Mohamed Hassan Abdel-Aziz

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Mohamed Hassan Abdel-Aziz
Causal Diffusion and Survival of net charge
fluctuation

• Physics Department Wayne Sate University.
• Detroit, MI.
• USA

This work done with collaboration with Sean
Gavin
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Motivation Problem QCD phase transition in ion
collisions can produce fluctuations of charge and
net baryon number in a rapidity slice Ask Can
diffusion and expansion in hadronic phase dilute
fluctuations? Net Electric Charge are Conserved
quantities Complication classic diffusion not
causal Solution formulate causal diffusion for
RHIC collisions Grad, Comm. Pure Appl. Math. 2
(1949) 331 Israel and Stewart, Ann. Phys. (N.Y.)
118 (1979) 341 Muronga, Phys. Rev. Lett. 88,
062302 (2002)
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Dynamic Charge Fluctuations
P. G. V .
Charge variance
Statistical Fluctuation Poisson
Dynamical Fluctuations
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• Values exist all over the place.
• Bialas, phys. Lett. B
  523, 249 2002.
• S. Jeon and V.Koch,
  phys.Rev.Lett. 85 (2000) 2076.
• Dynamical model initial final
• Shuryak, Stephanov, phys.Rev. C63
  (2001) 064903
• Not causal
• Effects of charge transport between different
  rapidity regions may be present.
• None equilibrium theory does not exist yet.

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STAR experiment finds Nn -1.5 at RHIC J. Adams
et al. STAR, Phys. Rev. C bf 68, 044905 (2003).
This is close to result in M. Asakawa, U.
Heinz, B. Muller, Phys. Rev. Lett. 85,2072
(2000) S. Jeon and V. Koch,ibid, 2076 V.
Koch, M. Bleicher, S. Jeon, Nucl. Phys. A698
(2002) 261. we emphasize that those estimates
were constructed for an equilibrium resonance gas
assuming no prior plasma stage.

IS THIS TRUE??????????
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• Flow and jet quenching measurements provide
  strong indications if not proof of plasma
  formation M. Gyulassy, arXivnucl-th/0403032.
• Extraordinary charge fluctuations should be
  seen, but are not. !!!!!!!
• Net charge fluctuations from plasma
  hadronization benchmark hadronic estimates, as
  suggested by Bialas Coalescence.

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Solution

• What to do? Stochastic Causal Diffusion.
• Extension of diffusion model to have radial flow
  work in progress.
• Use stochastic technique to compute the
  fluctuations,
• N.G. Van Kampen Stochastic processed in physics
  and chemistry. 1992.
• K. M. van Vleit J. Math. Phys 12,1981(1971).
• K. M. van Vleit J. Math. Phys 12,1998(1971).

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Large Bubbles Causality Problems?

• "classic" diffusion dynamics
• random walk ??x2? ? ?t
• infinite propagation speed
• v ?x/?t ? ? as ?t ? 0
• causal alternative diffusion equation

?x
Grad Israel Stewart

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

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"hot spots" in a rapidty slice due, e.g., to a
phase transition

Expansion and diffusion distort rich "hot spots"
expansion stretches ?z ? diffusion
homogenizes ?z (D?)1/2
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Boltzmann Equation
perturbation to boltzmann equation to linear
order in perturbation
this is the key equation in deriving causal
equation
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Maxwell-Cattaneo Equation
Telegraph Equation
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Nuclear Collisions
Charges flowing with velocity u?.
Classic diffusion Causal diffusion (Grad
Israel Stewart)
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Constant D and td
Classic
Rapidity Spread vs. time t0/td
0.5,1.0, 1.5 and 2.0
Causal
Causal gave slower spread compared to
Classic Both solution approach one another for t
gtgt t0
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Effect of rarefaction
Classic
Rapidity Spread vs. time
Causal
The difference of the ratio from unity in the
long time limit reflects the fact that the
rarefaction rate t-1 and diffusion rate td-1 n
are in fixed proportion for all time
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Correlation and Diffusion
ISR and FNL data Ggaussian near mid
rapidity. Weak dependence on the (h1h2)/2.
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Survival of signals
The ratio indicates how much the fluctuations
are reduced as the width increases form s0 to sf.
We use tf / t0 1-2 fm. The difference between
Causal and classic substantial.
Rapidity dependence of dynamic charge
fluctuations assuming diffusion has increased the
width from s0 1 to sf 2 (bottom) and s0
0.25 to sf 0.5 (top).
We take D 2 fm and td 6 fm from SMN,
Europhys.Lett. 54, 38 (2001) arXivhep-ph/0007121
.
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Can diffusion help?

• QGP hadronize at t0 producing dynamic charge
  fluctuation n.
• J. K estimated Nn -3 , and also estimated the
  value for hadrons gas to be in the range -1
  -1.7
  Nucl. Phys. A698 (2002) 261.
• Hadronic diffusion , form t0 to tf freeze out
  time, can dissipate these fluctuations
  reducing n. Let see.

classic diffusion can bring Nn to this level if
the system lives as long as 20 fm, while causal
diffusion cannot.
Current estimation

• t0 9 fm , t0 / td 1.5
• D 1 and s0 0.25

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Summary

• Causal diffusion inhibits dissipation
• Net charge fluctuations induced by quark gluon
  plasma hadronization can plausibly survive
  diffusion in the hadronic stage.
• This result bolsters our optimism for
  fluctuation and correlation probes of
  hadronization and other interesting dynamics.