Various Faces of Extreme QCD

Kenji Fukushima
Yukawa Institute for Theoretical Physics
Kyoto University
December 2008 at Kyusyu

Extreme QCD – Faces
Color Superconductivity, Quark-Gluon Plasma, Color Glass Condensate(Combined with Other Extremes) Strong Magnetic Field, Large Nc, Strong Coupling, etc(With Various Methods) Lattice Simulation, Effective Model (PNJL Model), Gravity Dualetc, etc, etc, etc, ...

High μ High T High E

December 2008 at Kyusyu

Two "Simplest"sSimplest Questions□ What happens at extreme high-density?
□ What happens at extreme high-temperature?
□ What happens at extreme high-energy?

Simplest Answers□ Color Superconductivity (CSC)□ Quark-Gluon Plasma (QGP)□ Color Glass Condensate (CGC)
December 2008 at Kyusyu

Extreme QCD !

QCD Paradigms
Temperature

QGP(Entropy Density)

Cerv
sos
ro

CGC
Electron-Ion Collider
ColorDensity

Relativistic Heavy-Ion Collider

DCQ

alci
itr
Ctni
Po

CSC
rdOt
1ser

No experiment…
Quark
ChemicalPotential(Quark Density)

December 2008 at Kyusyu

Dense Quark Matter
Temperature

Color SuperconductivityQuark
ChemicalPotential

ColorDensity
December 2008 at Kyusyu

Key Issues
Color-Flavor Locked (CFL) Phase□ Ground state of three-flavor symmetric matter

Electric and Color Neutrality Conditions□ s breaks neutrality Æ Fermi surface mismatch

Gapless State ÅÆ Unstable
Quest for the true ground state...???
□ Crystalline CSC, LOFF, meson supercurrent CSC□ Gluonic Phase
December 2008 at Kyusyu

Superconductivity
μq ~ 500MeV ↔ ρ ~ 10ρ0Fermi surface
3+3 → 3
Attractive interaction
Forming a pairs hole

Gap Δu quark

Bailin-Love (’84)

Color superconductivity is inevitable.
Many possible pairing patterns
Spin Color Flavor

Fermi
momentum

p 2 + ms2 − μq ≈ p − μq +2s2mμq+L

Strange quark mass ~ 100 ~ 200MeV
Characteristic scale ~ ms2/μq (~50MeV)
Breaking a pair

December 2008 at Kyusyu

Color-Flavor Locked Phase
Order parameter2 ε ijk ε αβγ q jβ γ 5 qkCγ = φLiα − φRiα

Alford-Rajagopal-Wilczek (’99)
Schafer-Wilczek (’99)
K.F. (’04)
Yamamoto et al. ('06)φLiα[SUC(3)] x SUL(3) x UL(1)[SUC+L(3)] x ZL(2)φ Ri α[SUC(3)] x SUR(3) x UR(1)[SUC+R(3)] x ZR(2)[SUC(3)] x SUL(3) x SUR(3) x UV(1) x UA(1)SUC+L+R(3) x ZL(2) x ZR(2)Gauge-invariant order parameter q ↔ φ , q ↔ φσ ~ φLφR

H ~ ε ijk ε αβγ φLiαφLjβ φLkγ
December 2008 at Kyusyu

Hadron ↔ Quark (CFL)Four-Fermi (NJL) ModelNOT useful to estimate the pairing gap itself.
♦ Gluon part of interaction is in Δ(g)Δ( g ) = 2 ⋅ 256π ⋅ (1 / g ) μq e45−3π 2 / 2 g

Pisarski-Rischke (’00)(2SC; Δ ~ 0.1μq for g 2 / 4π ~ 1)

Useful to examine the property of dense quark matterwith the pairing gap Δ given.
♦ Mean-field quark propagator = QCD in the mean-field approx.
♦ Only relevant interaction near the Fermi surface

Assumptions:
Quasi-particle picture = Non-interacting quarks with Δ
Δ(2SC) ~ 50MeV around μq ~ 500MeV (c.f. ms2/μq ~ 50MeV)
December 2008 at Kyusyu

Robust Part (after chiral restoration)
From K.F. (’05)

u-dMany many many…

u-dd-s"Understood"

u-ds-uu-d-s

December 2008 at Kyusyu

Condensed Matter Physics
of QCD is established.
Analogy to 3Hee.g.)
Zero Sound, Phonon, etc
Hands et al. (’04)
Fukushima-Iida (’05)

Toward the True Ground State(Chromomagnetic) Instability# ms2/μq > Δ Æ Unstable w.r.t. Δ(q), AT, n(q)Shovkovy-Huang (’04)
Casalbuoni et al. (’04)
Fukushima (’05)

Iida-Fukushima (’06)

Pressure to tear the Cooper pair apart
Energy gain by condensation

Crystalline Color Superconductivity (LOFF)((∂ − igA) Δ = ∂ Δ e− igA⋅ x) Giannakis-Ren ('04)

Larkin-Ovchinnikov ('65)
Fulde-Ferrell ('64)

One component gluon condensation == Plane-wave LOFF

VS

Multiple-wave = Crystalline Phase

Multi component = Gluonic Phase

Gorbar-Hashimoto-Miransky ('06) December 2008 at Kyusyu

Alford-Bowers-Rajagopal ('01)
Rajagopal-Sharma ('06)
Alford et al. RMP80:1455 (2008)

Hot Quark (and Gluon) Matter
Temperature

Effective Model Approach
Quark
ChemicalPotential

ColorDensity
December 2008 at Kyusyu

History of the Phase Diagram
The very first "QCD" phase diagramtaken from Cabibbo-Parisi (1975).
They say "Quarks are confined in phase I
and unconfined in phase II".
Interpretation of the exponentially increasing
spectrum by Hagedorn.

Deconfinement Transition

December 2008 at Kyusyu

Bielefeld Proceedings in 1982
Taken from Baym (1982)

Can we exclude
this possibility ???
Lee-Wick abnormal matter

December 2008 at Kyusyu

Lattice QCD
Taken from
Kogut, Stone, Wyld, Gibbs,
Shigemitsu, Shenker, Sinclair (1983)

ψψ[W ~ exp − f q / T

Chiral Condensate] Polyakov Loop

Chiral Restoration
occurs simultaneouslywith Deconfinement !

December 2008 at Kyusyu

Long Range Plan in 1983
By Baym (1983)

Deconfinement andChiral Transitions
December 2008 at Kyusyu

Discontinuous Leap?

supported by the PNJL model
December 2008 at Kyusyu

PNJL Model[]trL ~ exp − f q / T ~ 0 in the confinement phaseLquark excitation()(1 + e))(1 + L e⇒ ∏ det (1 + L eZ ~ ∏ 1+ e

− (ε − μ ) / T− (ε + μ ) / T−(ε − μ ) / TOnly

L⋅L+ andmeson-like+ −(ε + μ ) / T)L⋅ L⋅ L nonvanishingbaryon-like

December 2008 at Kyusyu

Chiral Condensate

in PNJL
December 2008 at Kyusyu

Polyakov Loop

[trL ~ exp − f q / T]in PNJL
December 2008 at Kyusyu

PNJL Phase Diagram
in PNJL

Quarkyonic Matter?
or CSC
McLerran-Pisarski ('07)
Miura-Ohnishi ('08)

December 2008 at Kyusyu

Chiral Susceptibility

in PNJL
December 2008 at Kyusyu

Quark Number Susceptibility

in PNJL
December 2008 at Kyusyu

Adiabatic (Isentropic) Path

Schmidt ('08)

d ( s / n B ) / dτ = 0

in PNJLConsistent with the lattice results so far.
December 2008 at Kyusyu

As a "Toy" Model
Sign Problem()()

ln Z ~ ln ∏ det 1 + L e − (ε − μ ) / T 1 + L+ e − (ε + μ ) / T(~ ∫ tr L e −(ε − μ ) / T + tr L+ e −(ε + μ ) / T)

Fukushima-Hidaka ('05)

Complex for general L !

Imaginary Chemical Potential∫ (tr L e− (ε − μ ) / T+ tr L+ e − (ε + μ ) / T()→ ∫ e −ε / T tr L eiμ / T + tr L+ e −iμ / T
December 2008 at Kyusyu) Real number !

Sakai-Kashiwa-Kouno-Yahiro ('08)

PNJL to CSC ?
There are already some applications of thePNJL model to Color Superconductivity.
Roessner-Ratti-Weise ('06)
Blaschke ('08)
Abuki et al ('08)

There are some technical difficulties left
unsolved, however.
□ How to compute the "color density"?
□ 2-flavor CSC incompatible with diagonal L .
Abuki-Fukushima ('09) under completion
December 2008 at Kyusyu

Dense Gluon Matter
Temperature

Color Glass Condensate
Quark
ChemicalPotentialColorDensity
December 2008 at Kyusyu

How is dense color possible?
Large quark density Æ CSC

Dense when μq> ΛQCD

□ Quark or baryon # has a conserved U(1) charge.

Chromo (Gluo)dynamics□ Gauge charge is SU(3) without conservation.
□ Color is confined.

Large gluon density Æ Color Glass Condensate
Parton overlapping
resolution ~ 1/Qs
Qs2 ~ A1/3
nucleus ~A

If seen with a probe at 1/Q >> 1/Qs
Æ Dense!
If seen with a probe at 1/Q << 1/Qs
Æ Dilute!

December 2008 at Kyusyu

More Gluons from Quantum Radiation
Gluon increases as going to higher energy

Parton picture in the infinite momentum framePpp⊥2ΔE ~ p =2 xP−High Energy Æ Dense Gluon Matter
December 2008 at Kyusyu

HERA (ep collider)
Quantum Evolution of PDFs
As x goes smaller
than ~ 10−2
gluon is dominant.

× 20 !

small-x = high energy
Only one energy scale

Qs
December 2008 at Kyusyu

Initial Condition for HIC
Characterized by T

Characterized by Qs
Initial condition for HIC can be given!
December 2008 at Kyusyu

c.f. Very similar in the dual
gravity description.

SummaryDense Quark Matter□ Color Superconductivity□ What is the true ground state?

Various faces of ...
┐(￣ヘ￣）┌ ﾌｩｩ～

Hot Quark (and Gluon) Matter□ Quark-Gluon Plasma□ PNJL model is successful!

（⌒▽⌒）

Dense (and Hot) Gluon Matter□ Color Glass Condensate
く(￣△￣)ノ□ Initial condition for the heavy-ion collisions.
December 2008 at Kyusyu