Hadronic Shear Viscosity from a Microscopic Transport Model

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Hadronic Shear Viscosity from a Microscopic
Transport Model
Nasser Demir in collaboration with Steffen A.
Bass Duke University Hot Quarks August 18, 2007
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Overview

• Motivation Low Viscosity Matter at RHIC
  Consequences
• Theory Kubo Formalism for Transport Coefficients
• Analysis/Results Chemical Potentials, Results
  for Viscosity
• Summary/Outlook

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Low Viscosity Matter at RHIC
large viscosity
QGP and hydrodynamic expansion
initial state
freeze-out
low viscosity
pre-equilibrium
hadronic phase

• Why study hadronic phase?
• Need to know hadronic
• viscosity to constrain QGP
• viscosity.
• Viscosity changes as function
• of time in a heavy ion collision!
• 3) Viscous hydro calculations assume fixed ?/s
  throughout entire evolution (need low ?/s)

QGP-like phase at RHIC observed to behave
very much like ideal fluid ideal hydro treatment
of QGP phase works well but what about
hadronic phase?
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Question re low viscosity

• How low is it? (AdS/CFT ?/s1/4p? KSS bound)

PRL 94. 111601 (2005) Kovtun, Son, Starinets
NOTE Hadronic phase of HIC not a chiral pion
gas, nor a binary pion-kaon mixture!
Viscous hydro needs ?/s(2-3)/4p !
Csernai, Kapusta, McLerran nucl-th/0604032 PRL
97. 152303 (2006)
Luzum, Romatschke arXiv0804.4015  nucl-th
Pert. Theory N/A here.
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What do we know thus far?

• Determining hadronic viscosity necessary to
  constrain viscosity of QGP.
• Perturbative methods not well trusted near
• Tc on hadronic side ? microscopic transport
  model can help here!

Next Question How do we compute transport
coefficients?
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Linear Transport Coefficients Green-Kubo
Relations
Phenomenological Transport Equation
thermodynamic/mechanical flux linearly
proportional to applied field in small field
limit.
Examples of transport coefficients thermal
conductivity, diffusion, shear viscosity.
Shear Viscosity Coefficient
y
x
Vx v2
ya
Pyx
y0
Vx v1
Green-Kubo compute linear transport coefficients
by examining near-equilibrium correlations!
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Modeling the Hadronic MediumUrQMD
(Ultrarelativistic Quantum Molecular Dynamics)
- Transport model based on Boltzmann Equation
-Hadronic degrees of freedom. -Particles interact
only through scattering. ( cascade ) -Classical
trajectories in phase space. -Interaction takes
place only if
(dmin is distance of closest approach between
centers of two hadrons)
- Values for s of experimentally measurable
processes input from experimental data.

• 55 baryon- and 32 meson species, among those 25
  N, ? resonances and 29 hyperon/hyperon
  resonance species
• Full baryon-antibaryon and isospin symmetry
• - i.e. can relate nn cross section to pp cross
  section.

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Box Mode for Infinite Hadronic Matter
Equilibriation

• Strategy PERIODIC BOUNDARY CONDITIONS!
• Force system into equilibrium, and PREVENT
  FREEZEOUT.

Equilibrium Issues
- Chemical equilibrium DISABLE multibody
decays/collisions. ? RESPECT detailed balance!
- Kinetic Equilibrium Compute TEMPERATURE by
fitting to Boltzmann distribution!
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Kubo Formalism Calculating Correlation Functions
NOTE correlation function found to empirically
obey exponential decay.
T52.1 /- 1.3 MeV µ 0
Assumption also made in Muronga, PRC
69044901,2004
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Entropy Considerations
Method I Gibbs formula for entropy (extract µB
for our system from SHAREv2, P and e known from
UrQMD.) Denote as sGibbs.

• SHARE v2 Torrieri et.al.,nucl-th/0603026
• Tune particles/resonances to those in UrQMD.

Method II Weight over specific entropies of
particles, where s/n is a function of m/T µB/T!
Denote as sspecific
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Entropy Scaling
For system with fixed volume in equilibrium
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Chemical Potential in Hadronic Phase

• Chemical Freezeout Tchem160 MeV.
• Kinetic Freezeout Tkin130 MeV.
• For ideal hydro evol.
• At TTchem, fix hadronic ratios by introducing
  finite chemical potential for species (pions,
  baryons).
• Keep hadron ratios fixed, but chemical potentials
  increase as system cools to TTkin.

See PCE scheme(Hirano et. al. nucl-th/0208068
Kolb et. al. hep-ph/0210222)
NOTE In heavy ion collision, can approximate
hadronic phase with µB0, but not µp0 !!
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Where is the minimum viscosity? (for µ0)

• - ?/s decreases with increasing T in hadronic
  phase.
• ?/s(T195 MeV)0.3, ?/s(T160 MeV)0.4.
• Is minimum ?/s near Tc? Limit of our
  calculations for hadronic phase agree with
  suggestion.

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What happens at FINITE CHEMICAL POTENTIAL?
- ?/s decreases with finite chemical potential!
- ?/s(T160 MeV) 0.3 at finite µp! (reduced
from ?/s0.4) - Viscous hydro needs ?/s 0.24 in
hadronic freezeout range.
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Summary/Outlook

• Can apply Green-Kubo formalism to hadronic matter
  in equilibrium
• Use UrQMD to model hadronic matter.
• Use box mode to ensure equilibrium.
• Calculated entropy via 2 different methods
  (microscopic and
• macroscopic pictures self-consistent).
• Preliminary results
• Hadronic ? /s satisfies viscosity bound from
  AdS/CFT.
• ?/s notably reduced at finite chemical potential,
  to value near what viscous hydro calculations
  suggest in hadronic freezeout range.
• Outlook
• - Describe time-evolution of transport
  coefficient in relativistic heavy-ion reaction
  through hybrid macro micro calculation.

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Luzum, Romatschke arXiv0804.4015  nucl-th
Elliptic flow strongly depends on initial
condition! CGC allows larger viscosity than
Glauber initial condition.