Phase Diagram of QCD - U of T Physicscolloq/Talk1/Presentation1.pdf · Phase Diagram of QCD –...

Phase Diagram of QCD

M. Stephanov

U. of Illinois at Chicago

Phase Diagram of QCD – p.1/16

QCD – the theory of strong interactionsHadrons: protons, neutrons, π-ons, resonances, strange hadrons, etc.



FLAVOR: Flavor symmetry (e.g., p and n, or π0 and π+).“Periodic table” of hadrons from a small number of quarks – u, d, s, . . .(only 6 flavors are needed for all known hadrons, and only 2 are needed forp ∼ uud, n ∼ udd, π ∼ qq).



FLAVOR: Flavor symmetry (e.g., p and n, or π0 and π+).“Periodic table” of hadrons from a small number of quarks – u, d, s, . . .(only 6 flavors are needed for all known hadrons, and only 2 are needed forp ∼ uud, n ∼ udd, π ∼ qq).COLOR: Each quark should be able to take on one of 3 “colors”.Changing flavor of quarks (e.g., u → d) gives another hadron. Butchanging color has no observable consequence(“hidden” symmetry). Why? quark

COLORFLAVORSPIN




COLORFLAVORSPIN

PARTONS Deep-inelastic (e.g., e + p) scattering: shows proton has a simplestructure — pointlike constituents, which do not “feel” each other. Quarks?




COLORFLAVORSPIN


What force holds quarks together in hadrons? It weakens if the interaction isbrief or if quarks are close to each other (r Rproton ∼ 10−13 cm ≡ 1 fermi).

αstrong(r) =Fr2

~c

r→0→ 0

Compare to E.M.: α = 1/137 (and only grows as r → 0).In contrast αstrong(1fermi) ∼ 1 and → 0 as r → 0.




COLORFLAVORSPIN


What force holds quarks together in hadrons? It weakens if the interaction isbrief or if quarks are close to each other (r Rproton ∼ 10−13 cm ≡ 1 fermi).

αstrong(r) =Fr2

~c

r→0→ 0 ASYMPTOTIC FREEDOM

Compare to E.M.: α = 1/137 (and only grows as r → 0).In contrast αstrong(1fermi) ∼ 1 and → 0 as r → 0.


QCD – asymptotically free field theory

Only one such class of theories: Non-abelian gauge theories. (QED isabelian gauge theory.)

Bonus: it involves a hidden symmetry (in QED – U(1) – phase rotation).In QCD it is the color symmetry – SU(3).

QCD is a quantum field theory:

S =

∫

d4x

Nf∑

f=1

qf

(

i/∂ + g /A − mf

)

qf − 1

2Tr FµνF µν

;

Predictive power


QCD thermodynamicsApplications:

Neutron stars (large density, low T )Heavy-ion collisions (large T , large density)

QCD allows first principle calculations


QCD thermodynamicsApplications:

Neutron stars (large density, low T )Heavy-ion collisions (large T , large density)

QCD allows first principle calculations

Questions: phases, phase diagram, as function of T , µB , . . .

Early expectations ⇒

Natural scale:

kT ∼ ~c

1fm2= 0.2 GeV.

(T ∼ 1012K)

or

ρB ∼ 1fm−3.

, GeVµB

T

0 1

QGP

0.1

, GeV

quark matter

dilute hadron gas

vacuum

Asymptotic freedom

r ∼ 1/T → 0

r ∼ 1/µ → 0

(Fermi gas)

U/K ∼ αs 1

K ∼ T

K ∼ µ

U ∼ αs/r


Contemporary view

, GeVµB

T, GeV

10

nuclear

0.1

CFL

QGP

E

criticalpoint

vacuum matter quark matter quark matter

“Minimal” phase diagram


Contemporary view

, GeVµB

T, GeV

10

0.1

E

criticalpoint

nuclearvacuum quark matter quark matterCFL

QGP

matter

Latticesimulations

Empiricalnuclear physics

Only models

αs 1



Contemporary view

, GeVµB

T, GeV

10

0.1

E

criticalpoint

nuclearvacuum quark matter quark matterCFL

QGP

matter

Latticesimulations

Empiricalnuclear physics

Only models

neutron stars, quark stars

Heavy ion collisions

αs 1



Role of chiral symmetry (mq = 0)

q ≡(

u

d

)

Chiral:(

uL

dL

)

→ e+iα·τ

(

uL

dL

)

,(

uR

dR

)

→ e−iα·τ

(

uR

dR

)



q ≡(

u

d

)

Chiral:(

uL

dL

)

→ e+iα·τ

(

uL

dL

)

,(

uR

dR

)

→ e−iα·τ

(

uR

dR

)

Order parameter:〈qq〉 = 〈q†LqR + h.c.〉

non-zero in one phase (in vacuum),

exactly zero in another phase — protected by sym-metry!

Compare ferromagnet : for T < Tc 〈M〉 6= 0, while for T > Tc 〈M〉 = 0.



q ≡(

u

d

)

Chiral:(

uL

dL

)

→ e+iα·τ

(

uL

dL

)

,(

uR

dR

)

→ e−iα·τ

(

uR

dR

)

Order parameter:〈qq〉 = 〈q†LqR + h.c.〉

non-zero in one phase (in vacuum),

exactly zero in another phase — protected by sym-metry!

Compare ferromagnet : for T < Tc 〈M〉 6= 0, while for T > Tc 〈M〉 = 0.This requires singularity ≡ phase transition

T, GeV

, GeV10

nuclearmattervacuum

hot QGP

µB

0.1

cold quark matter

qm = 02nd order (lattice MC)

3cr. point

1st order (models: MIT bag, NJL, RM, ...)


mq 6= 0

Compare ferromagnetat H 6= 0:

<M>

TTc

H = 0

H = 0

no phase transition, butcrossover

T, GeV

, GeV10

nuclearmattervacuum

hot QGP

µB

0.1

cold quark matter

qm = 0

cr. pointcrossover


mq 6= 0


<M>

TTc

H = 0

H = 0


T, GeV

, GeV10

nuclearmattervacuum

hot QGP

µB

0.1

cold quark matter

qm = 0

cr. pointcrossover

Why all phases (can be) connected? Because @ order parameters:no chiral symmetry (mq 6= 0);. . .No phase boundary does not mean same physics, of course – (comparewater-vapor, gas-plasma, . . . ) Critical point in many liquids – criticalopalescence


mq 6= 0


<M>

TTc

H = 0

H = 0


T, GeV

, GeV10

nuclearmattervacuum

hot QGP

µB

0.1

cold quark matter

qm = 0

cr. pointcrossover

0.0

0.2

0.4

0.6

0.8

1.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0

T/Tc

p/pSB

3 flavour2 flavour

2+1 flavour

(Bielefeld group, lattice Monte Carlo)



, GeVµB

T, GeV

10

nuclear

0.1

CFL

QGP

E

criticalpoint



Large µ, color superconductivity and CFL

Asymptotic freedom ⇒ αs(µ) → 0.

Quarks of “different color” (color antisymmetricstate) attract. Fermi sphere is unstable towardscondensation of quark pairs (Cooper).

filledfilledp

s

−p

−sThe simplest and favorable is (for 2 flavors) uRdR.

Does not break chiral symmetry(unlike qq = q†LqR + h.c.).





filledfilledp

s

−p



However, for 3 flavors, analogous SU(3)chiral is broken.X = uRdR + sRuR + dRsR is not flavor singlet.





filledfilledp

s

−p



However, for 3 flavors, analogous SU(3)chiral is broken.X = uRdR + sRuR + dRsR is not flavor singlet.

But flavor transformation on X can be undone by a color transformation,which is “invisible”. However, there is also Y = uLdL + . . ., and although itcan also be undone by a color rotation...

the simultaneous transformations of qL and qR do change the ground state ifthey are not equal. This is the broken chiral symmetry.

Ground state locks color and flavor: CFL (Alford, Rajagopal, Wilczek)Phase Diagram of QCD – p.9/16


, GeVµB

T, GeV

10

nuclear

0.1

CFL

QGP

E

criticalpoint



Location of the CP (theory)

NJL

CJT

RM

CO

T

µB

LTELR-1

LR-2

HB

NJL-2

NJL-1

LSM

NJL-inst

0

50

100

150

200

0 200 400 600 800 1000 1200 1400 1600


Event


Heavy-ion collisions and the phase diagram

(from Braun-Munzinger, Redlich,Stachel)

10-1

1

10

10 2

10 3

10-1

1 10 102

Multiplicity (model)

Mul

tiplic

ity (

data

)

SpS Pb+Pb collisions 158A GeV

T=157.8±1.9 MeV

µB=247.4±7.7 MeV

γs=0.843±0.033

χ2=16.9/9 dof

πBK+

K0

K-

Λ

φΛ–

Ξ-

Ξ–+Ω-

Ω–+

Λ(1520)

π+ π- K+ K- K0 Λ Λ* φ Ξ- Ξ–+

Λ–

Ω- Ω–+

B

Res

idua

ls

-5

0

5

(from Becattini et al)


Locating the QCD critical point experimentally

NJL

CJT

RM

CO

T

µB

LTELR-1

LR-2

HB

NJL-2

NJL-1

LSM

NJL-inst

0

50

100

150

200

0 200 400 600 800 1000 1200 1400 1600

Energy scan.

Signatures: event-by-event fluctuations.

Susceptibilities diverge ⇒ fluctuations grow towards the critical point.


Data (example):pT fluctuations (CERES)

(GeV)NNs10 10

2

(%

)T

pΣ

-0.5

0

0.5

1

1.5

2

(MeV)Bµ50100200300400500 25

CERES, present dataSTARRQMD

UrQMD

Near the critical point (for CERES ac-ceptance):

∼ 2% ×(

G

300 MeV

)2 (

ξσ

3 fm

)2

(ξσ = 1/mσ)

Signal one is looking for:non-monotonic dependence on

√s.


Summary and conclusions

Phase diagram of QCD is a challenging, long-standing problem.

αs 1 calculations can address regions of T , µ 1 fm−1. Many interestingphenomena.

The most interesting region is still out of reach of controllable calculations.

Existence of the critical point on the QCD phase diagram is suggested bymany theoretical approaches, including, recently, lattice QCD.

Heavy ion experiments can discover the critical point – by measuringfluctuation observables as a function of collision parameters.

Search is underway.

Needed:

Theory: a reliable (systematically improvable) method to study Tµ plane andlocate CP.

Experiment: scan of the QCD phase diagram —√

s scan.


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