21 May 2011 Three Days on Quarkyonic Island@Wroclaw, Poland 1

Kenji Morita

Probing deconfinement in a chiral Probing deconfinement in a chiral effective model with Polyakov loop effective model with Polyakov loop from imaginary chemical potentialfrom imaginary chemical potential

Kenji MoritaKenji Morita(Yukawa Institute for Theoretical Physics, Kyoto (Yukawa Institute for Theoretical Physics, Kyoto

University)University)

In collaboration with In collaboration with B. Friman (GSI), K. Redlich (Wroclaw), and V. Skokov (GSI)B. Friman (GSI), K. Redlich (Wroclaw), and V. Skokov (GSI)

1. QCD at imaginary chemical potential

2. Phase diagram / Order parameters in PNJL model

3. Deconfinement CEP from imaginary to real

4. Dual parameters for deconfinement

21 May 2011 2/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

QCD at imaginary QCD at imaginary ??Goal : QCD thermodynamics at finite Goal : QCD thermodynamics at finite

Sign problem!Sign problem!

Imaginary Imaginary Lattice – OKLattice – OK

Phase structurePhase structure

Testing ground Testing ground

for understandingfor understanding

phase transitionsphase transitions

Model calculations help to connect with real Model calculations help to connect with real Analytic continuation, canonical ensemble

T

Re

det M : Complex

MC Simulation

Taylor expansion around =0

T=3/

Im

det M : Realas rich as

real

Talk by O.Philipsen

Talk by B.Friman

21 May 2011 3/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Property of Property of ZZQCDQCD((TT,,VV,,TT))RW Periodicity RW Periodicity (Roberge-Weiss ’86)(Roberge-Weiss ’86)

Schematic phase diagramSchematic phase diagramRoberge-Weiss transition : from

one to another sector of Z(3)

Chiral/confinement-deconfinement transition

(coincidence)

TE : Roberge-Weiss endpoint Lattice: ～ 1.1Td

Td : Transition temperature at vanishing

21 May 2011 4/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Polyakov-loop-extended NJLPolyakov-loop-extended NJL modelmodel

A model with the relevant propertiesA model with the relevant properties Confinement-deconfinement + chiral Confinement-deconfinement + chiral (Fukushima, PLB591,’04) (Fukushima, PLB591,’04)

RW periodicity RW periodicity (Sakai et al., PRD77 ’08)Z(3) symmetic

Polynomial / Logarithmic forms by

Ratti et al.

21 May 2011 5/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Mean field approximationMean field approximation

21 May 2011 6/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Two extreme limits:Two extreme limits:

Couple to the phase

21 May 2011 7/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Phase diagramPhase diagram

Deconfinement : Potential dependent in qualitative level

Poly : crossover + 2nd order RW endpoint

Log : CEP at ~0.6/3, 1st order RW endpoint

21 May 2011 8/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Phase diagram / RW transitionPhase diagram / RW transition

21 May 2011 9/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Phase diagram / chiral Phase diagram / chiral transitiontransition

Discontinuity induced by ||

Smooth change

Cusp induced by RW

transition

21 May 2011 10/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

What determines the location of What determines the location of CEP?CEP?

Change Change GGss (preserve (preserve symmetry) symmetry)

CEP ↑ as Gs ↑

21 May 2011 11 /18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

CEP MechanismCEP Mechanism

> 0O()

< 0O()

< 0O()

21 May 2011 12/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

CEP MechanismCEP MechanismInfluence of dyn. quark mass on deconfinementInfluence of dyn. quark mass on deconfinement

Large M →Approach to pure gauge (1Large M →Approach to pure gauge (1stst order) order)

Large GLarge Gss → Higher T needed to melt → Higher T needed to melt

Relation to Large NRelation to Large Ncc：：similar in quark sectorsimilar in quark sector

21 May 2011 13/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

polypoly dependence dependenceCEP in Polynomial potential?CEP in Polynomial potential?

M→∞ Limit : 1M→∞ Limit : 1stst order order

• RW endpoint : Gs=12.4GeV-2

• =0 : Gs=25GeV-2

1st order PT takes place

T=T0=270 MeVLog: =0.47Pol: =0.072

[Log : strong / pol : weak] 1st order transition

21 May 2011 14/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Summary of Summary of dependence dependence

cos3

cos

cos(

Effective order parameter utilizing this?

21 May 2011 15/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Dual parametersDual parametersTalks by J.Pawlowski,

C.Fischer

21 May 2011 16/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Sensitivity to the transitionsSensitivity to the transitions

Deconfinement Chiral

21 May 2011 17/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

n=3 n=3 n=3 : “Baryons”n=3 : “Baryons”

CEP

RW endpoint

Tat

Tat

21 May 2011 18/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

SummarySummary““Statistical confinement” explains Statistical confinement” explains dependence : dependence :

coscos in confined in confined coscoscusp (RW transition) in deconfinedcusp (RW transition) in deconfined

DynamicalDynamical quark mass and the latent heat in the gauge quark mass and the latent heat in the gauge sector control interplay btw chiral & deconfinementsector control interplay btw chiral & deconfinement

poly poly dependent CEP of deconfinement dependent CEP of deconfinement transitiontransition

““Dual parameter” using Dual parameter” using Characteristic behavior at n=1 and 3Characteristic behavior at n=1 and 3

Different sensitivity to the transitions Different sensitivity to the transitions from the (dressed) Polyakov loopfrom the (dressed) Polyakov loop

21 May 2011 19/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Backup Slides

21 May 2011 20/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Property of Property of ZZQCDQCD((TT,,VV,,) ) [Roberge-[Roberge-

Weiss ’86]Weiss ’86]

21 May 2011 21/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Polyakov loops at phys. quark Polyakov loops at phys. quark massmass

21 May 2011 22/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

n=3 for phys. quark massn=3 for phys. quark mass

21 May 2011 23/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Polyakov Loop PotentialPolyakov Loop Potential T0=270 MeV

21 May 2011 24/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

11stst order transition at order transition at intermediate intermediate

Log-potential caseLog-potential case

Example at T=Example at T=MeV, MeV,

==//

CEP at T=CEP at T=MeV, MeV,

Effect on Effect on

Remnant of the 1Remnant of the 1stst order order

RW endpoint RW endpoint

21 May 2011 25/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

RW endpointRW endpointLattice : non-trivial Lattice : non-trivial mmqq dependence dependence de-Forcrand, Philipsen : Nde-Forcrand, Philipsen : Nff=3=3

Bonati, D’Elia, Sanfilippo, NBonati, D’Elia, Sanfilippo, Nff=2=2

Model calculationModel calculation Larger quark massLarger quark mass

= Stronger transition= Stronger transition

Attempt : Entangle PNJL (by Kyushu grp.) Attempt : Entangle PNJL (by Kyushu grp.)

1st

1st2nd

Non-trivial dynamical mass?

Ｍ

21 May 2011 26/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

RW Transition on target RW Transition on target spacespace

Opposite behavior of log- to poly- potential

Transition of vacuum

from = 0 to = -2/3

Determined by poly

21 May 2011 27/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

vs vs

Periodicity : 2

Configuration independent of

dressed Polyakov loop

21 May 2011 28/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

RW endpoint / Phase diagramRW endpoint / Phase diagram

21 May 2011 29/18

Kenji Morita

Three Days on Quarkyonic Island@Wroclaw, Poland

Modified dual order Modified dual order parametersparametersUse Use Confinement : Confinement : ~ cos ~ cos deconfinement : deconfinement : ~ cos ~ cos

Comparison with Polyakov loop (n=1)Comparison with Polyakov loop (n=1)