New View of the QCD Phase Diagram

Krzysztof Redlich (Wroclaw, GSI)

Chihiro Sasaki (Munich)

Rob Pisarski and Yoshimasa Hidaka

BNL RBRC

Confined World

O(1)

Unconfined World

Conventional Wisdom

Will argue real world looks more like large N

Unconfined World

Confined World

O(1)

Quarkyonic World

Large N

Conjectured Phase Diagram for Nc = 3

Brief Review of Large N

Mesons: quark-antiquark, Non-Interacting, masses ~

Baryons: N quarks, masses ~ , baryon interactions ~

Spectrum of Low Energy Baryons:

Multiplets with I = J; I,J = 1/2 -> I,J = N/2

The confined world has no baryons!

About 20 degenerate lowest mass baryons

Confinement at Finite Density:

Generates Debye Screening => Deconfinement at Tc

Quark loops are always small by 1/N_c

For finite baryon fermi energy, confinement is never affected by the presence of quarks!

T_c does not depend upon baryon density!

Finite Baryon Density:

No baryons in the confined phase for

For weakly coupled gas of quarks.

If T < T_c, no free gluons, degrees of freedom are ~ Nc

Unconfined World

Confined World

O(1)

Quarkyonic World

Large N

Quarkyonic Matter:

Confined gas of perturbative

quarks!

Confined: Mesons and Glueballs

Quarkyonic: Quarks and Glueballs

Unconfined: Quarks and Gluons

Some Properties of Quarkyonic Matter

Quarks inside the Fermi Sea: Perturbative Interactions => At High Density can use

perturbative quark Fermi gas for bulk properties

At Fermi Surface: Interactions sensitive to infrared => Confined baryons

Perturbative high density quark matter is chirally symmetric but confined => violates intuitive

arguments that confinement => chiral symmetry

Quarkyonic matter appears (at T= 0) when

Width of the Transition Region:

Baryons are non-relativistic:

Nuclear physics is in a width of order 1/N around the baryon mass!2

c

Large Nc world looks like our world: Nuclear matter is non-relativistic, and there is a narrow transition between

confined and quarkyonic world

Nf/Nc fixed, large Nc

Confinement not an order parameter

Baryon number is

Large density of states:

Number of Lowest mass baryons

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Straight line in temperature-chemical potential plane

As T increases from Hadronic world => Quark

Gluon Plasma

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Quarks

Great Wall of Weakly Interacting Mesons

Hadronic World:

Confined world of very weakly interacting mesons. At low

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Mesons and glueballs

As baryon chemical potential increases:

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Mesons and glueballs

Great Wall of Strongly Interacting Lowest Mass Baryons =>

Triple point where walls meet

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With Redlich and Sasaki

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The Non-Perturbative Fermi Surface:

Deep in the Fermi sea, a momentum of order the Fermi momenta must be exchanged in interactions

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Excitations are confined and color singletIf form a bound state with negative biding energy =>

Chiral condensate

Condensate breaks translational invariance => crystal

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Quarkyonic phase at most weakly breaks chiral symmetry

Might be parity double and chiral symmetric

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Conclusions:

There are three phases of QCD at large N:

Confined

Unconfined

Quarkyonic

They have very different bulk properties

There may be a tri-critical point somewhere near AGS energies

The early observations of Cleymans, Redlich,Braun-Munzinger and Stachel

strongly support that this picture reflects N = 3.