1. Kenji Morita 21 May 2011Three Days on Quarkyonic Island@Wroclaw, Poland1 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  4.Dual parameters for deconfinement

2. Kenji Morita 21 May 2011 2/18 Three Days on Quarkyonic Island@Wroclaw, Poland QCD at imaginary  ? QCD at imaginary  ? Goal : QCD thermodynamics at finite m Sign problem! Sign problem! Imaginary m Lattice – OK Lattice – OK Phase structure Phase structure Testing ground Testing ground for understanding for understanding phase transitions phase transitions Model calculations help to connect with real m Model calculations help to connect with real m Analytic continuation, canonical ensemble T m Re det M : Complex MC Simulation Taylor expansion around m =0 T =3 m / p Im m det M : Real as rich as real m Talk by O.Philipsen Talk by B.Friman

3. Kenji Morita 21 May 2011 3/18 Three Days on Quarkyonic Island@Wroclaw, Poland Property of Z QCD ( T, V, q=m I / T ) RW Periodicity (Roberge-Weiss ’86) Schematic phase diagram Roberge-Weiss transition : from one to another sector of Z(3) Chiral/confinement- deconfinement transition (coincidence) T E : Roberge-Weiss endpoint Lattice: ～ 1.1T d T d : Transition temperature at vanishing m

4. Kenji Morita 21 May 2011 4/18 Three Days on Quarkyonic Island@Wroclaw, Poland Polyakov-loop-extended NJL model A model with the relevant properties Confinement-deconfinement + chiral (Fukushima, PLB591,’04) Confinement-deconfinement + chiral (Fukushima, PLB591,’04) RW periodicity RW periodicity (Sakai et al., PRD77 ’08) Z(3) symmetic Polynomial / Logarithmic forms by Ratti et al.

5. Kenji Morita 21 May 2011 5/18 Three Days on Quarkyonic Island@Wroclaw, Poland Mean field approximation Thermodynamic potential Order parameters

6. Kenji Morita 21 May 2011 6/18 Three Days on Quarkyonic Island@Wroclaw, Poland Two extreme limits: Gap eq. for M with For F =0 (Confinement limit) For F =0 (Confinement limit) Characterizing confinement Characterizing confinement Periodicity 2 p /3 Periodicity 2 p /3 cos3 q p /6 cos3 q p /6 For F =1 (NJL) For F =1 (NJL) Characterizing deconfined quark Characterizing deconfined quark Periodicity 2 p Periodicity 2 p Couple to the phase

7. Kenji Morita 21 May 2011 7/18 Three Days on Quarkyonic Island@Wroclaw, Poland Phase diagram Deconfinement : Potential dependent in qualitative level Poly : crossover + 2 nd order RW endpoint Log : CEP at q ~ 0.6 p /3, 1 st order RW endpoint

8. Kenji Morita 21 May 2011 8/18 Three Days on Quarkyonic Island@Wroclaw, Poland Phase diagram / RW transition

9. Kenji Morita 21 May 2011 9/18 Three Days on Quarkyonic Island@Wroclaw, Poland Phase diagram / chiral transition Discontinuity induced by | F | Smooth change Cusp induced by RW transition

10. Kenji Morita 21 May 2011 10/18 Three Days on Quarkyonic Island@Wroclaw, Poland What determines the location of CEP? Change G s (preserve  symmetry)  CEP ↑ as G s ↑

11. Kenji Morita 21 May 2011 11/18 Three Days on Quarkyonic Island@Wroclaw, Poland CEP Mechanism G s cr G s < 4.12 GeV -2 G s < 4.12 GeV -2 ( L =0.6315 GeV, m =0) ( L =0.6315 GeV, m =0) Always  symmetric Always  symmetric T ~ T d : M=0 T ~ T d : M=0 → G s does not change dyn. quark mass Thermal terms ＠ q ~ p /3 All terms > 0 at real m (cosh n m ) All terms > 0 at real m (cosh n m ) > 0 O( F ) < 0 O( F ) < 0 O( 1 )

12. Kenji Morita 21 May 2011 12/18 Three Days on Quarkyonic Island@Wroclaw, Poland CEP Mechanism Influence of dyn. quark mass on deconfinement Large M → Approach to pure gauge (1 st order) Large M → Approach to pure gauge (1 st order) Large G s → Higher T needed to melt Large G s → Higher T needed to melt Relation to Large N c ： similar in quark sector Relation to Large N c ： similar in quark sector

13. Kenji Morita 21 May 2011 13/18 Three Days on Quarkyonic Island@Wroclaw, Poland  poly dependence CEP in Polynomial potential? M →∞ Limit : 1 st order M →∞ Limit : 1 st order RW endpoint : G s =12.4GeV -2 m =0 : G s =25GeV -2 1 st order PT takes place T=T 0 =270 MeV Log: DF =0.47 Pol: DF =0.072 [Log : strong / pol : weak] 1 st order transition

14. Kenji Morita 21 May 2011 14/18 Three Days on Quarkyonic Island@Wroclaw, Poland Summary of  dependence s~ cos3 q s~ cos q s=0 s~ cos( q-2p/3) Effective order parameter utilizing this?

15. Kenji Morita 21 May 2011 15/18 Three Days on Quarkyonic Island@Wroclaw, Poland Dual parameters Dual condensate (Bilgici et al., PRD77) j : twisted angle of b.c. j : twisted angle of b.c. Use q Use q Expectation Expectation n=1 resembles Polyakov loop ( S (1) : “ dressed ” ) n=1 resembles Polyakov loop ( S (1) : “ dressed ” ) n=3 picks up “ Baryons ” n=3 picks up “ Baryons ” Talks by J.Pawlowski, C.Fischer

16. Kenji Morita 21 May 2011 16/18 Three Days on Quarkyonic Island@Wroclaw, Poland Sensitivity to the transitions DeconfinementChiral

17. Kenji Morita 21 May 2011 17/18 Three Days on Quarkyonic Island@Wroclaw, Poland n=3 n=3 : “Baryons” CEP RW endpoint T c at q=0 T c at q=p/3

18. Kenji Morita 21 May 2011 18/18 Three Days on Quarkyonic Island@Wroclaw, Poland Summary “Statistical confinement” explains q dependence : cos 3q in confined cos 3q in confined cos q + cusp (RW transition) in deconfined cos q + cusp (RW transition) in deconfined Dynamical quark mass and the latent heat in the gauge sector control interplay btw chiral & deconfinement  poly dependent CEP of deconfinement transition  poly dependent CEP of deconfinement transition “Dual parameter” using q Characteristic behavior at n=1 and 3 Characteristic behavior at n=1 and 3 Different sensitivity to the transitions from the (dressed) Polyakov loop Different sensitivity to the transitions from the (dressed) Polyakov loop

19. Kenji Morita 21 May 2011 19/18 Three Days on Quarkyonic Island@Wroclaw, Poland Backup Slides

20. Kenji Morita 21 May 2011 20/18 Three Days on Quarkyonic Island@Wroclaw, Poland Property of Z QCD ( T, V, q ) [Roberge-Weiss ’86] Introducing imaginary m Change of variable : change of the boundary condition Change of variable : change of the boundary condition Z(3) transformation Z(3) transformation Keeps the action invariant, but Keeps the action invariant, but

21. Kenji Morita 21 May 2011 21/18 Three Days on Quarkyonic Island@Wroclaw, Poland Polyakov loops at phys. quark mass

22. Kenji Morita 21 May 2011 22/18 Three Days on Quarkyonic Island@Wroclaw, Poland n=3 for phys. quark mass

23. Kenji Morita 21 May 2011 23/18 Three Days on Quarkyonic Island@Wroclaw, Poland Polyakov Loop Potential Polynomial form (Ratti et al., ’06) Logarithmic form (Ratti et al., ’07) Qualitative features at real m : same T 0 =270 MeV

24. Kenji Morita 21 May 2011 24/18 Three Days on Quarkyonic Island@Wroclaw, Poland 1 st order transition at intermediate q Log-potential case Example at T= 250 MeV, q = 0.91p / 3 CEP at T= 240 MeV, q=0.6p/3 Effect on s Remnant of the 1 st order RW endpoint

25. Kenji Morita 21 May 2011 25/18 Three Days on Quarkyonic Island@Wroclaw, Poland RW endpoint Lattice : non-trivial m q dependence de-Forcrand, Philipsen : N f =3 de-Forcrand, Philipsen : N f =3 Bonati, D ’ Elia, Sanfilippo, N f =2 Bonati, D ’ Elia, Sanfilippo, N f =2 Model calculation Larger quark mass Larger quark mass = Stronger transition = Stronger transition Attempt : Entangle PNJL (by Kyushu grp.) Attempt : Entangle PNJL (by Kyushu grp.) 1st 2nd Non-trivial dynamical mass? Ｍ

26. Kenji Morita 21 May 2011 26/18 Three Days on Quarkyonic Island@Wroclaw, Poland RW Transition on target space Opposite behavior of log- to poly- potential Transition of vacuum from f = 0 to f = -2 p /3 Determined by  poly

27. Kenji Morita 21 May 2011 27/18 Three Days on Quarkyonic Island@Wroclaw, Poland j vs q Lattice result on s ( j ) (Bilgici et al., ‘09) Imaginary m : change configuration Model w/o Z(3) : q = j + p (cf. NJL, Mukherjee et al., PRD’10) Model w/o Z(3) : q = j + p (cf. NJL, Mukherjee et al., PRD’10) w/ Z(3) : fix F = F(q=0) then re-calculate s(q) w/ Z(3) : fix F = F(q=0) then re-calculate s(q) Periodicity : 2 p Configuration independent of j S (1) : dressed Polyakov loop

28. Kenji Morita 21 May 2011 28/18 Three Days on Quarkyonic Island@Wroclaw, Poland RW endpoint / Phase diagram q=p/3

29. Kenji Morita 21 May 2011 29/18 Three Days on Quarkyonic Island@Wroclaw, Poland Modified dual order parameters Use q Confinement : s ~ cos 3q Confinement : s ~ cos 3q deconfinement : s ~ cos q deconfinement : s ~ cos q Comparison with Polyakov loop (n=1)