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QCD Phase diagram and its verification in HIC

QCD Phase diagram and its verification in HIC. Krzysztof Redlich University of Wroclaw. Chiral transition and O(4) pseudo-critical line in LGT Probing O(4) criticality with Charge fluctuations theoretical expectations and STAR data

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QCD Phase diagram and its verification in HIC

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  1. QCD Phase diagram and its verification in HIC Krzysztof Redlich University of Wroclaw • 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 T A-A collisions fixed LHC Quark-Gluon Plasma Chiral symmetry restored Hadronic matter Chiral symmetry broken x B Collaboration: B. Friman, O. Kaczmarek,, F. Karsch, K. Morita, Pok. Man Lo, C. Sasaki & V. Skokov Collaboration: P. Braun-Munzinger, B. Friman , F. Karsch, K. Morita, C. Sasaki & V. Skokov 1st principle calculations: perturbation theory pQCD LGT

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

  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? Asakawa-Yazaki Stephanov et al., Hatta & Ikeda CP At the CP: Divergence of Fluctuations, Correlation Length and Specific Heat

  4. The phase diagram at finite quark masses Critical region • 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 Phys. Rev. D83, 014504 (2011) Phys. Rev. D80, 094505 (2009)

  5. O(4) scaling and magnetic equation of state QCD chiral crossover transition in the critical region of the O(4) 2nd order • Phase transition encoded in • the magnetic equation • of state O(4)/O(2) 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)

  6. Quark fluctuations and O(4) universality class • 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 with HRG

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

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

  9. A. Andronic et al., Nucl.Phys.A837:65-86,2010. • Particleyields and their ratio, as well as LGT results (F. Karsch, A. Tawfik, S. Ejiri & K.R.) welldescribed by the HRG . Budapest-Wuppertal 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 B.J. Schaefer & J. Wambach,; B. Stokic, B. Friman & K.R. q q - Full propagators with k < q < L GL=S classical Integrating from k=L to k=0 gives a full quantum effective potential Put Wk=0(smin) into the integral formula for P(N)

  11. Ratios of cumulantsatfinitedensity: PQM +FRG B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694 HRG HRG HRG 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 !

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

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

  14. 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 ?

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

  16. 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.

  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 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

  19. 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

  20. 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

  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) 2-flavors of improved Wilson quarks WHOT QCD Coll:

  22. 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

  23. 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

  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 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)

  26. 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

  27. 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)

  28. 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]

  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

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