Third Moments of Conserved Charges as Probes of QCD Phase Structure

1. xQCD, Bad Honnef, June 22, 2010 Third Moments of Conserved Chargesas Probes of QCD Phase Structure Masakiyo Kitazawa (Osaka Univ.) M. Asakawa, S. Ejiri and MK, PRL103, 262301 (2009).

2. Third moments of conserved charges (including skewness) would smartly do this! Phase Diagram of QCD T Quark-Gluon Plasma QCD critical point Hadrons Color SC m 0 How can we map these components of phase diagram in heavy-ion collision experiments?

3. 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. Fluctuations at QCD Critical Point Stephanov, Rajagopal, Shuryak ’98,’99 2nd order phase transition at the CP. baryon # susceptibility divergences of fluctuations of • pT distribution • freezeout T • baryon number, • proton, chage, …

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

5. 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 • Failure of QGP formation? • Is the diffusion so fast? NO!The result does not contradict these statements. Large uncertainty in Nch. Bialas(’02), Nonaka, et al.(’05)

6. Higher Order Moments Ratios between higher order moments (cumulants) RBC-Bielefeld ’09 Ejiri, Karsch, Redlich, ’05 Gupta, ’09 4th/2nd at m=0 reflects the charge of quasi-particles Quarks:1/32 Hadrons:1 Higher order moments increase much faster near the CP. Stephanov, ’09 We want much clearer signals to map the phase diagram, such as changing signs.

7. Note: : third moment of fluctuations Dy Take a Derivative of cB cB has an edge along the phase boundary changes the sign at QCD phase boundary! • m3(BBB) can be measured by event-by-event • analysis if NB in Dy is determined for each event. NB

8. No dependence on any specific models. • Just the sign! No normalization (such as by Nch). Impact of Negative Third Moments Once negative m3(BBB) is established, it is evidences that (1) cB has a peak structure in the QCD phase diagram. (2) Hot matter beyond the peak is created in the collisions.

9. mQ : chemical potential associated to NQ Third Moment of Electric Charge Experimentally, • net baryon # in Dy : difficult to measure • net charge # in Dy : measurable!

10. mQ : chemical potential associated to NQ Third Moment of Electric Charge Experimentally, • net baryon # in Dy : difficult to measure • net charge # in Dy : measurable! cB cI/9 Under isospin symmetry, isospin susceptibility (nonsingular) singular @CEP Hatta, Stephanov ’02

11. The Ridge of Susceptibility Region with m3(BBB)<0 is limited near the critical point: = 0 at mB=0 (C-symmetry) m3(BBB) is positive for small mB (from Lattice QCD) ~ mB at mB>>LQCD (since W~mB4 for free Fermi gas) T m

12. m3(BBB)<0 m3(QQQ)<0 The Ridge of Susceptibility Region with m3(BBB)<0 is limited near the critical point: = 0 at mB=0 (C-symmetry) m3(BBB) is positive for small mB (from Lattice QCD) ~ mB at mB>>LQCD (since W~mB4 for free Fermi gas) Analysis in NJL model: T m

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

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

15. E : total energy in a subvolume measurable experimentally Signs of m3(BBE) and m3(QQE) change at the critical point, too. Derivative along T Direction T m

16. “specific heat” at constant • diverges at critical point • edge along phase boundary More Third Moments T m

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

18. 2-flavor NJL; G=5.5GeV-2, mq=5.5MeV, L=631MeV Model Analysis • Regions with m3(*EE)<0 exist even on T-axis. •  This behavior can be checked • on the lattice • at RHIC and LHC energies

19. Trails to the Edge of Mountains m3(EEE) on the T-axis • Experimentally: RHIC and LHC • On the lattice:

20. c4 c6 Cheng, et al. ‘08 Trails to the Edge of Mountains m3(EEE) on the T-axis • Experimentally: RHIC and LHC • On the lattice: m3(QQQ), etc. at mB>0 • Experimentally: energy scan at RHIC • On the lattice: ex.) Taylor expansion

21. Summary 1 Seven third moments m3(BBB), m3(BBE), m3(BEE), m3(EEE), m3(QQQ), m3(QQE), and m3(QEE) 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. Negative moments would be measured and confirmed both in heavy-ion collisions and on the lattice. In particular, (1)m3(EEE) at RHIC and LHC energies, (2)m3 (QQQ)=0 at energy scan, are interesting!

22. Critial Point Let’s go see the scenery over the ridge! But, do not forget to first draw a map for a safe expedition. Summary 2 Loreley, photo by MK, 2005

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

24. Further Possibility • If measured moments originate from a narrow • region in the T-m plane, and • if experimental resolution is sufficiently fine, This formula is used to determine m/T experimentally. lattice exp. exp. Moreover, third moments provide the divergence vector of c and Cm . These information may enable us to pin down the initial state of fireballs.

25. Loreley