# Presentation: 698353

## Mohamed Hassan Abdel-Aziz

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

**Causal Diffusion **
**and **
**Survival of net charge fluctuation**

**This work done with collaboration  with **
**Sean Gavin**

- Hot Quarks 2004,Taos,  NM

## 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)

- Hot Quarks 2004,Taos,  NM

## Dynamic Charge Fluctuations

**Charge variance**

**Dynamical Fluctuations**

**Statistical Fluctuation**
**Poisson **

**P. G. V  .**

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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.

-                         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.

- Hot Quarks 2004,Taos,  NM

## STAR experiment finds N -1.5 at RHIC

**STAR experiment finds N******** -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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##  Net charge fluctuations from plasma hadronization ~ benchmark hadronic estimates, as suggested by Bialas  “ Coalescence”.

** ****Extraordinary charge fluctuations should be seen, but are not. !!!!!!!**
** ****Net charge fluctuations from plasma hadronization ****~**** benchmark hadronic estimates, as suggested by ***Bialas***  **_**“ Coalescence**_**”.**

- Hot Quarks 2004,Taos,  NM

## Solution

- 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).*

**Solution**

- Hot Quarks 2004,Taos,  NM

## Large Bubbles: Causality Problems?

**"classic" diffusion dynamics:**
- random walk *x**2*  *t*
- infinite propagation speed
- v = *x/**t *  as *t** * 0
**causal alternative diffusion equation**

**Grad moment method – Muronga **
**propagation speed v = ********D/********d**
**diffusion** time* ****d*
**classic** regime: ***d * 0*, **v*  

*******x***

**Grad; Israel & Stewart**

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## expansion stretches

** **

- z ~ 
- diffusion homogenizes
- z ~ (D)1/2

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

**Expansion and diffusion distort rich "hot spots"**

- Hot Quarks 2004,Taos,  NM

## Boltzmann Equation

**to linear order in perturbation**

**Boltzmann Equation**

**this is the key equation in **
**deriving causal equation**

- Hot Quarks 2004,Taos,  NM

## Maxwell-Cattaneo Equation

- Telegraph Equation

- Hot Quarks 2004,Taos,  NM

## Nuclear Collisions

- Charges flowing with velocity *u*.

- Classic diffusion:
- Causal diffusion:
- (Grad; Israel & Stewart)

- Hot Quarks 2004,Taos,  NM

## Constant D and d

**Constant D and ********d**

**Rapidity Spread vs. time**
- 0/d =0.5,1.0, 1.5 and 2.0

**Causal gave *****slower spread*****  compared to Classic**
**Both solution approach one another for** ******>> **********

**Classic **

**Causal**

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## Effect of rarefaction

**Classic **

**Causal **

**The difference of the ratio from unity in the long time limit reflects the fact that the rarefaction rate**** ********-1**** ****and diffusion rate**** ********d****-1**** ~ ******** ****are in fixed proportion for all time**

**Rapidity Spread vs. time**

- Hot Quarks 2004,Taos,  NM

## Correlation and Diffusion

**ISR and FNL data:**
**Ggaussian  near mid rapidity.**
**Weak dependence on the****  (************+************)/2.**

- Hot Quarks 2004,Taos,  NM

## Survival of signals

- The ratio indicates how much the fluctuations  are reduced as the width increases form0 to f.
- We use f / 0 ~ 1-2 fm.
- The difference between Causal and classic  substantial.

**Survival of signals**

-  Rapidity dependence of dynamic charge fluctuations assuming diffusion has increased the width from 0 = 1 to f = 2 (bottom) and 0 = 0.25 to f = 0.5 (top).

- We take D ~ 2 fm and  ******d ****~ 6** fm from
- {S&M&N, Europhys.Lett. 54, 38 (2001) [arXiv:hep-ph/0007121].}

- Hot Quarks 2004,Taos,  NM

## Can diffusion  help?

******= 1 and ********0**** ****= 0****.****25**

***classic diffusion can bring N************ to this level if the system lives as long as 20 fm, while causal diffusion cannot.***

**Can diffusion  help?**

**Current estimation**

-   QGP hadronize – at ********  producing dynamic charge fluctuation ****.
-   J. K  estimated N-3 , and also estimated  the value for hadrons gas to be in the range -1 ~ -1.7                                           *Nucl. Phys***
-   Hadronic diffusion , form ******0** to******f** freeze out time, can dissipate these fluctuations     reducing |****|. Let ’ see.

- Hot Quarks 2004,Taos,  NM

## 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.**

- Hot Quarks 2004,Taos,  NM