The Polyakov loop and charge fluctuations and QCD critical points 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 Krzysztof Redlich University of Wroclaw Coll. with: Bengt Friman, Olaf Kaczmarek, Pok. Man Lo, Kenji Morita & Chihiro Sasaki

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

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.

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)

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

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

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

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)

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. D (2010) WHOT QCD Coll: 2-flavors of improved Wilson quarks

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

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 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,... the invariant Polyakov loop potential ( C. Sasaki et al; J. Pawlowski et al,.) B. Friman, V. Skokov, B. Stokic & K.R., …..

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

C. Sasaki, et al. PRD (13)

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

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

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

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

Susceptibility at the critical point Divergent longitudinal susceptibility at the critical point =1.48 GeV

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

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

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

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.

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

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:

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

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

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 T[MeV]

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 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 Quark fluctuations and O(4) universality class 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) V. Skokov, B. Stokic, B. Friman &K.R. Phys. Rev. C82 (2010) F. Karsch & K. R. Phys.Lett. B695 (2011) 136 B. Friman, et al.. Phys.Lett. B708 (2012) 179, Nucl.Phys. A880 (2012) 48

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

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

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

Theoretical predictions and STAR data 33 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 ?

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

What is the influence of O(4) criticality on P(N)? 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 Skellam distribtuion P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R. Phys.Rev. C84 (2011) Nucl. Phys. A880 (2012) 48)

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 K. Morita, B. Friman &K.R. (PQM model within renormalization group FRG) The influence of O(4) criticality on P(N) for

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 K. Morita, B. Friman et al.

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

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

Centrality dependence of probability ratio O(4) critical Non- critical behavior 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. K. Morita et al. Cleymans & Redlich Andronic, Braun- Munzinger & Stachel

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