Diffusion and Two Particle Correlations

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Diffusion and Two Particle Correlations

Sean Gavin
Wayne State University
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Charge fluctuations from QGP hadronizationDoes
diffusion hide them?

• why diffusion?
• causal diffusion
• how diffusion modifies correlations and
  fluctuations
• results
• rapidity fluctuations
• angular correlations (in progress)
• Mohamed Abdel-Aziz S.G.
• Phys.Rev. C70 (2004) 034905

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Charge Fluctuation Puzzle

• quark-gluon degrees of freedom seen at RHIC
• expect hadronization changes net-charge
  fluctuations
• phase transition Rajagopal, Stephanov Shuryak
  Mishustin
• Bower Gavin Antoniou et al., Wilk et al.
• hadronization Jeon Koch Asakawa et al.
  Bialas
• Jeon Koch (N?)qgp ? 2? hadron gas values
• problem STAR, PHENIX, NA49, CERES not seen!
• ask how does the hadronic medium hide
  hadronization?

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How to Reduce Net-Charge Fluctuations

• Flow - advection
• cant reduce charge fluctuations
• can increase them

• Diffusion
• smooths distribution
• reduces fluctuations

charge conserved ? diffusion is only mechanism
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Causal Diffusion
"classic" diffusion dynamics random walk ??x2? ?
?t infinite propagation speed v ?x/?t ? ? as ?t
? 0 causal diffusion equation
?x
Grad Israel Stewart

• Grad moment method Muronga Koide
• propagation speed v ?D/?d
• diffusion time ?d
• classic regime ?d ? 0, v ? ?

v
-v
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Diffusion Current
diffusion particle flow from high to low density
classic

• problem current responds instantly to gradients
• particles know the surrounding density
  beforehand

• causal

• relaxation time ?d ? time lag
• approximate

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Causal vs. Classic Diffusion
Bjorken flow plus causal diffusion ? ?
dN?dy rapidity width
Abdel-Aziz S.G.
?V? 2D/?0
?V/?V?
classic
1.5
1.0
?0??d 0.5
Find width spreads more slowly for causal
diffusion
?/?0
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Diffusion and Correlations
spatial correlation function for single charge
species

• diffusion equation for r(x1, x2)
• Van Kampen, Stochastic Processes in Physics and
  Chemistry, (Elsevier, 1997)
• Gardiner, Handbook of Stochastic Methods,
  (Springer, 2002)
• fluctuations equilibrate by diffusing through
  volume
• global equilibrium diffusion drives r ? ?

equilibrium

• Poisson fluctuations

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Diffusion on Net-Charge Correlations

• charge species a, b ? ?, ?

annihilation/creation ? reaction-diffusion eqns
for rab
net charge correlation function
diffusion equation
reaction terms cancel due to charge conservation
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Dynamic Fluctuations from Correlations
Pruneau, Voloshin S.G.

• correlation function
• pair distribution ??

correlations ? fluctuations dynamic fluctuations
variance thermal contribution
net charge fluctuations for ?, ? species
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Dynamic Net-Charge Fluctuations

• correlation function
• net charge fluctuations
• Nch N?N ? and Ntot NN ?

diffusion drives q ? ? in global equilibrium
equilibrium
dynamic fluctuations ? ?? for N N ?
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Fluctuations

• correlation function gaussian near midrapidity

• relative rapidity ?r ? ?1??2
• weak dependence on ?a ? ??1??2???

two-body diffusion equation ? ?? grows ? one body
width, ?V
fluctuations, rapidity window ?
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Can Diffusion Obliterate Fluctuations?

• JeonKoch estimate
• QGP N? ? ??
• ? initial value at hadronization
• STAR N? ? ?1.5
• Can hadronic diffusion dissipate the difference?
• Not likely lifetime of HG from resonances 5 to
  10 fm

Abdel-Aziz, S.G
? ? ?? ?? ? ????, D 2 fm, ?d ? ? fm, ??? 9 fm
J-K estimate wrong? Bialas C. Nonaka, B.
Muller, S. A. Bass, M. Asakawa Maybe the whole
picture is wrong sQGP? bsQGP?
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Angular Correlations
Abdel-Aziz, S.G

• correlation function with radial expansion
• diffusion ? radial velocity
• boosts particles into an opening angle

vr
????
?r (fm)
azimuthal separation ? ? ?? ? ??
diffusion ? ?r???, ?r??? find broadening with
time ? importance of diffusion
? (rad)
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Summary Diffusion Alters Charge Correlations

• Diffusion may explain part of the fluctuation
  puzzle
• Rapidity fluctuations
• Probe contribution azimuthal correlations
• Causal Diffusion relativistic transport is
  interesting
• Muronga Moore Teaney Koide Sasaki at al.
• Probe Correlations and Fluctuations

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Classic Diffusion in Rapidty
diffusion broadens rapidity density diffusion
Bjorken flow, ? ? n?
random walk in rapidity y vs. proper time ?
?V? 2D/?0
?V
diffusion coefficient D hadron formation at ?0
?/?0
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