New View of the QCD Phase Diagram Krzysztof

New View of the QCD Phase Diagram Krzysztof Redlich (Wroclaw, GSI) Chihiro Sasaki (Munich) Rob Pisarski and Yoshimasa Hidaka BNL RBRC Unconfined World Confined World O(1) Conventional Wisdom Large N Will argue real world looks more like large N Quarkyonic World

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 Quarkyonic Matter: Confined gas of perturbative quarks! Confined: Mesons and Glueballs Quarkyonic: Quarks and Glueballs Large N 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 2 c around the baryon mass! 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 Straight line in temperature-chemical potential plane

Hadronic World: Confined world of very weakly interacting mesons. At low Goldstone Bosons Mesons and glueballs As T increases from Hadronic world => Quark Gluon Plasma Gluons Quarks Great Wall of Weakly Interacting Mesons As baryon chemical potential increases: Hadronic World => Quarkyonic Matter Quarks Goldstone Bosons Mesons and glueballs Great Wall of Strongly Interacting Lowest Mass Baryons => Triple point where walls meet

With Redlich and Sasaki

The Non-Perturbative Fermi Surface: Deep in the Fermi sea, a momentum of order the Fermi momenta must be exchanged in interactions Near the Fermi surface, interactions are strong Excitations are confined and color singlet If form a bound state with negative biding energy => Chiral condensate Condensate breaks translational invariance => crystal Chiral symmetry breaking of order Quarkyonic phase at most weakly breaks chiral symmetry Might be parity double and chiral symmetric

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.