Fluctuations, Correlations and bound states in the QGP

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1 Fluctuations, Correlations and bound states in the QGP Introduction BS correlations Some speculations Work in collaboration with: A. Majumder and J. Randrup

2 Phase diagram Z. Fodor et al., PLB

3 Susceptibilities E = E 0 m H Q M df dh df Q = d m = Susceptibilities d2 F m= 2 dh d2 F Q = 2 d H m = m H Q = Q Linear response m 2 = m Q 2 = Q Fluctuations

4 The mother of all thermal spectra and fluctuations Fluctuations at the level of 10-5!!!

5 Heavy Ions: Event-by-Event <x2> <x> The physics is in the width E-by-E measures 2-particle correlations

6 Fluctuations in thermal system e.g. Lattice QCD Z =Tr[exp H Q Q B B S S ] X =T log Z = F X X Mean : X =Q, B, S 2 2 X 2 =T 2 2 log Z = T 2 F X X Variance: Co-Variance: X Y =T 2 Susceptibility: 2 2 log Z = T F X Y X Y XY = F = Y V X Y V X

7 Simple Observation Or how can we test the sqgp Simple QGP: strangeness is carried by strange quarks Baryon Number and Strangeness are correlated Hadron Gas: strangeness is carried mostly by mesons Baryon Number and Strangeness are uncorrelated Bound state QGP: strangeness is carried by partonic bound states Baryon Number and Strangeness should be uncorrelated

8 <BS> and the Bound State QGP Define: C BS 3 In Experiment B S 2 S C BS = 3 Uncorrelated particles: = 3 B B S S 2 S S 1 1 B S B S N eve. i i i N 2eve. i i j j 1 1 S 2i 2 S i S j N eve. i N eve. i j C BS = 3 N i S i Bi i N i S i2 i X BS BS = 3 = 3 2 X SS S

9 Canonical QGP vs. Hadron gas BS is carried by s, s Strangeness carriers s, s BS is carried by strange Baryons Strangeness carriers: Strange Baryons and Mesons B and S locked together in a QGP, But not in a hadron gas Correlation in B & S Fluctuations of S x(-3) as quarks have B=1/3, and S=-1

10 Simple estimates In a QGP phase 3 BS S 2 n n s s n In hadron gas phase n s 3 BS s S 2 0 K K K... At T=170MeV, μ=0 CBS = 1 CBS = 0.66

11 Hadron gas estimate sensitive to chemical potential and temperature. Estimate along the freeze-out line Increasing the baryon chemical potential, increases baryons. At large m S is carried by Kaons and S by and 3 CBS 3 K 2

12 The Bound State QGP Gluon-Gluon states do not contribute!

13 Heavy quark, antiquark quasiparticle have C=1 Quark-antiquark states: 8 like, 24 like (They have no Baryon number) These states have C = 0 Quark gluon states in triplet color representation 36 states, have C = 1 Quark gluon states in hexaplet color representation considered unbound at T=1.5Tc All together at T=1.5Tc, CBS = 0.61 Similar to Hadron gas estimate

14 Estimates from the Lattice T BS LogZ (T ) V m B m S m 0 BS Need off-diagonal susceptibilities s in unquenched QCD BS C BS = 3 2 = 3 S 1 u d s s 3 S2 X ss X us X ds X us X ds = = 1 X ss X ss Calculated by R.V. Gavai, S. Gupta, Phys.Rev.D66:094510,2002, But in the quenched approximation At T = 1.5 Tc Off-Diagonal susceptibilities are very small compared to diagonal susceptibilities, CBS = (3)/0.53(1)

15 Results Hadron Gas CBS = 0.66 Bound State QGP CBS = 0.62 Independent quarks CBS = 1 Lattice QCD CBS = 1

16 From C.R. Alton et. al. Phys.Rev.D71:054508,2005 Full QCD, but with 2 flavors, gives similar insight! X T, q T q q = 2 c 2 12 c 4 30 c 6 T T

17 Ratio of Susceptibilities 2 X ud X dd Tc

18 c2 Taylor expansion coefficients c4 Quasi-particle model by Bluhm et al, hep-ph/ c6

19 Correlations and Lattice (quenched) Lattice QCD: X ud = X us = X ds 0 NO cross correlations among quark flavors! quark anti-quark bound states? Strongly interacting QGP??? Why are there no correlations?

20 Some issues No statement about gluon bound states No statement about quark gluon bound states No statement about the heavy states (> 1.5 GeV) seen in correlation functions (Hatsuda et al, Karsch et al.) Susceptibilities only measure the bulk! Possibly collective modes????? (G. Brown, QM 04)

21 Ways out... As many quark-quark states as quark-antiquark states Not consistent with Shuryak model Problem with charge - baryon-number correlations Large width of bound states ~1 % correction is allowed by lattice What is a bound state with large width?

22 Charge Baryon Number Correlations C BQ = Consider: Di-quarks: Lattice: C BQ = BQ B2 2 X uu X dd X ud 1 = X uu X dd 2 X ud 2 uu, dd, 1 ud ±du BQ = N qq = N qq B2 = N qq 9 C BQ =2 NO di-quarks either!!!

23 Measuring RBS RBS can be measured in principle Advantages: Conserved quantities Heavy particles Less uncertainty due to hadronization Issues: Baryon number (neutrons) Weak decay corrections for strangeness

24 Speculations! Lattice suggests a quasi-particle picture for QGP Lattice EOS requires massive quasi-particle This suggests a repulsive mean field (~500 MeV!!!) A repulsive mean field generates flow! RHIC data possibly consistent with large viscosity Alternative: Glue has low viscosity and quarks tag along A. Peshier, B. Kampfer and G. Soff, Phys.Rev. D66:094003,2002. J. P. Blaizot, E. Iancu and A. Rebhan, Phys.Rev. D63:065003,2001.

25 No Chance for Thermal Charm B. Kaempfer, SQM 2004

26 Summary Fluctuations measure response of system BS correlation valuable diagnostic for structure of matter BS correlations impose strong limit on existence of bound states in the QCP Lattice QCD consistent with quasi-particle quarks Higher order susceptibilities need to be analyzed as well Mean field? Flow? High Viscosity??????

27 Charge Fluctuations Events

28 Fluctuations of conserved quantities Quantum numbers conserved in Heavy ion collisions: Baryon number B (exactly) Charge Q (exactly) Strangeness S (almost!) Combinations are also conserved : BS, QS, BQ etc. dn /dy } D Ycoll D Yaccept Condition for charge fluctuations: D Ytotal >> D Yaccept >> D Ycoll y