1. Third Moments of Conserved Charges in Phase Diagram of QCD Masakiyo Kitazawa (Osaka Univ.) M. Asakawa, S. Ejiri and MK, PRL103, 262301 (2009). Baryons’10, Dec. 9, 2010, Osaka U.

2. Phase Diagram of QCD Phase Diagram of QCD T 0 Hadrons Color SC  Quark-Gluon Plasma ? RHIC, LHC lattice

3. QCD Critical Point QCD Critical Point Where is the QCD critical point? And, how many? Stephanov, ’07 MK, et al.,2002

4. QCD Critical Point QCD Critical Point Where is the QCD critical point? And, how many? Stephanov, ’07 GL analysis induced by axial anomaly Yamamoto, et al. ’06 Zhang, et al., ’09 Basler, Buballa, ’10

5. Phase Diagram of QCD Phase Diagram of QCD T 0 Hadrons Color SC  Quark-Gluon Plasma ? RHIC, LHC lattice non-uniform states? quarkyonic state? BEC/pseudogap region?

6. QCD Thermodynamics on the Lattice QCD Thermodynamics on the Lattice Phase diagram for   =0 Equation of States Hot QCD, 2009 physical?

7. Ultra-Relativistic Heavy Ion Collisions Ultra-Relativistic Heavy Ion Collisions from PHENIX collaboration Observables: collective flow photon / dilepton production rates jet / particle correlations event-by-event fluctuations and higher order moments and etc… NOTE: Experimental data @ LHC is available! ALICE, 1011.3913/3914

8. Dilepton Production Rate Dilepton Production Rate PHENIX, 2009 Most direct probes of the QGP. They are produced in all stages of time evolution. e+e+ e-e- 

9. Phase Diagram of QCD Phase Diagram of QCD T 0 Hadrons Color SC  ? RHIC, LHC lattice RHIC energy scan

10. Fluctuations at QCD Critical Point Fluctuations at QCD Critical Point 2 nd order phase transition at the CP. divergences of fluctuations of p T distribution freezeout T baryon number, proton, chage, … Stephanov, Rajagopal, Shuryak ’98,’99 baryon # susceptibility However, Region with large fluctuations may be narrow. Fluctuations may not be formed well due to critical slowing down. Fluctuations will be blurred by final state interaction.

11. (Net-)Charge Fluctuations (Net-)Charge Fluctuations D-measure: Asakawa, Heinz, Muller, ’00 Jeon, Koch, ’00 When is experimentally measured D formed? Conserved charges can remember fluctuations at early stage, if diffusions are sufficiently slow. NQNQ N Q : net charge # / N ch : total # yy hadrons:quark-gluon: D ~ 3-4 D ~ 1 large  small values of D:

12. Experimental Results for D-measure Experimental Results for D-measure RHIC results: D ~ 3 PHENIX ’02, STAR ’03 hadron gas: D ~ 3-4 free quark-gluon gas: D ~ 1 STAR, ’10

13. Experimental Results for D-measure Experimental Results for D-measure Failure of QGP formation? Is the diffusion so fast? NO! The result does not contradict these statements. Large uncertainty in N ch. Bialas(’02), Nonaka, et al.(’05) RHIC results: D ~ 3 PHENIX ’02, STAR ’03 hadron gas: D ~ 3-4 free quark-gluon gas: D ~ 1 STAR, ’10

14. Take a Derivative of  B Take a Derivative of  B  B has an edge along the phase boundary changes the sign at QCD phase boundary! m 3 (BBB) can be measured by event-by-event analysis if N B in  y is determined for each event. : third moment of fluctuations (skewness) yy NBNB

15. Impact of Negative Third Moments Impact of Negative Third Moments Once negative m 3 (BBB) is established, it is evidences that (1)  B has a peak structure in the QCD phase diagram. (2) Hot matter beyond the peak is created in the collisions. No dependence on any specific models. Just the sign! No normalization (such as by N ch ).

16. Third Moment of Electric Charge Third Moment of Electric Charge net baryon # in  y : difficult to measure net charge # in  y : measurable! Experimentally,  Q : chemical potential associated to N Q

17. Under isospin symmetry, singular @CEP isospin susceptibility (nonsingular) Hatta, Stephanov ’02 Third Moment of Electric Charge Third Moment of Electric Charge net baryon # in  y : difficult to measure net charge # in  y : measurable! Experimentally,  Q : chemical potential associated to N Q  B  I /9

18. The “Ridge” of Susceptibility The “Ridge” of Susceptibility = 0 at  B =0 (C-symmetry) m 3 (BBB) is positive for small  B (from Lattice QCD) Region with m 3 (BBB)<0 is limited near the critical point: ~  B at  B >>  QCD (since  ~  B 4 for free Fermi gas) T 

19. The “Ridge” of Susceptibility The “Ridge” of Susceptibility Analysis in NJL model: = 0 at  B =0 (C-symmetry) m 3 (BBB) is positive for small  B (from Lattice QCD) Region with m 3 (BBB)<0 is limited near the critical point: ~  B at  B >>  QCD (since  ~  B 4 for free Fermi gas) T  m 3 (BBB)<0 m 3 (QQQ)<0

20. Derivative along T Direction Derivative along T Direction Signs of m 3 (BBE) and m 3 (QQE) change at the critical point, too. T  E : total energy in a subvolume measurable experimentally

21. More Third Moments More Third Moments T  “specific heat” at constant diverges at critical point edge along phase boundary

22. More Third Moments More Third Moments Signs of these three moments change, too! T  “specific heat” at constant diverges at critical point edge along phase boundary

23. Model Analysis Model Analysis Regions with m 3 (*EE)<0 exist even on T-axis.  This behavior can be checked 2-flavor NJL; G=5.5GeV -2, m q =5.5MeV,  =631MeV on the lattice at RHIC and LHC energies

24. Trails to the Edge of Mountains Trails to the Edge of Mountains m 3 (EEE) on the T-axis Experimentally: RHIC and LHC On the lattice:

25. Trails to the Edge of Mountains Trails to the Edge of Mountains m 3 (EEE) on the T-axis Experimentally: RHIC and LHC On the lattice: Experimentally: energy scan at RHIC On the lattice: ex.) Taylor expansion Cheng, et al. ‘08 c4c4 c6c6 m 3 (QQQ), etc. at   >0

26. Summary Summary Seven third moments all change signs at QCD phase boundary near the critical point. To create a contour map of the third moments on the QCD phase diagram should be an interesting theoretical subject. m 3 (BBB), m 3 (BBE), m 3 (BEE), m 3 (EEE), m 3 (QQQ), m 3 (QQE), and m 3 (QEE) Negative moments would be measured and confirmed both in heavy-ion collisions and on the lattice. In particular, (1) m 3 (EEE) at RHIC and LHC energies, (2) m 3 (QQQ)=0 at energy scan, are interesting!

27. Proton # Skewness @STAR Proton # Skewness @STAR STAR, 1004.4959 Measurement of the skewness of proton number @STAR shows that for 19.6-200GeV.

28. Proton # Skewness @STAR Proton # Skewness @STAR Remark: Proton number, N P, is not a conserved charge. No geometrical connection b/w 2nd & 3rd moments. Measurement of the skewness of proton number @STAR shows that for 19.6-200GeV. STAR, 1004.4959

29. Higher Order Moments Higher Order Moments Ratios between higher order moments (cumulants) Higher order moments increase much faster near the CP. Ejiri, Karsch, Redlich, ’05 Gupta, ’09 Stephanov, ’09 Rajagopal, et al., ’10 RBC-Bielefeld ’09 Hadrons:1 Quarks:1/3 2 4th/2nd at  =0 reflects the charge of quasi-particles

30. Derivative along T direction Derivative along T direction simple T-derivative: E : total energy in a subvolume measurable experimentally Problem: T and  can not be determined experimentally. mixed 3 rd moments:

31. Elliptic Flow 1 Elliptic Flow 1 reaction plane beam axis x z Ｙ Elliptic flow v 2 reaction plane v 2 >0 v 2 <0

32. Quark # Scaling of v 2 Quark # Scaling of v 2 Nonaka, et al., ’03 Divide by quark number. Clear quark number scaling! How to interpret?

33. Elliptic Flow @ ALICE Elliptic Flow @ ALICE Heavy ion collisions have been performed at LHC! ALICE, 1011.3914 new data