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

1
Probing deconfinement in a chiral effective model
with Polyakov loop from imaginary chemical
potential

• Kenji Morita
• (Yukawa Institute for Theoretical Physics, Kyoto
  University)
• In collaboration with
• 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 m
4. Dual parameters for deconfinement

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QCD at imaginary m?

• Goal QCD thermodynamics at finite m
• Sign problem!
• Imaginary m
• Lattice OK
• Phase structure
• Testing ground
• for understanding
• phase transitions
• Model calculations help to connect with real m
  
• Analytic continuation, canonical ensemble
  

T3m/p
T
Talk by O.Philipsen
det M Complex
m
Re
Taylor expansion around m0
Talk by B.Friman
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Property of ZQCD(T,V,qmI/T)

• RW Periodicity (Roberge-Weiss 86)
• Schematic phase diagram

Roberge-Weiss transition from one to another
sector of Z(3)
TE Roberge-Weiss endpoint Lattice 1.1Td
Td Transition temperature at vanishing m
Chiral/confinement-deconfinement
transition (coincidence)
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Polyakov-loop-extended NJL model

• A model with the relevant properties
• Confinement-deconfinement chiral (Fukushima,
  PLB591,04)
• RW periodicity (Sakai et al., PRD77 08)

Z(3) symmetic Polynomial / Logarithmic forms by
Ratti et al.
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Mean field approximation

• Thermodynamic potential
• Order parameters

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Two extreme limits

• Gap eq. for M with
• For F0 (Confinement limit)
• Characterizing confinement
• Periodicity 2p/3
• cos3q lt 0 for q gt p/6
• For F1 (NJL)
• Characterizing deconfined quark
• Periodicity 2p

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Phase diagram
Deconfinement Potential dependent in
qualitative level Poly crossover 2nd order RW
endpoint Log CEP at q0.6p/3, 1st order RW
endpoint
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Phase diagram / RW transition
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Phase diagram / chiral transition
Smooth change
Discontinuity induced by F
Cusp induced by RW transition
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What determines the location of CEP?

• Change Gs (preserve c symmetry)

mCEP ? as Gs ?
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CEP Mechanism

• Gscr
• Gs lt 4.12 GeV-2
• (L0.6315 GeV, m0)
• Always c symmetric
• TTd M0
• ? Gs does not change dyn. quark mass
• Thermal terms_at_qp/3
• All terms gt 0 at real m (coshnm)

gt 0 O(F)
lt 0 O(F)
lt 0 O(1)
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CEP Mechanism

• Influence of dyn. quark mass on deconfinement
• Large M ?Approach to pure gauge (1st order)
• Large Gs ? Higher T needed to melt
• Relation to Large Ncsimilar in quark sector

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Upoly dependence

• CEP in Polynomial potential?
• M?8 Limit 1st order

• RW endpoint Gs12.4GeV-2
• m0 Gs25GeV-2
• 1st order PT takes place

TT0270 MeV Log DF0.47 Pol DF0.072
Log strong / pol weak 1st order transition
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Summary of q dependence
s0
scosq
scos(q-2p/3)
scos3q
Effective order parameter utilizing this?
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Dual parameters
Talks by J.Pawlowski, C.Fischer

• Dual condensate (Bilgici et al., PRD77)
• j twisted angle of b.c.
• Use q
• Expectation
• n1 resembles Polyakov loop (S(1) dressed)
• n3 picks up Baryons

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Sensitivity to the transitions
Deconfinement
Chiral
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n3

• n3 Baryons

Tc at q0
RW endpoint
CEP
Tc at qp/3
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Summary

• Statistical confinement explains q dependence
  
• cos3q in confined
• cosq cusp (RW transition) in
  deconfined
• Dynamical quark mass and the latent heat in the
  gauge sector control interplay btw chiral
  deconfinement
• Upoly dependent CEP of deconfinement transition
• Dual parameter using q
• Characteristic behavior at n1 and 3
• Different sensitivity to the transitions from
  the (dressed) Polyakov loop

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Backup Slides
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Property of ZQCD(T,V,q) Roberge-Weiss 86

• Introducing imaginary m
• Change of variable change of the boundary
  condition
• Z(3) transformation
• Keeps the action invariant, but

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Polyakov loops at phys. quark mass
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n3 for phys. quark mass
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Polyakov Loop Potential
T0270 MeV

• Polynomial form (Ratti et al., 06)
• Logarithmic form (Ratti et al., 07)
• Qualitative features at real m same

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1st order transition at intermediate q

• Log-potential case
• Example at T250MeV, q0.91p/3
• CEP at T240MeV, q0.6p/3
• Effect on s
• Remnant of the 1st order RW endpoint

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RW endpoint

• Lattice non-trivial mq dependence
• de-Forcrand, Philipsen Nf3
• Bonati, DElia, Sanfilippo, Nf2
• Model calculation
• Larger quark mass
• Stronger transition
• Attempt Entangle PNJL (by Kyushu grp.)

1st
2nd
1st
M
Non-trivial dynamical mass?
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RW Transition on target space
Opposite behavior of log- to poly- potential
Determined by Upoly
Transition of vacuum from f 0 to f -2p/3
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j vs q

• Lattice result on s(j) (Bilgici et al., 09)
• Imaginary m change configuration
• Model w/o Z(3) q jp (cf. NJL, Mukherjee et
  al., PRD10)
• w/ Z(3) fix F F(q0) then re-calculate s(q)

Periodicity 2p
Configuration independent of j S(1) dressed
Polyakov loop
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RW endpoint / Phase diagram
qp/3
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Modified dual order parameters

• Use q
• Confinement s cos3q
• deconfinement s cosq
• Comparison with Polyakov loop (n1)