# Presentation: 035508

## Chasing the Unicorn:  the QGP & RHIC 

- Unicorn = fantastic and mythical beast!
- Quark Gluon Plasma: deconfined, chirally symmetric matter

- Q: Have AA collisions @ RHIC made the QGP?
*Triumph* of experiment: wealth of precise data
- In central AA, some quantities change by ~ 5 from lower energies
-          Geometrical evidence: matter at high energy density “eats” jets
- Exp. surprise: the (high-pt) tail wags the (low-pt) body of the Unicorn
- Even qualitatively, *no* theory explains *all* interesting features.
- A:  *Some *type of QGP has been created

## Hunting for the “Unicorn” @ SPS, RHIC, LHC, GSI

- ⇑Hunters = experimentalists.  So: “All theorists are dogs...”
- RHIC: Exp.’y, charm quarks “flow” (v2) like pions!  sQGP?
- “Most Perfect Fluid on Earth”: Gyulassy, Heinz, Hirano, Teaney, Shuryak...
- N.B.: but with *wrong* (bag) Equation of State!
- Huovinen: v2 OK for bag EoS, but lattice EoS is as bad as purely hadronic EoS.

## Lattice: SU(3) thermo., c & c/o quarks

- With NO quarks:  1st order deconfining trans at T_d ≈ 270 MeV ± 5%
- 3 flavors of quarks:  crossover, chiral sym restoration & deconfinement
- 	T_chiral ~ 175 MeV

- T = temperature, p(T) = pressure

**Notes:**
Review of Lattice: unscaled pressures

## Lattice SU(3) thermo.: “Flavor Independence”

- Perhaps:* *even with quarks, “transition” *dominated by gluons*
*	*=> Polyakov loops (matrix model)

**Notes:**
Flavor independence

## Non-perturbative QGP,  Td ⇒ 3 Td

- Polyakov loop ~1 in pert thy.  Lattice: above 3 Td.  Not Td => 3 Td.

## NpQGP: electric (not magnetic), not strong coupling

- Giovannangeli; Laine & Schroder: in dim.’y reduced 3D theory, compare
- 	(spatial) string tension to that in full theory.  Works very well!

*Only* electric sector non.-pert., not magnetic.
- QCD: α_s at 175 MeV ~ 0.28: at T=0, mom. scale ~ 2.2 GeV.
-            *Not* (very) strong coupling!

## Deconfinement: 1st order transition for N ≥ 3

- Lucini, Teper, Wenger ‘03, ‘04, ‘05: Latent heat ~ N^2 for N= 4, 6, 8

- Ordinary 1st order trans.: latent heat, masses nonzero at transition.
*Perhaps: *Large N near “Gross-Witten point”:
- 	                                    transition first order, but masses vanish.

**Notes:**
Order of the deconf’g trans. for N=4,6...

## Deconfinement and the Gross-Witten point 

- A. Dumitru,  Y. Hatta, J. Lenaghan, K. Orginos, & RDP, hep-th/0311223: DHLOP
- Aharony, Marsano, Minwalla, Papadodimas, & Van Raamsdonk:
- 	hep-th/0310285: AMMPR ‘03; hep-th/0502149: AMMPR ‘05
- A. Dumitru, J. Lenaghan, & RDP, hep-ph/0410294: DLP ‘04
- A. Dumitru, RDP, D. Zschiesche, hep-ph/0505256: DPZ ‘05
- M.Oswald & RDP, hep-ph/0510?: OP ‘05

- Take “pure” SU(N) gauge theory, *no* dynamical quarks.
- Rigorously, a deconfining phase transition at a temperature T.

## Mean field phase diagram

- When N≠3, all phase diagrams look alike:
- Lines of 1st and 2nd order transitions meet at a tri-critical point

## Matrix mean field theory

## Deconfinement

## Matrix models

- Matrix in the measure:
- Adjoint loop:
- Z(N) charge: fundamental loop = charge 1.  Adjoint loop = charge 0.
- Most general potential sum of Z(N) *neutral* loops:
- Adjoint loop “mass” term.  Higher loops “interactions”

## Large N matrix models

## Large N:  Vandermonde “potential”

- Brezin, Ityzkson, Parisi & Zuber ‘78; Gross & Witten ‘81
- Kogut, Snow & Stone = KSS ‘82; Green & Karsch ‘84
- AAMPR ‘03, ‘05.  DHLOP ‘03.  DLP ‘04.

## Gross-Witten point

## Near the GW point

## At the GW point

##   Away from the GW point

## GW = “ultra”-critical point 

- Phase diagram: tri-critical => Gross-Witten point.

- Away from GW point,
- 	*ordinary* 1st or 2nd order transitions.
- Only at GW point:
- Nonzero latent heat, jump in order parameter
- AND zero masses
- “Ultra”-critical as infinite # couplings vanish
- AMMPR ‘03, DLP ‘04

## Finite N:  Vandermonde potential

- Infinite N: discontinuity of 3rd order at 1/2.  Continuous at finite N.
- Numerically, N=2 and 3 *close* to infinite N. DLP ‘04

## N = 3: matrix models

## Lattice: N = 3 close to GW point

- N=3 analogy of GW point =>

- Best fit to lattice data =>

- Take ren’d loops from lattice data.
- Fit matrix model, with                 *       *Only need* small* cubic term. DLP ‘04

## Renormalized Polyakov Loops

- Gervais & Neveu ‘80. Polyakov ‘80. Dotsenko & Vergeles ‘80....
- Kaczmarek, Karsch, Petreczsky & Zantow = KKPZ ‘02 +...  DHLOP ‘03.

## Ren.’d Polyakov loops on lattice

- Coupling for transition changes with N_t
- => to obtain the same T at different N_t, must compute at different β.
- Doable, not trivial.
- SU(3) Wilson action, N_t = 4,6,8,10; # spatial steps = 3 N_t
- Lattice coupling constant β = 6/g^2: related to temperature by Non-Pert. Ren.

**Notes:**
Lattice reg. of Polyakov loops

## Bare triplet loop vs T,  Nt

## Bare octet  loop vs T, Nt

## Lattice SU(3): Renormalized Polyakov loops

-                    DHLOP ‘03                                             KKPZ ‘02

- Agree to ~ 10%: difference due to cusp renormalization?

## Lattice: SU(3) ≈ SU(∞) to ~25%

- Lattice:
- Corrections to factorization
- very small,  except near T_d
- Above T_d:
- “spikes” in difference loops

- At large N, “factorization” => all loops product of fundamental (& anti-fund.)
- Migdal & Makeenko ‘80, Eguchi & Kawai ‘82...Gross & Taylor ‘93
- “Difference” loops vanish at infinite N

## Lattice: String tension vs. T, N= 3, 4 & 6

- Confined phase: string tension at T≠0/at T=0 (y-axis)

## Nonzero quark density

- Quarks act like background Z(3) field,  ~ real part of loop.
- Quark chemical potential, μ: background field for imaginary part of loop,
- 	with* imaginary* coefficient!  Karsch & Wyld ‘86, DPZ ‘05

## Fluctuations in matrix model

## Slide 32

## Mass div.’s exponentiate: log(bare loop) vs. N_t

**Notes:**
Bare triplet loop vs Nt

## Lattice SU(3): divergent masses

- DHLOP:  Triplet, sextet, octet loops.
- KKPZ: Triplet loop, Z_R from short distance behavior of two-point functions.
- Casimir scaling of divergent masses at 3 Td.

## Bare loops don’t factorize

- Bare octet difference loop/bare octet loop: violations of factor.
- 50% @
- Nt =4
- 200% @ Nt = 10.

**Notes:**
Bare loops don’t exhibit factorization