kenji morita 21 may 2011three days on quarkyonic island@wroclaw, poland1 probing deconfinement in a...
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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)