The Polyakov loop and charge fluctuations and QCD critical points

1. The Polyakov loop and charge fluctuations and QCD critical points Krzysztof Redlich University of Wroclaw • Deconfinement in SU(N) pure gauge theory and Polyakov loop fluctuations • Modelling deconfinement in the limit of heavy quarks • Polyakov loop fluctuations in the presence of dynamical quarks • Chiral transition and O(4) • criticality: charge fluctuations and • their probability distributions Coll. with: BengtFriman, Olaf Kaczmarek, Pok. Man Lo, Kenji Morita & Chihiro Sasaki

2. Polyakov loop on the lattice needs renormalization • Introduce Polyakov loop: • Renormalized ultraviolet divergence • Usually one takes as an order parameter HotQCD Coll.

3. To probe deconfinement : consider fluctuations SU(3) pure gauge: LGT data • Fluctuations of modulus of the Polyakov loop However, the Polyakov loop Thus, one can consider fluctuations of the real and the imaginary part of the Polyakov loop. HotQCD Coll.

4. Fluctuations of the real and imaginary part of the renormalized Polyakov loop • Imaginary part fluctuations • Real part fluctuations Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013)

5. Compare different Susceptibilities: • Systematic differences/simi-larities of the Polyakov lopp susceptibilities • Consider their ratios!

6. Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • In the deconfined phase Indeed, in the real sector of Z(3) Expand modulus and find: Expand the modulus, get in the leading order thus

7. Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • In the confined phase Indeed, in the Z(3) symmetric phase, the probability distribution is Gaussian to the first approximation, with the partition function consequently Expand modulus and find: Thus and In the SU(2) case is in agreement with MC results

8. Ratio Imaginary/Real of Polyakov loop fluctuations Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) • In the confined phase for any symmetry breaking operator its average vanishes, thus and thus • In deconfined phase the ratio of and its value is model dependent

9. Ratio Imaginary/Real and gluon screening WHOT QCD Coll: • In the confined phase • WHOT QCD Coll. (Y. Maezawa et al.) and WHOT-coll. identified as the magnetic and electric mass: Since Phys. Rev. D81 091501 (2010) 2-flavors of improved Wilson quarks

10. String tension from the PL susceptibilities Pok Man Lo, et al. ( in preparation) • Common mass scale for • In confined phase a natural choose for M O. Kaczmarek, et al. 99 string tension

11. Effective chiral models and gluon potential • coupling with meson fields PQM chiral model • FRG thermodynamics of PQM model: • Nambu-Jona-Lasinio model PNJL chiral model the invariant Polyakov loop potential (C. Sasaki et al; J. Pawlowski et al,.) the SU(2)xSU(2) invariant quark interactions described through: K. Fukushima;C. Ratti & W. Weise; B. Friman , C. Sasaki ., …. B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman, V. Skokov, ... B. Friman, V. Skokov, B. Stokic & K.R., …..

12. Polyakov loop parameters, fixed from a pure glue Lattice Thermodynamics • Polynomial potential results in thus is not applicable! • fixed to reproduce pure SU(3) lattice results K. Fukushima, C. Ratti & W. Weise

13. C. Sasaki, et al. PRD (13)

14. The minimal potential needed to incorporate Polyakov loop fluctuations Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.

15. Deconfinement phase transition in the heavy quark region 2nd order • Modelling the partition function • background field approach a

16. PL and heavy quark coupling • Effective potential • Tree level result where Compare with LGT: G. Green & F. Karsch (83)

17. The critical point of the 2nd order transition Pok Man Lo, et al. ( in preparation)

18. Susceptibility at the critical point • Divergent longitudinal susceptibility at the critical point =1.48 GeV

19. Critical masses and temperature values Pok Man Lo, et al. • Different values then in the matrix model by K. Kashiwa, R. Pisarski and V. Skokov, Phys. Rev. D85 (2012) LGT C. Alexandrou et al. (99)

20. Polyakov loop and fluctuations in QCD • Smooth behavior for the Polyakov loop and fluctuations difficult to determine where is “deconfinement” HOT QCD Coll The inflection point at

21. The influence of fermions on the Polyakov loop susceptibility ratio • Z(3) symmetry broken, however ratios still showing deconfinement • Dynamical quarks imply smoothening of the susceptibilities ratio, between the limiting values as in the SU(3) pure gauge theory Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. • Change of the slope in the narrow temperature range signals color deconfinement this work

22. The influence of fermions on ratios of the Polyakov loop susceptibilities • Z(3) symmetry broken, however ratios still showing the transition • Change of the slopes at fixed T Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.

23. Heavy quarks contribution Pok Man Lo, et al. ( in preparation) • Heavy quark mass limit consitent with pure gauge theory results • Ratio obtained by integrating Polyakov loop correlations

24. Probing deconfinement in QCD lattice with p4 fermion action • HRG factorization of pressure: Pok Man Lo, B. Friman, (013) O. Kaczmarek, C. Sasaki & K.R. • Kurtosis measures the squared of the baryon number carried by leading particles in a medium S. Ejiri, F. Karsch & K.R. (06) S. Ejiri, F. Karsch & K.R. (06) S. Ejiri, F. Karsch & K.R. (06)

25. Kurtosis of net quark number density in PQM model V. Skokov, B. Friman &K.R. due to „confinement” properties • For the assymptotic value • Smooth change with a very weak dependence on the pion mass • For

26. Probing deconfinement in QCD lattice with p4 fermion action Pok Man Lo, B. Friman, (013) O. Kaczmarek, C. Sasaki & K.R. • The change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value • In the presence of quarks there is “remnant” of Z(N) symmetry in the ratio, indicating deconfi- nement of quarks S. Ejiri, F. Karsch & K.R. (06)

27. Probing deconfinement in QCD Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. Change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value • In the presence of quarks there is “remnant” of Z(N) symmetry in the ratio, indicating deconfi- nement Still the lattice finite size effects need to be studied S. Ejiri, F. Karsch & K.R. (06) Ch. Schmidt This paper 150 200 T[MeV]

28. Polyakov loop susceptibility ratios still away from the continuum limit: • The renormalization of the Polyakov loop susceptibilities is still not well described: Still strong dependence on in the presence of quarks. Ch. Schmidt et al.

29. Quark fluctuations and O(4) universality class • Due to the expected O(4) scaling in QCD the free energy: • Consider generalized susceptibilities of the net-quark number • Since for , are well described by the search for deviations (in particular for larger n) from HRG to quantify the contributions of , i.e. the O(4) criticality with HRG S. Ejiri, F. Karsch & K.R. Phys. Lett. B633, (2006) 275 M. Asakawa, S. Ejiri and M. Kitazawa, Phys. Rev. Lett. 103 (2009) 262301 V. Skokov, B. Stokic, B. Friman &K.R. Phys. Rev. C82 (2010) 015206 F. Karsch & K. R. Phys.Lett. B695 (2011) 136 B. Friman, et al. . Phys.Lett. B708 (2012) 179, Nucl.Phys. A880 (2012) 48

30. Ratios of cumulantsatfinitedensity in PQM model with FRG B. Friman, V. Skokov &K.R. Phys.Rev. C83 (2011) 054904 B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694 18 HRG value 9 HRG value -9 -18 Deviations from low -T HRG values are increasing with and the cumulant order . Negative fluctuations near the chiral crossover.

31. O(4) pseudo- critical line LHC Chiral crossover • Is therea memorythatthe system haspassedthrough a region of QCD O(4)-chiral crossover transition? • Chemical freezeout and the QCD chiral crossover O(4) universality A. Andronic et al., Nucl.Phys.A837:65-86,2010. LHC J. Stachel et. al. HotQCD Collaboration HRG model Chiral crossover Temperature from LGT HotQCD Coll. (QM’12) Chemical Freezeout LHC (ALICE) Peter Braun-Munzinger

32. STAR data on the first four moments of net baryon number STAR DATA Deviations from the HRG Data qualitatively consistent with the change of these ratios due to the contribution of the O(4) singular part to the free energy HRG

33. Theoretical predictions and STAR data Deviation from HRG if freeze-out curve close to Phase Boundary/Cross over line L. Chen, QM 12 STAR Data Polyakov loop extended Quark Meson Model Lattice QCD STAR Preliminary Strong deviatins of data from the HRG model (regular part of QCD partition function) results: Remnant of O(4) criticality ?

34. Moments obtained from probability distributions • Moments obtained from probability distribution • Probability quantified by all cumulants • In statistical physics Cumulants generating function:

35. What is the influence of O(4) criticality on P(N)? P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R. Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48) • For the net baryon number use the Skellam distribution (HRG baseline) as the reference for the non-critical behavior • Calculate P(N) in an effective chiral model which exhibits O(4) scaling and compare to the Skellamdistribtuion

36. The influence of O(4) criticality on P(N) for K. Morita, B. Friman &K.R. (PQM model within renormalization group FRG) • Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance at different • Ratios less than unity near the chiral crossover, indicating the contribution of the O(4) criticality to the thermodynamic pressure

37. The influence of O(4) criticality on P(N) for K. Morita, B. Friman et al. • Take the ratio of which contains O(4) dynamics to Skellam distribution with the same Mean and Variance near • Asymmetric P(N) • Near the ratios less than unity for

38. Probability distribution of net proton number STAR Coll. data at RHIC Thanks to Nu Xu and Xiofeng Luo STAR data Do we also see the O(4) critical structure in these probability distributions ? Efficiency uncorrected data!!

39. The influence of O(4) criticality on P(N) for K. Morita, B. Friman & K.R. • In central collisions the probability behaves as being influenced by the chiral transition STAR DATA

40. Centrality dependence of probability ratio K. Morita et al. Non- critical behavior O(4) critical Cleymans & Redlich Andronic, Braun- Munzinger & Stachel • For less central collisions, the freezeout appears away of the pseudocritical line, resulting in an absence of the O(4) critical structure in the probability ratio.

41. Conclusions: • Ratios of the Polyakov loop and the Net-charge susceptibilities are excellent probes of deconfinement and/or the O(4) chiral crossover transition in QCD • Systematics of the net-proton fluctuations and their probability distributions measured by STAR are qualitatively consistent with the expectations that they are influenced by the O(4) criticality. • quantitative consistency will be possible by comparing • data with LGT results