# Presentation: 205898

## Quantum Opacity, RHIC HBT Puzzle, and the Chiral Phase Transition 

**RHIC Physics, HBT  and RHIC HBT Puzzle**
**Quantum mech. treatment of optical potential, U (Chiral symmetry)** , DWEF
**Reproducing ****π**** ****data**
**Summary, future plans**** **
**     ****Phys.Rev.Lett.94:102302,2005**     **and J.Phys.G34:703-740,2007**

**Gerald Miller and John Cramer, UW**

## The RHIC HBT Puzzle 

**Pratt’s talk- can’t fit entropy**
**and HBT radii with same model**
**Hydrodynamics works**
**BUT NOT FOR HBT**

**p****1**

**p****2**

**p****2**

- +

**p****2**

**p****1**

**q**

**Quantum mechanical interference-space time**
**separation of source**** **

**q=p****1****-p****2**

**K=(p****1****+p****2****)/2**

**C(q,K) ************p****1****,p****2****)**** ************p****1********p****2****))-1 ****~**
** ****λ****(1-q****2****L**** R****2****L****-q****2****S**** R****2****S ****–q****2****O**** R****2****O  ****)**

_**HBT- 2 particle interferometry**_

**Hydrodynamics predicts big R****O****/R****S,**
**Data R****O****/R****S **** about 1 ****HBT puzzle**

## Old Formalism

-  source current density =J

****

**Chaotic sources, Shuryak ‘74**

- S0~<J  J*>

**σ****(p****1****)**

## Source Properties “Hydro-Inspired” Emission Function

**(Bose-Einstein thermal function)**

**(medium density)**

**(Space-time function)**

- includes radial flow

## Formalism

**Pions interact**** U ****with dense medium**

****

**is distorted (not plane) wave**

- Gyulassy et al ‘79

**DWEF- distorted wave emission function**

**U - ******** self energy**

- U :phenomenological-not from equil. thermo, J

## Wave Equation Solutions

**Matter is infinitely long Bjorken tube and azimuthal symmetry,   wave functions  factorize:  ****3D ********2D(distorted)********1D(plane)**

- We solve the reduced Klein-Gordon wave equation for ****p**:

**U time independent, cylindrical, Partial wave expansion ****!**** ordinary diff eq**

##  Meaning of U

**Im (U) : Opacity**,  **Re (U) :Refraction**

**pions lose energy and flux**

**Re(U) must exist. Next:**
**very strong attraction**
**chiral  phase transition **

## Chiral Symmetry, Son & Stephanov  2002

**v****2****, v****2****  m****2************approach ******** near  T = T****c**

**Both terms of U are negative (attractive)**

- =ω2-m2π

## Overview

- Pions   emitted  anywhere, any time,  not only at freeze-out surface
- Pions interact with the  surroundings during escape .* *
*These interactions  not included in the source function S- *
*No relation between U and S*
*Quarks, gluons are the dominant  source of the pions, but not the cause of  U*
* **Im [U] accounts for opacity*
***Re[U]*** must exist, causes refraction, acts  as ***mass-change*** of pions due to chiral-symmetry breaking as they pass from the hot, dense collision medium [m()0]) to the outside vacuum [m()140 MeV].
***Relativistic quantum mechanics*** , solve pion wave equation with partial wave expansion. * *

## Time-Independence,Resonances, and Freeze-Out

** ****Use of a time-independent phenomenological optical potential does *****not***** invoke the mean field approximation and represents an average over a duration  ******
** ****The effects of the optical potential disappear as the system decays.**
**  ****The optical potential also includes the effects of resonances, including the heavy ones.  **
**  ****Heavy resonances decay into ****π****’s**** outside of the plasma. We account for this by computing only that part of the spectra that is related to the pions in the HBT correlation function**
**λ**** parameter accounts for these**

## Recent Corrections

- We discovered in November a convergence vs. integration step size problem in our calculation of optical model wave functions.  This had no effect on the HBT radii, but had a strong effect on the ***slope of the spectrum***.  This problem was corrected by changing from Runge-Kutta to Numerov wave function solutions.
- We discovered in March that the effects of the strong chemical potential was being applied to the spectrum, but ***not*** to the HBT radii.  This error was corrected. M. Luzum (UW)
- The net result, after refitting, is that the “ambiguities” mentioned previously are gone, and the emission temperature of the model has dropped from T=193 MeV to T=161 MeV.  The need for a very deep and absorptive optical potential remains.
- Result:  ***The New Improved DWEF Model (DWEF v.2.1).***

## Fit STAR Data

**6  source, 3 optical potential parameters**
**Fit central STAR data at ********s****NN****=200 GeV**
**T=160 MeV,  ****μ****π**** =pion mass**
**reproduce R****o****,  R****s****,  R****l**
**reproduce dN************dy (both *****magnitude***** and shape) **
**8 momentum values  (i.e., 32 data points)**
- Correct spectrum for contribution of resonances
- decaying  outside the target

## DWEF Fits toSTAR 200 GeV Pion HBT Radii

**DWEF Fits to****STAR 200 GeV Pion HBT Radii**

**K****T**** (MeV/c)**

**R****O****(fm)**

**R****S****(fm)**

**K****T**** (MeV/c)**

**R****L****(fm)**

**R****O****/R****S**

**K****T**** (MeV/c)**

**K****T**** (MeV/c)**

-  Temperature is about 160 MeV

## Components of DWEF Calculations

**Components of DWEF Calculations**

**Red Solid****           -  Full DWEF****Yellow Dots****         -  Plane wave (U=0, no flow)****Green Short Dash ****-  Re( p^2 term) only, no flow****Aqua Long Dash  ****  -  Im(p^2 term) only, no flow****Cyan Dot Dash****     -  Re(Const term) only, no flow****Blue 2-Dot Dash****   -  Flow only, U=0****Violet 3-Dot Dash****  -  DWEF with no BE correction **

**K****T**** (MeV/c)**

**K****T**** (MeV/c)**

**R****O****(fm)**

**R****S****(fm)**

**K****T**** (MeV/c)**

**Spectrum**
**dN********2****/2********M****T****dM****T****dy**

## DWEF Fit toSTAR 200 GeV Pion Spectrum

**DWEF Fit to****STAR 200 GeV Pion Spectrum**

- _Note:_  accurate predictionof ***spectrum slope*** involvessubtle cancellations among wavefunctions

**K****T**** (MeV/c)**

**Spectrum**
**dN********2****/2********M****T****dM****T****dy**

## Meaning of the Parameters

**Temperature: 160 MeV **
**Transverse flow rapidity: 1.2 ******** ****v****max****=0.83 c, v****av****=0.6 c**
**Pion emission between 6.2 fm/c and 11 fm/c ********soft EOS .**
**WS radius: 12  fm = R (Au) + 4.4 fm  > R @ SPS**
**Re(U):  0.5 + 0.85 p****2**** ************deep well ********strong attraction size consistent with chiral phase transition ****(.49 +1 p****2****).**
**Im(U):  0.13 p****2**** ********mfp ********8 fm @ K****T****=1 fm****-1 ********strong  absorption ******** high density**
**Pion chemical potential: ************= mass(********)**** **

## Optical Wave Functions [||2(b)]

**Optical Wave Functions**** [|********|****2********(b)]**

**K****T ****=****250 MeV/c**

**K****T ****=****600 MeV/c**

**K****T ****=****100 MeV/c**

**Eikonal**
**Approx.**

**DWEF**

## Centrality: 200 GeV Au+Au

_**Centrality:**_** 200 GeV Au+Au**

**R****O****(fm)**
- Au+Au Fit

**Au+Au Predictions**

**R****L****(fm)**Au+Au Fit

**Au+Au Predictions**

**R****S****(fm)**Au+Au Fit

**Au+Au Predictions**

- Space-time parameters RWS, aWS, are scaled by participant number.  Emission duration **** is constant.

**K****T**** (MeV/c)**

**K****T**** (MeV/c)**

**K****T**** (MeV/c)**

## Centrality: 200 GeV Cu+Cu

_**Centrality:**_** 200 GeV Cu+Cu**

**Cu+Cu Predictions**

**Cu+Cu Predictions**

**Cu+Cu Predictions**

- Space-time parameters RWS, aWS, are scaled by participant number.  Emission duration **** is scaled as A1/3.

**R****O****(fm)**
- Au+Au Fit

**R****S****(fm)**
- Au+Au Fit

**R****L****(fm)**
- Au+Au Fit

**K****T**** (MeV/c)**

**K****T**** (MeV/c)**

**K****T**** (MeV/c)**

## Low pT Behavior:Ramsauer Resonances in Well

**Low p****T**** Behavior:****Ramsauer Resonances in Well**

**K****T**** (MeV/c)**

**Phobos 0-6%**

**K****T**** (MeV/c)**

**R****O**** (fm)**

**R****S**** (fm)**

**R****L**** (fm)**

**Spectrum**
**dN********2****/2********M****T****dM****T****dy**

## Summary and Plans

- Quantum mechanical treatment of opacity and refraction
- Excellent fits- many parameters
- Parameters of U consistent with chiral phase transition, but no relation between U and S implemented
-  Other tests needed-
-          lower energy data –John
- 	 	 v2  Matt Luzum, UW