QCD Phase Diagram p. 1/13 QCD Phase Diagram M. Stephanov U. of Illinois at Chicago
QCD Phase Diagram p. 2/13 QCD phase diagram (contemporary view) T, GeV QGP 0.1 crossover critical point hadron gas vacuum nuclear matter quark matter phases CFL µ B, GeV Minimal phase diagram
QCD Phase Diagram p. 3/13 QCD phase diagram (building blocks) T, GeV QGP restored chiral symmetry massless quarks 0.1 hadron gas broken chiral symmetry vacuum µ B, GeV What is the order of the transition?
QCD Phase Diagram p. 3/13 QCD phase diagram (building blocks) T, GeV tricritical point 2 massless quarks 0.1 Lattice Models nuclear matter quark matter phases µ B, GeV Note: nuclear matter is on the chirally broken side.
QCD Phase Diagram p. 3/13 QCD phase diagram (building blocks) T, GeV QGP 0.1 crossover critical point hadron gas vacuum nuclear matter quark matter phases CFL µ B, GeV Lattice: Crossover is firmly established (most recently Aoki et al) RHIC: Matter near/above crossover stongly coupled liquid. LHC will study it.
QCD Phase Diagram p. 4/13 Critical points in known liquids Critical point in many liquids (critical opalescence). Water:
QCD Phase Diagram p. 5/13 Locating the QCD critical point 200 T, MeV 150 LTE04 HB02 LTE03 LR04 00 11 LR 100 50 CO94 INJL98 LSM RM98 CJT02 3NJL05 PNJL06 NJL NJL89a NJL89b 0 0 200 400 600 80002040600 µ B, MeV
QCD Phase Diagram p. 5/13 Locating the QCD critical point 200 T, MeV 150 130 LTE04 17 HB02 LTE03 LR04 9 00 11 LR 100 50 CO94 5 INJL98 LSM RM98 2 CJT02 3NJL05 PNJL06 NJL NJL89a NJL89b 0 0 200 400 600 80002040600 µ B, MeV
QCD Phase Diagram p. 5/13 Locating the QCD critical point 200 T, MeV 150 130 LTE04 17 HB02 LTE03 LR04 9 00 11 LR 100 50 RHIC scan CO94 5 INJL98 LSM RM98 2 CJT02 3NJL05 PNJL06 NJL NJL89a NJL89b 0 0 200 400 600 80002040600 µ B, MeV Experiments can scan the phase diagram by changing s: RHIC. Signatures: event-by-event fluctuations. Susceptibilities diverge fluctuations grow towards the critical point.
QCD Phase Diagram p. 6/13 Critical point on the lattice 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 χ q T/T 0 µ q /T=0.0 µ q /T=0.5 µ q /T=1.0 0.8 1..2 1.4 1.6 1.8 2.0 Allton, et al: peak in χ B, but not in χ I Several approaches: Reweighting: Fodor-Katz 20: µ B 725 MeV 2004: µ B 360 MeV (smaller m q and larger V ) Taylor expansion: Bielefeld-Swansea (to µ 6 ) 2003: µ B 420 MeV 2005: 300 MeV µ B 500 MeV (is agreement with res. gas a problem?) Taylor expansion: Gavai-Gupta (to µ 8 ) From convergence radius: µ B 180 MeV (more precisely > 180 MeV) Imaginary µ: Philipsen-deForcrand, Lombardo, et al Sensitive to m s, perhaps µ B 300 MeV Fixed density: deforcrand, Kratochvila? (N f = 4, small volumes)
QCD Phase Diagram p. 7/13 Radius of convergence Taylor expansion can be used to find singularities the critical point. 2.5 T/T 0 SB(ρ 0 ) SB(ρ 2 ) 2 1.5 1 0.5 ρ 0 ρ 2 ρ 4 T c (µ q ) Questions: What is the temperature T E? What singularity sets µ R (T)? µ q /T 0 0 0 2 4 6 8 12 (RBC-Swansea) 1.4 1.2 T/T c Need to understand location of singularities in the complex plane near µ = 0. Use universality. In a random matrix model: 0.8 0.6 µ R 2 0.1 0.2 0.3
QCD Phase Diagram p. 8/13 Summary Phase diagram of QCD at nonzero baryon density is under active theoretical investigation: much progress in lattice calculations. Still a lot to be done to narrow down the prediction for the critical point. Agreement between different approaches must be achieved. New methods are needed. Heavy ion collision experiments can discover the critical point by observing certain non-monotonous signatures RHIC scan ( 2009) or, for higher µ B, FAIR/GSI.
Appendix QCD Phase Diagram p. 9/13
QCD Phase Diagram p. 10/13 Fodor-Katz critical point Fodor-Katz: complex singularity reaches real axis critical point 1.2 1 Splittorff hep-lat/05050: both F-K points (different m π ) lie on phase quenched transition line. Coincidence? T/T 0 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 <cos θ > T/T 0 =1.07 T/T 0 =1.00 T/T 0 =0.90 0 0 0.5 1 1.5 2 2µ/m π Ejiri hep-lat/0506023: statistical fluctuations of arg(det) cause spurious Imβ = 0 points. These fluctuations become large at the phase quenched transition line (see also Splittorff-Verbaarschot). 0 0 0.2 0.4 0.6 0.8 1 µ q /T Golterman et al hep-lat/0602026: det 1/4 is problematic at µ 0 (Svetitsky, Sharpe)
QCD Phase Diagram p. 11/13 de Forcrand-Philipsen scenario For m strange < m c (µ = 0) the transition at µ = 0 is a 1st order one (by universality argument due to Pisarski-Wilczek) Standard expectation (also in models): df-p: T, GeV m s m < m c (0) 0.1 critical point 01 01 0011 0011 000111 000000 111111 000000 111111 0000000 1111111 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 00000000 11111111 1st order 00000000 11111111 00000000 11111111 000000000 111111111 000000000 111111111 physical point 0 m ud µ B, GeV T T c df P critical pt. QGP moves in for lighter strange quark confined µ Color superconductor Many caveats (coarse lattices, small volume, etc), but: If indeed dm c (µ)/dµ 2 < 0 then critical point as a function of m strange is not continuously related to the critical point (if it exists) predicted by models. Unusual feature of the df-p critical point: the 1st order transition is on the high T side opposite to normal (e.g. Ising). Not impossible?