1. Phases of QCD
Normal points and phase transitions; types of transitions; order parameters and susceptibilities; phase diagrams; how transitions are found; uncertainties in lattice computations (1)
The QCD phase diagram: finite temperature, finite chemical potential, the full phase diagram (1)
What do we know about the properties of QCD matter? (2)

2. Lecture 2

3. Phase diagram of QCD

4. Quantitative knowledge

5. Extensions
Apart from T and , 2-flavour QCD has the coupling m (quark mass).
In a 3-dimensional phase diagrams there are surfaces of 1st order transitions and lines of 2nd order transitions. Also, special critical points called tricritical points (three phases become indistinguishable).
Example: QCD, mixture of two chemically pure substances (steel and other alloys), He3-He4 mixtures.

6. Extended QCD phase diagram

7. New dimensions
For Nf=2 one has 2 quark masses mu and md, 2 chemical potentials u and d, and 1 temperature, T.
In a 5 dimensional phase diagram there are 4-d regions of 1st order transitions, bounded by 3-d critical volumes, intersecting in 2-d tricritical surfaces, capped by tetracritical lines, ending in pentacritical points!!! Gibbs' phase rule
Hard to draw.

8. The “real world”
Quark masses are fixed in the real world, and they do not vanish
Quotes denote equal quark masses: SU(2) flavour symmetry is exact in the “real world”
Two “order parameters” : s=andp=
s looks for chiral symmetry breaking, p for flavour symmetry breaking

9. “Real world” QCD phase diagram

10. Nf=2+1
Intensive parameters are three masses, three chemical potentials and T. 7 dimensions in the phase diagram.
Gibbs' phase rule: everything up to heptacritical points!
High order multicritical points usually exist in subspaces with high symmetry. May be easy to discover them in theoretical computations. Open problem

11. Phase diagram/Flag diagram
Couplings ms, mud, and T.
A phase diagram labels phases found at each coupling
Phases coexist along surfaces, bounded by critical lines.

12. Phase diagram/Flag diagram
Projection of the phase diagram into the plane of T=0 flags the phase transitions
This is not a phase diagram, because a point on this diagram is not a single phase.
Name flag diagram

13. Phase diagram/Flag diagram
The usual flag diagram of QCD
1st order transitions in quenched QCD and for large m
1st order transition in 3 flavour QCD and nearby
No transition in our universe

14. Funny things happen

15. Phase diagram/Flag diagram
Extend the flag diagram to include B
One way to show a four dimensional phase diagram
Otherwise cut “slices” through the 4-d phase diagram and show many slices.

16. Another dimension Two O(4) critical lines, two Z(2) critical lines,
and two tricritical points organize the phase
diagram.
The light quark condensate is an order parameter
everywhere for Nf=2+1 and 3.

17. The tricritical line Standard scenario.
3C line meets =0 plane at ms3C. For ms>ms3C, the Nf=2 phase diagram is accurate. Very likely, ms3c≈QCD.
Accurate location of 3C point: future.

18. A tetracritical point?
Two 3C lines meet at a 4C point. Since this is a point of higher symmetry, in this flag diagram it can only appear on the ms=0 line.
4C point in Nf=3 is a new universality class. Can be ruled out.

19. Two tricritical lines
Alternatively, 4C point can be pulled away to infinity.
Then phase diagram is qualitatively similar to Nf=2, but quantitatively very different.
Not ruled out. Effective models?

20. Experimenal challenge
The real QCD phase diagram is 3 dimensional: T, B, Q.
The only knobs that an experiment can turn are the energy and the nucleus, ie, 2 parameter variation.
How do you explore a 3 dimensional phase space if you have control over only two parameters?

21. Summary of Lecture 2
The Nf=2 phase diagram is beginning to take shape: various points in the phase diagram are being estimated numerically. Main open problem is the continuum limit at realistic quark mass.
The global structure of the Nf=2+1 phase diagram is now known. The state of the art is rather primitive here.
The primary open problem for Nf=2+1 is the location of the tricritical strange quark mass: ms3C