1. T BB Hadronic matter Quark-Gluon Plasma Chiral symmetry broken Chiral symmetry restored LHC A-A collisions fixed x 1 st principle calculations: perturbation theory pQCD LGT QCD Phase diagram and its verification in HIC Krzysztof Redlich University of Wroclaw Collaboration: P. Braun-Munzinger, B. Friman, F. Karsch, K. Morita, C. Sasaki & V. Skokov Chiral transition and O(4) pseudo-critical line in LGT Probing O(4) criticality with Charge fluctuations theoretical expectations and STAR data Deconfinement in SU(N) pure gauge theory and in QCD from LGT Collaboration: B. Friman, O. Kaczmarek,, F. Karsch, K. Morita, Pok. Man Lo, C. Sasaki & V. Skokov

2. QCD phase diagram and the O(4) criticality In QCD the quark masses are finite: the diagram has to be modified Expected phase diagram in the chiral limit, for massless u and d quarks: Pisarki & Wilczek conjecture TCP: Rajagopal, Shuryak, Stephanov Y. Hatta & Y. Ikeda TCP

3. The phase diagram at finite quark masses The u,d quark masses are small Is there a remnant of the O(4) criticality at the QCD crossover line? CP Asakawa-Yazaki Stephanov et al., Hatta & Ikeda At the CP: Divergence of Fluctuations, Correlation Length and Specific Heat

4. The phase diagram at finite quark masses Can the QCD crossover line appear in the O(4) critical region? YES, It has been confirmed in LQCD calculations TCP CP LQCD results: BNL-Bielefeld Critical region Phys. Rev. D83, 014504 (2011 ) Phys. Rev. D80, 094505 (2009)

5. O(4) scaling and magnetic equation of state Phase transition encoded in the magnetic equation of state pseudo-critical line F. Karsch et al universal scaling function common for all models belonging to the O(4) universality class: known from spin models J. Engels & F. Karsch (2012) QCD chiral crossover transition in the critical region of the O(4) 2 nd order O(4)/O(2)

6. 6 Due to expected O(4) scaling in QCD the free energy: Consider generalized susceptibilities of 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 F. Karsch & K. R. Phys.Lett. B695 (2011) 136 B. Friman, et al.. Phys.Lett. B708 (2012) 179, Nucl.Phys. A880 (2012) 48 Quark fluctuations and O(4) universality class with HRG

7. 7 Only 3-parameters needed to fix all particle yields Tests of equlibration of 1 st “moments”: particle yields resonance dominance: Rolf Hagedorn, Hadron Resonance Gas (HRG) partition funct ion Breit-Wigner res. particle yield thermal density BR thermal density of resonances

8. Thermal yields and parameters and their energy dependence in HIC Thermal origin of particle yields in HIC is well justified A. Andronic, P. Braun-Munzinger & J. Stachel, Nucl. Phys. (06) Phys.Rev. C73 (2006) 034905 J. Cleymans et al. P. Braun-Munzinger et al. QM^12

9. Particle yields and their ratio, as well as LGT results (F. Karsch, A. Tawfik, S. Ejiri & K.R.) well described by the HRG. A. Andronic et al., Nucl.Phys.A837:65-86,2010. Budapest-Wupperta l Chemical freezeout defines a lower bound for the QCD phase boundary HotQCD Coll.

10. Quark-meson model w/ FRG approach Effective potential is obtained by solving the exact flow equation (Wetterich eq.) with the approximations resulting in the O(4) critical exponents - Full propagators with k < q < L qq Integrating from k = L to k = 0 gives a full quantum effective potential Put W k =0 ( s min ) into the integral formula for P(N) B. Stokic, B. Friman & K.R. G L =S classical B.J. Schaefer & J. Wambach,;

11. Deviations of the ratios of odd and even order cumulants from their asymptotic, low T-value: are increasing with and the cumulant order Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations ! Ratios of cumulants at finite density: PQM +FRG HRG B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694 HRG

12. STAR data on the first four moments of net baryon number 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 STAR DATA Phys. Rev. Lett in print

13. Deviations of the ratios from their asymptotic, HRG values, are increasing with the order of the cumulants Ratio of higher order cumulants in PQM model B. Friman, V. Skokov &K.R. Phys. Rev. C83 (2011) 054904 Negative ratio! HRG

14. Theoretical predictions and STAR data 14 Deviation from HRG if freeze-out curve close to Phase Boundary/Cross over line Lattice QCD Polyakov loop extended Quark Meson Model STAR Data STAR Preliminary L. Chen, QM 12 Strong deviatins of data from the HRG model (regular part of QCD partition function) results: Remnant of O(4) criticality ?

15. Polyakov loop on the lattice needs renormalization Introduce Polyakov loop: Renormalized ultraviolet divergence Usually one takes as an order parameter 15 HotQCD Coll.

16. To probe deconfinement : consider fluctuations 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. SU(3) pure gauge: LGT data HotQCD Coll.

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

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

19. Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement 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: Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R., PRD (2013) In the SU(2) case is in agreement with MC resul ts Thus and

20. Ratio Imaginary/Real of Polyakov loop fluctuations 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 Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R., PRD (2013)

21. Ratio Imaginary/Real and gluon screening 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) WHOT QCD Coll: 2-flavors of improved Wilson quarks

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

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

24. 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

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

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

27. Probing deconfinement in QCD 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 Pok Man Lo, B. Friman, (013) O. Kaczmarek, C. Sasaki & K.R. S. Ejiri, F. Karsch & K.R. (06) lattice with p4 fermion action

28. Probing deconfinement in QCD 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 Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. S. Ejiri, F. Karsch & K.R. (06) Ch. Schmidt This paper 150 200 T[MeV]

29. 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.

30. Conclusions: Chiral transition in QCD belong to the O(4) universality class Ratios the Net-charge susceptibilities are excellent probes of the O(4) chiral crossover in QCD Systematics of the net-proton number fluctuations and their probability distributions measured by STAR are qualitatively consistent with the expectation, that they are influenced by the O(4) criticality. Ratios of different Polyakov loop susceptibilities are excellent and novel probe of deconfinement in QCD There is a coincident between deconfinement and O(4) chiral crossover in QCD at small baryon density