Kenji Morita 21 May 2011Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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.

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland Mean field approximation Thermodynamic potential Order parameters

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland Phase diagram / RW transition

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland Phase diagram / chiral transition Discontinuity induced by | F | Smooth change Cusp induced by RW transition

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

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland CEP Mechanism G s cr G s < 4.12 GeV -2 G s < 4.12 GeV -2 ( L = GeV, m =0) ( L = 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 )

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland Sensitivity to the transitions DeconfinementChiral

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland n=3 n=3 : “Baryons” CEP RW endpoint T c at q=0 T c at q=p/3

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland Backup Slides

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland Polyakov loops at phys. quark mass

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland n=3 for phys. quark mass

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic 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

Kenji Morita 21 May /18 Three Days on Quarkyonic Poland RW endpoint / Phase diagram q=p/3

Kenji Morita 21 May /18 Three Days on Quarkyonic 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)