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Critical endpoint for deconfinement in matrix model and other effective models

RIKEN L unch Seminar. Critical endpoint for deconfinement in matrix model and other effective models. Kouji Kashiwa (Koji Kashiwa). Recent works:. Todays main!. Phys. Rev. D 85 (2012) 114029 , 『 Critical endpoint for deconfinement in matrix and other effective models 』

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Critical endpoint for deconfinement in matrix model and other effective models

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  1. RIKEN Lunch Seminar Critical endpoint for deconfinement in matrix model and other effective models Kouji Kashiwa(Koji Kashiwa) Recent works: Todays main! Phys. Rev. D 85 (2012) 114029, 『Critical endpoint for deconfinement in matrix and other effective models 』 K.K., R. D. Pisarski, V. V. Skokov. Todays sub-main hep-ph/1206.0685, 『Polyakov loop and QCD thermodynamics from the gluon and ghost propagators』 K. Fukushima, K.K.. In preparation ( will be submitted soon), 『Extraction of nontrivial correlation between chiral and deconfinement transitions from two-color QCD at imaginary chemical potential』 K.K., T. Sasaki, H. Kouno, M. Yahiro. In preparation, 『Mesonic fluctuation effects on Roberge-Weiss endpoint』 K.K..

  2. Contents: Introduction Schematic figure of QCD phase diagram 3-d Colombia plot Chiral and deconfinement transition Formalism Polyakov-loop effective potential Matrix model for deconfinement transition Potential from Landau-gauge lattice propagators Numerical results and discussion Summary

  3. Introduction: QCD phase diagram K. Fukushima and T. Hatsuda, Rept.Prog.Phys.74 (2011) 014001. Schematic QCD phase diagram At m=0, lattice QCD simulations provide important information. At finite m, lattice QCD simulations are broken down… Effective model approaches are widely used.

  4. Introduction: Chiral and deconfinement transition Chiral condensate Chiral phase transition Order-parameter of the spontaneous chiral symmetry breaking. It generate the heavy constituent quark mass at low temperature and baryon density. Spontaneous mass generation (simple case) Polyakov-loop Deconfinement phase transition Order-parameter of the spontaneous center symmetry breaking. (at least in the infinite quark mass limit) Free energy for single quark excitation. L. D. McLerran and B. Svetitsky, Phys. Rev. D 24 (1981) 450.

  5. Introduction: Colombia plot C. Bonati, P. de Forcrand, M. D'Elia, O. Philipsen, F. Sanfilippo, arXiv:hep-ph/ 1201.2769. 3-d Clombia plot ex.) H. Saito, et al, (WHOT-QCD Collaboration), arXiv:1202.6113. ex.) M. D'Elia, F. Sanfilippo, PRD 80 (2009) 111501(R). ex.) P. de Forcrand, O. Philipsen, arXiv:hep-lat/1004.3144.

  6. Introduction: Colombia plot Recently, several situations are energetically considered. (Such situations are sometime not realistic, but it is very important!) Imaginary chemical potential So many works… Iso-spin chemical potential with zero baryon chemical potential or finite imaginary m. P. Cea, L. Cosmai, M. D'Elia, A. Papa, PoS LAT2009:192,2009. Y. Sakai, H. Kouno, M. Yahiro, J. Phys. G 37 (2010) 105007. Response of temporal boundary angle for quarks (Dual quark condensate) E. Bilgici, F. Bruckmann, C. Gattringer, C. Hagen, Phys. Rev. D 77 (2008)094007. C. S. Fischer, Phys. Rev. Lett. 103 (2009) 052003. K. K., H. Kouno, M. Yahiro, Phys. Rev. D 80 (2009) 117901. Flavor-dependent twisted boundary angle H. Kouno, Y. Sakai, T. Makiyama, K. Tokunaga, T. Sasaki, M. Yahiro, arXiv:hep-ph/1202.5584. To understand the QCD phase structure, different type of the chemical potential may be important!

  7. Introduction: Polyakov-loop dynamics Most simple method to investigate the chiral and deconfinement transition: Polyakov-loop extended Nambu—Jona-Lasinio (PNJL) model Polyakov-loop extended quark-meson (PQM) model Both models are consistent at least in the first-order derivative expansion. T. Eguchi,Phys. Rev. D14 (1976) 2755. The most important problem is how to describe the deconfinement transition. The gluon dynamics is introduced by additional terms in addition to the matter part. We need the effective potential to describe the Polyakov-loop dynamics!

  8. Formalism Polyakov-loop effective potential Matrix model for deconfinement transition Potential from Landau-gauge lattice gluon and ghost propagators

  9. Polyakov-loop effective potential Formalism Polyakov-loop effective potential Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Polyakov-loop effective potential Polyakov-loop effective potential are based on the strong coupling expansion K. Fukushima, Phys. Lett. B 591 (2004) 277. S. Rossner, C. Ratti and W. Weise. Phys. Rev. D75, 034007 (2007). … Logarithm term comes from the Haar measure. (Vandermond determinant) Parameters are fitted to reproduce LQCD data in pure gauge limit.

  10. Polyakov-loop effective potential Formalism Polyakov-loop effective potential Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Polyakov-loop effective potential Polyakov-loop effective potential are based on the strong coupling expansion K. Fukushima, Phys. Lett. B 591 (2004) 277. S. Rossner, C. Ratti and W. Weise. Phys. Rev. D75, 034007 (2007). … Recently, more systematic studies not this approach is done. C. Sasaki and K. Redlich, hep-ph/1204.4330. M. Ruggieri and , hep-ph/1204.5995. Above potential is the limiting case of their potential. Problem: We can not go large Nc easily. Transverse gluon effects are still bit unclear.

  11. Polyakov-loop effective potential Formalism Polyakov-loop effective potential Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Moreover, the potential can not be expressed by the Polyakov-loop and its conjugate in the case of the color number larger than four. For example, see P. N. Meisinger, T. R. Miller, M. C. Ogilvie, PRD 65 (2002) 034009. The perturbative potential at high T D. Gross, R. D. Pisarski, and L. Yaffe, Rev. Mod. Phys. 53(1981) 43. N. Weiss, Phys. Rev. D 24 (1981) 475. In following, I call it as Yaffe potential. M. Sakamoto, K. Takenaga. Phys. Rev. D 76 (2007) 085016. Polyakov-loop is expressed by the fundamental trace, but this one-loop potentials havethe adjoint trace. N. Weiss, Phys. Rev. D 24 (1981) 475. This potential leads the perturbative vacuum.

  12. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators The Polyakov-loop effective potential approach has some big problems. The natural approach is based on the perturbative potential to satisfy the clear Stefan-Boltzmann limit and have the connection with large Nc. Matrix model for deconfinement transition ! P. N. Meisinger, T. R. Miller, M. C. Ogilvie, PRD 65 (2002) 034009. A. Dumitru, Y. Guo, Y. Hidaka, C. P. K. Altes, R. D. Pisarski, PRD 83 (2011) 034022. This approach is based on the Weiss potential. Effects of transverse gluon are clear. To describe the deconfinement transition, we must introduce the non-perturbative effects. There is unclearness how to include the non-perturbative effect… ( In this study, we add additional one-loop potential with few parameter. )

  13. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Matrix model for deconfinement This work improves these studies: P. N. Meisinger, T. R. Miller, M. C. Ogilvie, PRD 65 (2002) 034009. A. Dumitru, Y. Guo, Y. Hidaka, C. P. K. Altes, R. D. Pisarski, PRD 83 (2011) 034022. Phys. Rev. D 85 (2012) 114029, 『Critical endpoint for deconfinement in matrix and other effective models 』 K.K., R. D. Pisarski, V. V. Skokov.

  14. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Polyakov-loop dynamics is dominated by thegluon one-loop potential Basic matrix model for deconfinement + SB limit It comes from the adjoint trace. This potential comes from transverse gluon. Longitudinalgluon contribution is vanished by the Fadeev-Popov determinant. There is the cubic term which can lead the first-order transition. Non-perturbative effects are taken into account by the one-loop order. A. Dumitru, Y. Guo, Y. Hidaka, C. P. K. Altes, R. D. Pisarski, Phys. Rev. D 83 (2011) 034022.

  15. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators New matrix model for deconfinement transition SB limit Confined vacuum is r = 0 Perturbative vacuum is r = 1 , ,

  16. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Modification of parameter Meisinger-Miller-Ogilvie model It is equivalent with the MIT Bag constant. A. Dumitru, Y. Guo, Y. Hidaka, C. P. Korthals Altes, R. D. Pisarski, arXiv:hep-ph/1205.0137.

  17. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators Fermion dynamics Some details at high T; P. N. Meisinger, M. C. Ogilvie, Phys. Rev. D 65 (2002) 056013. f Large quark mass expansion Boltzmann factor Asymptotic behavior (x to infinity) of the second kind of the modified Bessel function

  18. Polyakov-loop effective potential Formalism: Matrix model for deconfinement transition Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators We construct the effective model which based on the perturbative one-loop potential. To obtain better result, we newly introduce the one more parameter and r2 coefficient. We can describe all T region. New parameter make the interaction measure more consistent with lattice QCD data. r2 coefficient remove the unphysical behavior below Tc. There are other methods to include the non-perturbative effects. Potential from Landau-gauge lattice gluon and ghost propagators

  19. Numerical results: Gluon and ghost potential in Landau gauge Potential from Landau-gauge lattice gluon and ghost propagators This study is a extension to finite T of the paper J. Braun, H. Gies, J. M. Pawlowski, Phys. Lett. B 684 (2010) 262 by using more simple approach. They based on the FRG and DS equation. hep-ph/1206.0685, 『Polyakov loop and QCD thermodynamics from the gluon and ghost propagators』 K. Fukushima, K.K..

  20. Polyakov-loop effective potential Introduction: Gluon and ghost potential in Landau gauge Matrix model for deconfinement Potential from Landau gauge gluon and ghost propagators In the matrix model for deconfinement, the non-perturbative effects are taken in to account by the additional one-loop potential. We start from the Landau-gauge gluon and ghost propagators obtained by lattice QCD simulation. Transverse gluon and ghost propagators Zc Lattice data: R. Aouaneet al., PRD 85 (2012) 034501. The non-perturbative effect came into through the infrared and mid-momentum region of propagators. Main uncleanness come from error of lattice QCD data, for example the finite size effect.

  21. Numerical results Matrix model for deconfinement transition Potential from Landau-gauge lattice gluon and ghost propagators

  22. Numerical results: Matrix model for deconfinement transition Matrix model for deconfinement This work improves these studies: P. N. Meisinger, T. R. Miller, M. C. Ogilvie, PRD 65 (2002) 034009. A. Dumitru, Y. Guo, Y. Hidaka, C. P. K. Altes, R. D. Pisarski, PRD 83 (2011) 034022. Phys. Rev. D 85 (2012) 114029, 『Critical endpoint for deconfinement in matrix and other effective models 』 K.K., R. D. Pisarski, V. V. Skokov.

  23. Numerical results: Matrix model for deconfinement transition K.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029. 2-d Clombia plot Model dependence is quite large! It is reflected how strong the first-order is in heavy quark mass limit. The quark mass is then considered as the external field which breaks the Z3 symmetry explicitely.

  24. Numerical results: Matrix model for deconfinement transition K.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029. 2-d Clombia plot Model dependence is quite large! It is reflected how strong the first-order is in heavy quark mass limit. The quark mass is then considered as the external field which breaks the Z3 symmetry explicitely.

  25. Numerical results: Matrix model for deconfinement transition K.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029. Interaction measure Non-trivial structure appears! We can observe two-peak structure? The dynamical quark should be introduced. At this quark mass, previous approximated expression is already good. However, such simple term leads this nontrivial structure! T [GeV]

  26. Numerical results: Matrix model for deconfinement transition K.K., R. D. Pisarski, V. V. Skokov, Phys. Rev. D 85 (2012) 114029. Interaction measure Model difference also appears on the interaction measure. Log-type Polyakov-loop effective potential dose not have the two-peak structure.

  27. Numerical results: Gluon and ghost potential in Landau gauge Potential from Landau-gauge lattice gluon and ghost propagators This study is a extension to finite T of the paper J. Braun, H. Gies, J. M. Pawlowski, Phys. Lett. B 684 (2010) 262 by using more simple approach. They based on the FRG and DS equation. hep-ph/1206.0685, 『Polyakov loop and QCD thermodynamics from the gluon and ghost propagators』 K. Fukushima, K.K..

  28. Numerical results: Gluon and ghost potential in Landau gauge K. Fukushima, K.K., hep-ph/1206.0685. Propagators in Landau gauge We use Gribov-Stingl type function to fit LQCD data. Gluon propagator Ghost dressing function T = 0.86 Tc T = 0.84 Tc Lattice data: R. Aouaneet al., PRD 85 (2012) 034501.

  29. Numerical results: Gluon and ghost potential in Landau gauge K. Fukushima, K.K., hep-ph/1206.0685. Phase transition in SU(2) and SU(3) We can naturally reproduce the first and second order deconfinement transition! Tc = 286 MeV for SU(3) We use the same values shown in R. Aouane et al., PRD 85 (2012) 034501.

  30. Numerical results: Gluon and ghost potential in Landau gauge K. Fukushima, K.K., hep-ph/1206.0685. Thermodynamics Near Tc, we obtain consistent result with lattice QCD data. At low T, energy and entropy densities go to minus… Ghost effects are still bit strong… In this study, we neglect the temperature- dependence of propagators. SB limit can be obtained. Lattice data: S. Datta and S. Gupta, PRD 82 (2010) 114505.

  31. Numerical results: Gluon and ghost potential in Landau gauge K. Fukushima, K.K., hep-ph/1206.0685. NJL part: Quark contributions We introduce the NJL model as a mimic of matter part of QCD. LQCD data: S. Borsanyi, et al., arXiv:hep-lat/1005.3508. LQCD data: S. Borsanyi, et al., JHEP 11 (2010) 077.

  32. Summary

  33. Summary: We investigate the deconfinement transition by using matrix model which is based on the perturbative one-loop potential. In the upper part of the Colombia plot, we can see the large difference between effective models. There are several method to include the non-pertubative effects to describe the deconfinement transition: Additional one-loop potentials with one or two parameter, Landau-gauge lattice gluon and ghost propagators, These models can reproduce the correct form of perturbative behavior of QCD and therefore, it may suitable to investigate the QCD phase structure than the standard Polyakov-loop effective potential.

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