Phase diagram of QCD: the critical point

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1 Phase diagram of QCD: the critical point p. 1/1 Phase diagram of QCD: the critical point M. Stephanov U. of Illinois at Chicago

2 Phase diagram of QCD: the critical point p. 2/1 Phase Diagram of QCD Basic arguments, quark confinement and asymptotic freedom, predict a transition at T Λ QCD, µ B N color Λ QCD : Hadron/resonance gas (π,n, resonances) becomes a (color) plasma of quarks and gluons (Λ QCD (hadron size) 1 ). Simple arguments lead to the sketch: T, GeV r 1/T 0 Quark Gluon Plasma K T U α s /r U/K α s 1 Asymptotic freedom 0.1 hadron gas vacuum 0 1 K µ r 1/µ 0 quark (Fermi gas) µ B, GeV Order of transition? Originally, arguments suggested 1st order (discontinuous): e.g., S QGP N 2 color, while S HG N 0 color.

3 Lattice says: crossover (at µ = 0) Phase diagram of QCD: the critical point p. 3/1 Earliest: Columbia group, PRL 65(1990)2491 Recent: Wuppertal-Budapest group, Nature 443(2006)675. Wuppertal-Budapest: 20 RBC-BI: Tr 0 s SB /T s/t p4: N τ =4 6 asqtad: N τ =6 the peak should have grown 8 for 1st order transition 0 T [MeV] Entropy/T 3 # of d.o.f. grows (color is liberated) but no discontinuity Quarks are important: w.o. them the transition is 1st order.

4 Phase diagram of QCD: the critical point p. 4/1 QCD phase diagram (contemporary view) T, GeV QGP 0.1 crossover critical point hadron gas vacuum nuclear quark phases CFL 0 1 µ B, GeV Models (and lattice) suggest the transition becomes 1st order at some µ B.

5 Phase diagram of QCD: the critical point p. 4/1 QCD phase diagram (contemporary view) T, GeV QGP 0.1 crossover ESQGP critical point hadron gas vacuum nuclear quarkcolor superconductivity phases CFL 0 1 µ B, GeV Models (and lattice) suggest the transition becomes 1st order at some µ B. Color superconductivity shapes the landscape at low T, large µ B. CFL is the ice of QCD.

6 Phase diagram of QCD: the critical point p. 4/1 QCD phase diagram (contemporary view) 0.1 T, GeV Lattice simulations crossover ESQGP critical point hadron gas QGP Models vacuum nuclear Empirical quarkcolor superconductivity phases CFL α s 1 0 nuclear physics 1 µ B, GeV Models (and lattice) suggest the transition becomes 1st order at some µ B. Color superconductivity shapes the landscape at low T, large µ B. CFL is the ice of QCD. More structure possible/expected. Quarkyonic phase, crystals, critical points, etc.

7 Phase diagram of QCD: the critical point p. 4/1 QCD phase diagram (contemporary view) 0.1 T, GeV Lattice simulations crossover ESQGP critical point Heavy ion collisions hadron gas QGP Models vacuum nuclear Empirical quarkcolor superconductivity phases CFL α s 1 neutron stars, quark stars 0 nuclear physics 1 µ B, GeV Models (and lattice) suggest the transition becomes 1st order at some µ B. Color superconductivity shapes the landscape at low T, large µ B. CFL is the ice of QCD. More structure possible/expected. Quarkyonic phase, crystals, critical points, etc.

8 Phase diagram of QCD: the critical point p. 5/1 QCD critical point T, GeV QGP 0.1 crossover critical point hadron gas vacuum nuclear quark phases CFL 0 1 µ B, GeV

9 Phase diagram of QCD: the critical point p. 6/1 Water Critical point is a common feature of liquids

10 Phase diagram of QCD: the critical point p. 7/ It took a century to explain the phenomenon of critical opalescence divergent ξ of density fluctuations (Smoluchowski). And another 1/2 century to describe critical phenomena quantitatively scaling, universality, RG (Landau-Kadanoff-Wilson).

11 Phase diagram of QCD: the critical point p. 8/1 Can we discover the QCD critical point? 200 T, MeV µ B, MeV Freezeout conditions (T,µ B ) depend on s (GeV) What is special about the critical point? It is a point where the thermodynamic functions are singular Signatures: fluctuations րց near the point non-monotonically vs s.

12 Phase diagram of QCD: the critical point p. 8/1 Can we discover the QCD critical point? 200 T, MeV LTE04 LTE08 17 LR04 9 LTE03 LR µ B, MeV The lattice has a sign problem to deal with traditional Monte Carlo does not work. Clever methods to circumvent this problem: e.g., reweighting, Taylor expansion in µ B, imaginary µ B, etc.

13 Phase diagram of QCD: the critical point p. 8/1 Can we discover the QCD critical point? 200 T, MeV LTE04 LTE08 17 LR04 9 RHIC scan LTE03 LR µ B, MeV What do we need to discover the critical point: Experiments: RHIC, NA61(SHINE), FAIR/GSI Improve lattice predictions (both algorithm and CPU), understand systematic errors. Understand critical phenomena in the dynamical environment of a h.i.c., develop better signatures

14 Phase diagram of QCD: the critical point p. 9/1 Fluctuation signatures of the QCD critical point Experiments measure for each event: multiplicities N π, N p,..., momenta p, etc. These quantities fluctuate event-by-event. What is the magnitude of these fluctuations near the c.p.? (Rajagopal, Shuryak, M.S.) Events M(p T ) (GeV/c) Universality tells how it grows at the critical point: (δn) 2 ξ 2. Correlation length is a universal measure of the distance from the c.p. It diverges as ξ ( µ) 2/5, or ( T) 2/5 as the c.p. is approached Shape of the fluctuations can be also measured and it has even stronger dependence on ξ (arxiv: ): (δn) 3 ξ 4.5, (δn) 4 3 (δn) 2 2 ξ 7 These moments of the event-by-event distribution measure deviations from Gaussian shape. As ξ the distribution becomes more non-gaussian.

15 Phase diagram of QCD: the critical point p. 10/1 Scan T crossover ( λ 3 = 0) critical point 1st order freeze-out point with maxξ freeze-out vs points s contours of equal ξ µ B

16 Phase diagram of QCD: the critical point p. 11/1 Concluding remarks Phase diagram of QCD is full of puzzles and surprises. The location of the critical point is one of the central unknowns of the QCD phase diagram. Its discovery will transform the phase diagram from theoretical conjecture to solid knowledge. The lattice and experiment each have their own challenges. Which approach will be faster in overcoming them?