Shadowing effect (with
shMCGM) cannot be
introduced
Monte Carlo Model
•Fast since it involves only
counting Npart and Ncoll.
•Can generate higher
harmonics
•Shadowing effect can be
incorporated
7
Glauber ModelShortcomings
STAR Collaboration, arXiv:1505.07812
•The Glauber Model
predicts a negative slope
for U+U collisions and a
slightly positive slope for
Au+Au collisions.
• However, data shows
negative slopes for U+U
and Au+Au and slope is
less negative for U+U
•IP-Glasma model
provides a better
description.
8
Modified Counting Scheme in
Glauber Model (shMCGM)
( sh )


N
d N ch
part
( sh )
 n0  f N coll  (1  f )

d
2




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“ …. there is a number µ which is a kind of efficiency in a single
collision for doing whatever process interests us. So let us say, the
first collision, on a virgin nucleon produces one unit of whatever we
are looking for. The second one only produces a fraction of that, a
fraction we shall call µ. The third one produces µ2 , and so on. …. the
number of particles that get produced in these n collisions, well, you
have a finite geometrical series to sum and answer is”
1   
2
 ...  
n 1
1  n

1 
Glauber R J, Quantum Optics and Heavy Ion Physics, arXiv:nucl-th/0604021 (2006)
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First Check
shMCGM
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12
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Results
Disappearance of Knee structure
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2 
y2  x2
y2  x2
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Initial
Ellipticity
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Correlation
Plot
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Summary
•Shadowing has been incorporated in the
conventional MCGM by giving the leading sources
larger weight compared to the interior ones.
•Result of correlation plot is in agreement with the
experimental data.
•Presence of shadowing suppresses ellipticity
fluctuations.
Thank You
19