A-A collisions fixed T LQCD LHC Quark-Gluon Plasma Chiral symmetry

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Presentation transcript:

Confronting fluctuations of conserved charges in HIC at the LHC with lattice QCD A-A collisions fixed T LQCD LHC Quark-Gluon Plasma Chiral symmetry restored Hadronic matter Fluctuations of conserved charges at the LHC and LQCD results P. Braun-Munzinger, A. Kalweit and J. Stachel The influence of critical fluctuations on the probability distribution of net baryon number B. Friman & K. Morita Chiral symmetry broken x B > 1st principle calculations: perturbation theory pQCD > LGT

Deconfinement and chiral symmetry restoration in QCD The QCD chiral transition is crossover Y.Aoki, et al Nature (2006) and appears in the O(4) critical region Chiral transition temperature Deconfinement of quarks sets in at the chiral crossover The shift of with chemical potential LHC Pisarski & Wilczek; Critical region O. Kaczmarek et.al. Phys.Rev. D83, 014504 (2011) TCP Asakawa-Yazaki Rajagopal, Schuryak Stephanov; Hatta, et al. CP T. Bhattacharya et.al. Phys. Rev. Lett. 113, 082001 (2014) A.Bazavov, Phys.Rev. D85 (2012) 054503 See also: Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S. D. Katz, et al. JHEP, 0906 (2009) Ch. Schmidt Phys.Rev. D83 (2011) 014504

Excellent data of ALICE Collaboration for particle yields A. Kalweit ALICE Time Projection Chamber (TPC), Time of Flight Detector (TOF), High Momentum Particle Identification Detector (HMPID) together with the Transition Radiation Detector (TRD) and the Inner Tracking System (ITS) provide information on the flavour composition of the collision fireball, vector meson resonances, as well as charm and beauty production through the measurement of leptonic observables.

Consider fluctuations and correlations of conserved charges They are quantified by susceptibilities: If denotes pressure, then Susceptibility is connected with variance If probability distribution of then

Consider special case: P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R. Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48) Charge and anti-charge uncorrelated and Poisson distributed, then the Skellam distribution Then the susceptibility =>

Consider special case: particles carrying P. Braun-Munzinger, B. Friman, F. Karsch, V Skokov &K.R. Phys .Rev. C84 (2011) 064911 Nucl. Phys. A880 (2012) 48) The probability distribution Fluctuations Correlations

Variance at 200 GeV AA central coll. at RHIC Consistent with Skellam distribution The maxima of have a very similar values at RHIC and LHC STAR Collaboration P. Braun-Munzinger, et al. Nucl. Phys. A880 (2012) 48) thus const., indeed Momentum integrated:

Probing O(4) chiral criticality with charge fluctuations Due to expected O(4) scaling in QCD the free energy: Generalized susceptibilities of net baryon number At only with receive contribution from At only with receive contribution from Generalized susceptibilities of the net baryon number never critical with respect to ch. sym. F. Karsch & K. R. Phys.Lett. B695 (2011) 136 B. Friman, et al. . Phys.Lett. B708 (2012) 179, Nucl.Phys. A880 (2012) 48 with

Constructing net charge fluctuations and correlation from ALICE data Net baryon number susceptibility Net strangeness Charge-strangeness correlation

constructed from ALICE particle yields use also from pBe at Net baryon fluctuations Net strangeness fluctuations Charge-Strangeness corr. Ratios is volume independent and

Compare the ratio with LQCD data: A. Bazavov, H.-T. Ding, P. Hegde, O. Kaczmarek, F. Karsch, E. Laermann, Y. Maezawa and S. Mukherjee Phys.Rev.Lett. 113 (2014) and HotQCD Coll. A. Bazavov et al. Phys.Rev. D86 (2012) 034509 Is there a temperature where calculated ratios from ALICE data agree with LQCD?

Baryon number strangeness and Q-S correlations There is a very good agreement, within systematic uncertainties, between extracted susceptibilities from ALICE data and LQCD at the chiral crossover Compare at chiral crossover How unique is the determination of the temperature at which such agreement holds?

Consider T-dependent LQCD ratios and compare with ALICE data The LQCD susceptibilities ratios are weakly T-dependent for We can reject for saturation of at LHC and fixed to be in the range , however LQCD => for thermodynamics cannot be anymore described by the hadronic degrees of freedom

Extract the volume by comparing data with LQCD Since thus All volumes, should be equal at a given temperature if originating from the same source

Particle density and percolation theory Density of particles at a given volume Total number of particles in HIC at LHC, ALICE Percolation theory: 3-dim system of objects of volume take => => P. Castorina, H. Satz &K.R. Eur.Phys.J. C59 (2009)

Constraining the volume from HBT and percolation theory Some limitation on volume from Hanbury-Brown–Twiss: HBT volume Take ALICE data from pion interferometry If the system would decouple at the chiral crossover, then From these results: variance extracted from LHC data consistent with LQCD at where the fireball volume

Excellent description of the QCD Equation of States by Hadron Resonance Gas A. Bazavov et al. HotQCD Coll. July 2014 F. Karsch et al. HotQCD Coll. “Uncorrelated” Hadron Gas provides an excellent description of the QCD equation of states in confined phase “Uncorrelated” Hadron Gas provides also an excellent description of net baryon number fluctuations

Thermal origin of particle yields with respect to HRG Rolf Hagedorn => the Hadron Resonace Gas (HRG): “uncorrelated” gas of hadrons and resonances A. Andronic, Peter Braun-Munzinger, & Johanna Stachel, et al. Particle yields with no resonance decay contributions: Measured yields are reproduced with HRG at

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

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 at different K. Morita, B. Friman &K.R. (PQM model within renormalization group FRG) Ratios less than unity near the chiral crossover, indicating the contribution of the O(4) criticality to the thermodynamic pressure

Conclusions: From a direct comparison of fluctuations constructed with ALICE data to LQCD: Skellam distribution, and its generalization, is a good approximation of the net charge probability distribution P(N) for small N. The chiral criticality sets in at larger N and results in the shrinking of P(N) relative to the Skellam function . there is thermalization in heavy ion collisions at the LHC and the 2nd order charge fluctuations and correlations are saturated at the chiral crossover temperature

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

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 at different K. Morita, B. Friman &K.R. (QM model within renormalization group FRG) Ratio < 1 at larger |N| if c6/c2 < 1

Modelling O(4) transtion: effective Lagrangian and FRG 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)

Higher moments of baryon number fluctuations B. Friman, K. Morita, V. Skokov & K.R. If freeze-out in heavy ion collisions occurs from a thermalized system close to the chiral crossover temperature, this will lead to a negative sixth and eighth order moments of net baryon number fluctuations. These properties are universal and should be observed in HIC experiments at LHC and RHIC Figures: results of the PNJL model obtained within the Functional Renormalisation Group method

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 at different K. Morita, B. Friman &K.R. (QM model within renormalization group FRG) Ratios less than unity near the chiral crossover, indicating the contribution of the O(4) criticality to the thermodynamic pressure

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