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in collaboration with C. Nonaka, B. M ü ller, and S.A. Bass

New Ways to Look for the Critical Point and Phase Transition. Masayuki Asakawa. Department of Physics, Osaka University. in collaboration with C. Nonaka, B. M ü ller, and S.A. Bass S. Ejiri and M. Kitazawa. QCD Phase Diagram. LHC. RHIC.

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in collaboration with C. Nonaka, B. M ü ller, and S.A. Bass

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  1. New Ways to Look for the Critical Point and Phase Transition Masayuki Asakawa Department of Physics, Osaka University in collaboration with C. Nonaka, B. Müller, and S.A. Bass S. Ejiri and M. Kitazawa

  2. QCD Phase Diagram LHC RHIC QGP(quark-gluon plasma) Hadron Phase CSC (color superconductivity) T CEP(critical end point) 160-190 MeV crossover 1st order order ? • chiral symmetry breaking • confinement mB 5-10r0

  3. Punchlines: Quantities to Look at • Conserved Quantities unlike correlation lengths, (usual) fluctuations...etc. • Quantities not subject to Critical Slowing Down and Final State Interactions • Quantities sensitive to CEP or Phase Transition Question What to see? How to see?

  4. CEP = 2nd order phase transition, but... Divergence of Fluctuation Correlation Length Specific Heat ? Critical Opalescence? CEP = 2nd Order Phase Transition Point 2SC CFL even if the system goes right through the critical end point… Subject to Final State Interactions If expansion is adiabatic AND no final state int.

  5. Critical Slowing Down and Final State Int. x and xeq big difference almost no enhancement 1-dim Bjorken Flow Nonaka and M.A. (2004) Furthermore, critical slowing down limits the size of fluctuation, correlation length ! Time Evolution along given isentropic trajectories (nB/s : fixed) Model H (Hohenberg and Halperin RMP49(77)435)

  6. Locally Conserved Charges FluctuationsofLocally ConservedQuantities • only ~ 1/2 of d.o.f., i.e. • quarks and anti-quarks • carry electric charge • Net Electric Charge • Net Baryon Number • Net Electric Charge • Net Strangeness • Energy ... Hadron Gas Phase • ~2/3 of hadrons carry • electric charge QGP Phase Heinz, Müller, and M.A., PRL (2000) Also, Jeon and Koch, PRL (2000)

  7. Charge Fluctuation at RHIC (STAR) (PHENIX) • D-measure Predictions QGP phase Hadron phase ( : hadron resonance gas) Experimental Value Well-Explained by Quark Recombination Białas, PLB(2002) Nonaka, Müller, Bass, M.A., PRC (2005)

  8. Odd Power Fluctuation Moments even power • Usually fluctuations such as have been considered : positive definite • Usual Fluctuations such as • In general, do not vanish (exception, ) We are in need of observables that are not subject to final state interactions • Fluctuation of Conserved Charges: not subject to final state interactions One of exceptions: Stephanov (2008) in conjunction with CEP Absolute values carry information of states Asakawa, Heinz, Müller, Jeon, Koch On the other hand, • Odd power fluctuations : NOT positive definite • Sign also carry information of states

  9. Physical Meaning of 3rd Fluc. Moment cB : Baryon number susceptibility in general, has a peak along phase transition changes the sign at QCD phase boundary ! • In the Language of fluctuation moments: more information than usual fluctuation

  10. (Hopefully) More Easily Measured Moments • Third Moment of Electric Charge Fluctuation cB cI/9 singular @CEP iso-vectorsusceptibility nonsingular when Isospin-symm. Hatta and Stephanov 2002

  11. Mixed Moments • Energy is also a conserved charge • and mesurable ! T m E: total energy in a subvolume Regions with Negative fluctuation moments • Result with the standard • NJL parameters (Nf=2)

  12. More and More 3rd Moments These quantities are expressed concisely as derivatives of “specific heat” at constant “specific heat” at constant T m • diverges at critical end point • peaks on phase transition line

  13. Comparison of Various Moments 2-flavor NJL with standard parameters Far Side G=5.5GeV-2 mq=5.5MeV L=631MeV Near Side • Different moments have different regions with negative moments By comparing the signs of various moments, possible to pin down the origin of moments • Negative m3(EEE) region extends to T-axis (in this particular model) • Sign of m3(EEE) may be used to estimate heat conductivity

  14. Principles to Look for Other Observables After Freezeout, no effect of final state interactions Principle I 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 bT) dependent • Larger pT (or bT), earlier ch. freezeout

  15. Emission Time Distribution Emission Time • Larger bT, earlier emission • No CEP effect (UrQMD)

  16. Principle II Universality: QCD CEP belongs to the same universality class as 3d Ising Model h : external magnetic field same universality class QCD Critical End Point 3d Ising Model End Point (T,mB) (r,h) • Further Assumptions • Size of Critical Region • No general universality • Lattice calculation: not yet V limit • Effective Model Results ? need to be treated as an input, at the moment

  17. Singular Part + Non-singular Part crit Hadron Phase (excluded volume model) Bcrit QGP phase • Matching between Hadronic and QGP EOS • Entropy Density consists of Singular and Non-Singular Parts • Only Singular Part shows universal behavior • Requirement: reproduce both the singular behavior and known asymptotic limits • Matched Entropy Density • Dimensionless Quantity: Sc D: related to extent of critical region

  18. Isentropic Trajectories An Example • 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 change rapidly isentropic trajectories show non-trivial behavior CEP Bag Model EOS case

  19. Consequence For a given chemical freezeout point, prepare three isentropic trajectories: w/ and w/o CEP Along isentropic trajectory: • FO, CO • QCP Principle I As a function of pT(bT): • FO, CO • QCP Bag Model EOS (w/o CEP, usual hydro input) ratio : near CEP steeper

  20. Evolution along Isentropic Trajectory As a function of pT(bT): • FO, CO • QCP with CEP steeper spectra at high PT

  21. Summary Usual observables such as large fluctuation, critical opalescence, ...etc. do not work • Ratio : Two Principles ratio behaves non-monotonously near CEP • Final State Interaction and Critical Slowing Down • Conserved Charges and Higher Moments: i) Third Fluctuation Moments of Conserved Charges take negative values in regions on the FAR SIDE of Phase Transition (more information!) ii) Different Moments have different regions with negative moments By comparing different moments, possible to pin down the origin of hot matter, get an idea about heat conductivity...etc. i) Chemical Freezeout is pT(bT) dependent ii) Isentropic Trajectory behaves non-trivially near CEP (focusing) Information on the QCD critical point: such as location, size of critical region, existence...

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