# Presentation: 801468

## QCD Critical Point andIts Effects on Physical ObservablesSchematic Consideration

- Masayuki ASAKAWA

- Department of Physics, Osaka University

- in collaboration with C. Nonaka, B. Müller, S.A. Bass

## QCD Phase Diagram 

*T*

- B

** ****chiral symmetry breaking**
** ****confinement**

- order ?

- 1st order

- crossover

- CEP(critical end point)

- 160-190  MeV

- 5-100

- 100MeV ~ 1012 K

## 20th Anniversary of CEP in QCD

*20th Anniversary of CEP in QCD*

## Where is CEP, if any?

*Where is CEP, if any?*

## CEP = 2nd order phase transition, but...

*If expansion is adiabatic*

*There is no conservation law that slows down the change of those quantities ! *

## Furthermore...

*Furthermore,*
*    **critical slowing down limits the size of fluctuation, correlation length !*

- fluctuation ~ 

- Time Evolution along given
- isentropic trajectories (nB/s : fixed)

- Model H (Hohenberg and Halperin RMP49(77)435)

## Principles to Look for Other Observables

-  We are in need of observables that are not subject to final state interactions

- Chemical Freezeout

-  usually assumed
-      momentum independent

-  but this is not right

- chemical freezeout time:
-    pT (or yT) dependent

-  Larger pT (or yT),
-       earlier ch. freezeout

## Emission Time Distribution

*Emission Time Distribution*

- Emission Time

-  Larger yT, earlier emission

-  To minimize resonance effect,
-   yT is used instead of pT

-  No CEP effect (UrQMD)

## Principle II

**Universality**:
-       QCD CEP belongs to the same universality class as 3d Ising Model

- (*T,*****)        (*r,h*)

*QCD Critical End Point*

*3d Ising Model End Point*

*same universality class*

## What is not universal

-  Further Assumptions

-  Mapping

-  Size of Critical Region

-  No general universality
-  Lattice calculation: not yet V limit
-  Renormalization group analysis in Effective Models ?

## EOS on Ising Side

*EOS on Ising Side*

-  Critical Behavior on Ising Side

-  parametric representation

- R. Guida and J. Zinn-Justin,
- NPB486 (1997) 626

- 1st order

- cross over

- CEP

- Condition for M0 and h0

## Singular Part + Non-singular Part

*Singular Part + Non-singular Part*

-  Matched Entropy Density

-  Dimensionless Quantity: *S*c

- D: related to extent of critical region

-  Matching between Hadronic and QGP EOS

-  Entropy Density consists of *Singular* and *Non-Singular* Parts

-  Requirement:
-         reproduce both the singular behavior and know asymptotic limits

-  **Only Singular Part** shows universal behavior

## Isentropic Trajectories

-  In each volume element, Entropy (S) and Baryon Number (NB) are conserved,
-   as long as entropy production can be ignored (= when viscosities are small)

- Isentropic Trajectories (nB/s = const.)

- Near CEP s and nB changes rapidly

*isentropic trajectories show*
*non-trivial behavior*

- Bag Model EOS case

## With Large Critical Region

- without CEP (EOS in usual hydro calculation)

*Focusing of Isentropic Trajectories*

- Excluded Volume Approximation
-   + Bag Model EOS

- No Focusing

- used in most hydro calculations

## Consequence

*Consequence*

- For a given chemical freezeout point,
- prepare two isentropic trajectories:
- w/ and w/o CEP

- Along isentropic trajectory:

- As a function of pT(yT):

*Principle I*

- : near CEP steeper

## Evolution along Isentropic Trajectory

## Effect on Spectra ? 

*Effect on Spectra ? *

- NA49, PRC73, 044910(2006)

## Result of One Temperature Fit

- NA49, PRC73, 044910(2006)

## Summary

-  Two Principles:
-      i) Chemical Freezeout is pT(yT) dependent
-     ii) Isentropic Trajectory behaves non-trivially near CEP (focusing)

-  We then made a data search

- Information on the QCD critical point:
-  such as  location, size of critical region,existence...

-  still error bar is large, *finer energy scans at SPS, FAIR, RHIC*: desirable

-  Effect on Flow ?* *
-     cs changes differently from the case with EOS used in usual hydro cal.                                     (3D hydro cal. with CEP + UrQMD: C. Nonaka in progress)