Heavy-ion dynamics in the PHSD model

Transcription

1 Heavy-ion dynamics in the PHSD model Elena Bratkovskaya Institut für f r Theoretische Physik & FIAS, Uni. Frankfurt QCD Hadronization and Statistical Model, ECT, Trento, Italy, 6-10 October,

2 The holy grail of heavy-ion physics: Search for the possible critical point The phase diagram of QCD Study of the phase transition from hadronic to partonic matter Quark-Gluon Gluon-Plasma Study of the in-medium properties of hadrons at high baryon density and temperature 2

3 Signals of the phase transition: Multi-strange particle enhancement in A+A Charm suppression Collective flow (v 1, v 2, v 3, v 4 ) Thermal dileptons Jet quenching and angular correlations High p T suppression of hadrons Nonstatistical event by event fluctuations and correlations Chiral Magnetic Effect Experiment: measures final hadrons and leptons How to learn about physics from data? Compare with theory! Microscopic transport models provide a unique dynamical description of nonequilibrium effects in heavy-ion collisions! 3

4 Semi-classical BUU equation Boltzmann -Uehling-Uhlenbeck Uhlenbeck equation (non-relativistic formulation) - propagation of particles in the self-generated Hartree-Fock mean-field potential U(r,t) with an on-shell collision term: t r r f (, p,t r r f (, p,t ) + ) r p r m r r r f (, p,t ) r U(,t self-generated Hartree-Fock mean-field potential: r r r r r U(,t ) = d r d p V (,t ) f (, p,t ) 3 ( 2πh ) β occ ) r r r f (, p,t ) = r r r collision p term: coll eleastic and inelastic reactions is the single particle phase-space space distribution function - probability to find the particle at position r with momentum p at time t + ( Fock f t term ) Ludwig Boltzmann Collision term for (let s s consider fermions) : r r r r Icoll = d p2 d p3 d 12 ( p1 + p2 p3 p 3 4 ( 2 ) Ω υ δ π Probability including Pauli blocking of fermions: P = f3 f4 ( 1 f1 )( 1 f2 ) f1 f2( 1 f3 )( 1 f4 Gain term: Loss term: dσ ) ( ) P dω ) 1 2 t υ

5 Dynamical description of strongly interacting systems Semi-classical BUU solution for weakly interacting systems of particles How to describe strongly interacting systems?! Quantum field theory Kadanoff-Baym dynamics for resummed(!) single-particle Green functions S < (1962) Green functions S < /self-energies energies Σ: is is is is < xy > xy c xy a xy = η {Φ = {Φ( = T = T c a + ( y )Φ( x ) } y )Φ + {Φ( x )Φ {Φ( x )Φ ( x ) } + + ( y ) } ( y ) } causal anticausal S S ret xy adv xy = S = S c xy c xy S S < xy > xy = S η = ± 1( bosons / T a (T c = S > xy < xy S S a xy a xy fermions ) retarded advanced ) ( anti )time ordering Integration over the intermediate spacetime operator 1 µ x Ŝ0 x ( x µ + M 2 0 ) Leo Kadanoff Gordon Baym 5

6 From Kadanoff-Baym equations to generalized transport equations After the first order gradient expansion of the Wigner transformed Kadanoff-Baym equations and separation into the real and imaginary parts one gets: Generalized transport equations (GTE): drift term Vlasov term backflow term collision term = loss term - gain term Backflow term incorporates the off-shell behavior in the particle propagation! vanishes in the quasiparticle limit A XP δ(p 2 -M 2 ) GTE: Propagation of the Green s s function is < XP =A XP N XP, which carries information not only on the number of particles (N XP ),, but also on their properties, interactions and correlations (via A XP ) Spectral function: ret Γ XP = Im Σ XP width of spectral function = reaction rate of particle (at space-time position X) 4-dimentional generalizaton of the Poisson-bracket: W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445 6

7 General testparticle off-shell equations of motion W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445 Employ testparticle Ansatz for the real valued quantity i S < XP - insert in generalized transport equations and determine equations of motion! General testparticle off-shell equations of motion for the time-like particles: with 7

8 Collision term in off-shell transport models Collision term for reaction 1+2->3+4: with The trace over particles 2,3,4 reads explicitly for fermions for bosons additional integration The transport approach and the particle spectral functions are fully f determined once the in-medium transition amplitudes G are known in their off-shell dependence! 8

9 Detailed balance on the level of 2< >n: 2 treatment of multi-particle collisions in transport approaches Generalized collision integral for n <->m reactions: W. Cassing, NPA 700 (2002) 618 is Pauli-blocking or Bose-enhancement enhancement factors; η=1 for bosons and η= 1 for fermions is a transition probability 9

10 Antibaryon production in heavy-ion reactions Multi-meson fusion reactions m 1 +m m n B+Bbar (m=π,ρ,ω,..) important for antiproton, antilambda dynamics! W. Cassing, NPA 700 (2002) 618 2< > Pb+Pb, 160 A GeV dn/dt [arb. units] 10 1 central BB->X 3 mesons -> BB t [fm/c] approximate equilibrium of annihilation and recreation 10

11 From hadrons to partons In order to study the phase transition from hadronic to partonic matter Quark-Gluon Gluon-Plasma we need a consistent non-equilibrium (transport) model with explicit parton-parton interactions (i.e. between quarks and gluons) beyond strings! explicit phase transition from hadronic to partonic degrees of freedom lqcd EoS for partonic phase Transport theory: : off-shell Kadanoff-Baym equations for the Green-functions S < h(x,p) in phase-space space representation for the partonic and hadronic phase Parton-Hadron-String-Dynamics (PHSD( PHSD) QGP phase described by Dynamical QuasiParticle article Model (DQPM) W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3 A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 11

12 Dynamical QuasiParticle Model (DQPM) - Basic ideas: DQPM describes QCD properties in terms of resummed single-particle Green s functions in the sense of a two-particle irreducible (2PI( 2PI) ) approach: Gluon propagator: - 1 =P 2 -Π gluon self-energy: energy:π=m g2 -i2γ g ω Quark propagator: S -1 q = P 2 -Σ q quark self-energy: energy:σ q =M q2 -i2γ q ω the resummed properties are specified by complex self-energies energies which depend on temperature: -- the real part of self-energies energies (Σ q,π) describes a dynamically generated mass (M q,m g ); -- the imaginary part describes the interaction width of partons (Γ q, Γ g ) space-like part of energy-momentum tensor T µν defines the potential energy density and the mean-field potential (1PI) for quarks and gluons (U q, U g ) 2PI framework guaranties a consistent description of the system in- and out-of off equilibrium on the basis of Kadanoff-Baym equations with proper states in equilibrium A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 12

13 The Dynamical QuasiParticle Model (DQPM) Properties of interacting quasi-particles: massive quarks and gluons (g, q, q bar with Lorentzian spectral functions : 4ωΓi(T) ( i = q,q, g ) ρ i( ω,t ) = 2 v ω p M (T) + 4ω bar ) ( ) Γ (T) Modeling of the quark/gluon masses and widths HTL limit at high T quarks: mass: gluons: i i width: N c = 3, N f =3 running coupling (pure glue): fit to lattice (lqcd) results (e.g. entropy density) with 3 parameters: T s /T c =0.46; c=28.8; λ=2.42 (for pure glue N f =0) DQPM: Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) lqcd: pure glue 13

14 The Dynamical QuasiParticle Model (DQPM) fit to lattice (lqcd) results (e.g. entropy density) * BMW lqcd data S. Borsanyi et al., JHEP 1009 (2010) 073 Quasiparticle properties: large width and mass for gluons and quarks T C =158 MeV ε C =0.5 GeV/fm 3 DQPM matches well lattice QCD DQPM provides mean-fields (1PI) for gluons and quarks as well as effective 2-body 2 interactions (2PI) DQPM gives transition rates for the formation of hadrons PHSD Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 14 14

15 Parton Hadron String Dynamics I. From hadrons to QGP: Initial A+A collisions: - string formation in primary NN collisions - strings decay to pre-hadrons (B - baryons, m mesons) Formation of QGP stage by dissolution of pre-hadrons into massive colored quarks + mean-field energy based on the Dynamical Quasi-Particle Model (DQPM) which defines quark spectral functions, masses M q (ε) and widths Γ q (ε) + mean-field potential U q at given ε local energy density ( related by lqcd EoS to T - temperature in the local cell) II. Partonic phase - QGP: quarks and gluons (= dynamical quasiparticles ) with off-shell spectral functions (width, mass) defined by the DQPM in self-generated mean-field potential for quarks and gluons U q, U g EoS of partonic phase: crossover from lattice QCD (fitted by DQPM) (quasi-) ) elastic and inelastic parton-parton interactions: using the effective cross sections from the DQPM III. Hadronization: based on DQPM massive, off-shell (anti-)quarks with broad spectral functions hadronize to off-shell mesons and baryons or color neutral excited states - strings (strings act as doorway states for hadrons) IV. Hadronic phase: hadron hadron-string interactions off-shell HSD QGP phase: ε > ε critical W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; EPJ ST 168 (2009) 3; NPA856 (2011)

16 Properties of the QGP in equilibrium using PHSD 16

17 Properties of parton-hadron matter in equilibrium The goal: V. Ozvenchuk et al., PRC 87 (2013) V. Ozvenchuk et al., PRC 87 (2013) study of the dynamical equilibration of QGP within the non-equilibrium off-shell PHSD transport approach transport coefficients (shear and bulk viscosities) of strongly interacting partonic matter particle number fluctuations (scaled variance, skewness, kurtosis) Realization: Initialize the system in a finite box with periodic boundary conditions for some energy density ε and chemical potential µ q Evolve the system in time until equilibrium is achieved 17

18 Properties of parton-hadron matter: shear viscosity η/s using Kubo formalism and the relaxation time approximation ( kinetic theory ) T=T C : η/s shows a minimum (~0.1) close to the critical temperature T>T C : QGP - pqcd limit at higher temperatures T<T C : fast increase of the ratio η/s for hadronic matter lower interaction rate of hadronic system smaller number of degrees of freedom (or entropy density) for hadronic matter compared to the QGP QGP Virial expansion: S. Mattiello, W. Cassing, Eur.. Phys. J. C 70, 243 (2010) QGP in PHSD = strongly-interacting liquid V. Ozvenchuk et al., PRC 87 (2013)

19 Properties of parton-hadron matter: electric conductivity The response of the strongly-interacting system in equilibrium to an external electric field ee z defines the electric conductivity σ 0 : the QCD matter even at T~ T T c is a much better electric conductor than Cu or Ag (at room temperature) by a factor of 500! W. Cassing et al., PRL 110(2013)

20 Charm spatial diffusion coefficient D s in the hot medium D s for heavy quarks as a function of T for q = 0, µ q =0 T < T c : hadronic D s L. Tolos, J. M. Torres-Rincon, Phys. Rev. D 88, (2013) T > T c : QGP D s pqcd - G. D. Moore, D. Teaney, Phys. Rev. C 71, (for α s =0.3) DQPM - H. Berrehrah et al, arxiv: [hep-ph] lqcd - Banerjee et al., Phys. Rev. D 85, (2012). Continuous transition! H. Berrehrah et al, arxiv: [hep-ph ph] 20

21 Bulk properties: rapidity, m T -distributions, multi-strange particle enhancement in Au+Au 21

22 PHSD for HIC (highlights) dn/dy y=0 / N wound Λ+Σ 0 NA57 NA Pb+Pb, 158 A GeV, mid-rapidity HSD PHSD Λ+Σ N wound N wound PHSD provides a consistent description of p+a and HIC dynamics 22

23 Collective flow: anisotropy coefficients (v 1, v 2 ) in A+A z x 23

24 Anisotropy coefficients Non central Au+Au collisions : interaction between constituents leads to a pressure gradient => spatial asymmetry is converted to an asymmetry in momentum space => collective flow v 2 > 0 from S. A. Voloshin, arxiv: v 2 > 0 indicates in-plane emission of particles v 2 < 0 corresponds to a squeeze-out perpendicular to the reaction plane (out( out-of-plane emission) 24

25 Collective flow: v 2 excitation functions The excitation function for v 2 of charged particles from string-hadron transport models : PHSD UrQMD QGP v 2 Influence of hadron potentials EoS Au+Au, mid-rapidity, semi-central protons RBUU (Munich), potential RBUU (Giessen), potential RBUU (Giessen), cascade GiBUU, potential GBUU, cascade EOS/ E895/ E877 FOPI/ Plastic Ball/ LAND/ MSU E beam [GeV] 25

26 Development of azimuthal anisotropies in time Time evolution of v n for Au + Au collisions at s 1/2 = 200 GeV with impact parameter b = 8 fm: Flow coefficients reach their asymptotic values by the time of fm/c after the beginning of the collision V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, V Phys. Rev. C 85 (2012)

27 Elliptic flow scaling at RHIC The mass splitting at low p T is approximately reproduced in PHSD as well as the meson-baryon splitting for p T > 2 GeV/c! The scaling of v 2 with the number of constituent quarks n q is roughly in line with the data. E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011)

28 BES RHIC: n q scaling with energy - particles STAR: PRL 110 (2013) Quark number scaling holds within ~10% separately for particles and antiparticles, except φ φ meson deviates at the lowest two energies but large error bars! 28

29 STAR: PRL 110 (2013) BES RHIC: n q scaling of v 2 with energy STAR Remarkable difference in v 2 between particles and antiparticles is observed break down of n q scaling of v 2 between particles and antiparticles at lower energies With decreasing energy: large hadronic corona hadronic mechanisms for the production of antiparticles start to dominate Influence of hadron potentials

30 In-plane flow v 1 at RHIC versus beam energy versus centrality PHSD: v 1 vs. pseudo-rapidity follows an approximate scaling for high invariant energies s 1/2 =39, 62, 200 GeV - in line with experimental data whereas at low energies the scaling is violated! V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, V Phys. Rev. C 85 (2012)

31 Collective flow signals of the Quark Gluon Plasma H. Stöcker cker, Nucl.. Phys. A 750, 121 (2005) Early hydro calculation predicted the softest point at E lab = 8 AGeV A linear extrapolation of the data (HS: arrow) suggests a collapse of flow at E lab = AGeV 31

32 Recent STAR measurements of v 1 of identified hadrons STAR collaboration, PRL 112, (2014) measured y-distributions y are smooth! (Net-)proton v 1 slope at midrapidity changes sign at s NN ~10 GeV EOS softest point? (1st order phase transition?)

33 PHSD: snapshot of the reaction plane, Au+Au, 11.5 GeV,, b=6 fm t = 3 fm/c t = 6 fm/c Color scale: baryon number density Black levels: : QGP- parton density 0.6 and 0.01 fm -3 Red arrows: local velocity of baryon matter Directed flow v 1 is formed at an early stage of the nuclear interaction but late stages matter! Baryons reach a positive and mesons a negative value of v 1 V. Konchakovski,, W. Cassing,, Yu. Ivanov,, V. Toneev, PRC90 (2014)

34 Directed flow from PHSD and HSD Au+Au, b=7 fm/c Models: * HSD (red) warning: : NO hadronic potentials, cascade mode! * PHSD (blue) repulsive parton potential Antiprotons in PHSD are produced dominantly from hadronization at highest energies; multi-meson meson fusion reactions are important for the v 1 at low energies! higher energies influence of QGP lower energies dominance of hadronic matter and hadronic reaction channels (absorption and recreation) Discrepancies at low energy indication on the influence of hadronic potentials (cf. AMPT results) V. Konchakovski,, W. Cassing,, Yu. Ivanov,, V. Toneev, PRC90 (2014) STAR Collaboration, PRL 112, (2014) 34

35 Excitation function of v 1 The slope of v 1 (y) at y=0: I.Transport F = dυ dy 1 y=0 slopes at midrapidity I.Transport models STAR Collaboration, PRL 112, (2014) PHSD/HSD : V. Konchakovski et al., PRC90 (2014) UrQMD: J. Steinheimer et al., PRC 89 (2014)

36 Excitation function of v 1 slopes I.Transport models II. Hydro models The slope of v (y) 1 at midrapidity: dυ F = dy Models: I. Transport models: HSD, PHSD, UrQMD II. Hydro models: 3D-Fluid Dynamic approach (3FD) 1 y=0 1FD-hydro with chiral cross-over over (χ)( ) and Bag Model (BM) EoS Hybrid-UrQMD with BM and χ-eos (shaded arria) smooth crossover?! STAR Collaboration, PRL 112, (2014) PHSD/HSD and 3D-fluid hydro: V. Konchakovski,, W. Cassing,, Yu. Ivanov,, V. Toneev,, PRC90 (2014) Hybrid/UrQMD UrQMD/Hydro: J. Steinheimer,, J. Auvinen,, H. Petersen, M. Bleicher,, H. Stöcker cker, PRC 89 (2014)

37 Excitation function of v 1 slopes of K,Kbar Without K, Kbar potential Including K, Kbar potential: From G-matrix: L. Tolós et al, PRC 65, (2002) Potential: attractive for K -, repulsive for K + U K - relevant for ρ B <3ρ 0 Strong influence of (anti-) kaon potential at low energies! at high energies partonic interactions are important (differences between HSD and PHSD) v 1 slopes s of K, Kbar at midrapidity sensitive to the dynamics! PHSD/HSD: W. Cassing, V. P. Konchakovski,, A. Palmese,, V. D. Toneev,, and E. L. Bratkovskaya, arxiv:

38 Messages from the directed flow analysis The PHSD reproduces the general trends in the v 1 (y) excitation functions in the energy range s s = GeV. We don't see any "wiggle-like" like" structures as expected by early hydro calculations but see a softening of the EoS in the BES range. The PHSD results differ from those of HSD where no explicit partonic degrees of freedom are incorporated. A comparison of both microscopic copic models has provided detailed information on the effect of parton dynamics on the directed flow (especially for pions). Inclusion of antiproton annihilation into several mesons as well as the inverse multi-meson meson fusion processes in HSD/PHSD help to reproduce antiproton directed flow at lower energies. 3-Fluid Dynamic approach (3FD) gives reasonable results for proton and pion slopes of v 1 but fails at 7.7 GeV for antiprotons Crossover transition agrees better with the experimental data than a pure hadronic EoS Sizeable effect of momentum dependent mean-fields on directed flows 38

39 Outlook - Perspectives What is the stage of matter close to T c and large µ: Lattice EQS for µ=0 crossover, T > T c 1st order phase transition? Mixed phase = interaction of partonic and hadronic degrees of freedom? Open problems: How to describe a first-order phase transition in transport models? How to describe parton-hadron interactions in a mixed phase? 39

40 PHSD group FIAS & Frankfurt University Giessen University Elena Bratkovskaya Wolfgang Cassing Rudy Marty Olena Linnyk Hamza Berrehrah Volodya Konchakovski Daniel Cabrera Thorsten Steinert Taesoo Song Alessia Palmese Andrej Ilner Eduard Seifert External Collaborations SUBATECH, Nantes University: Jörg Aichelin Christoph Hartnack Pol-Bernard Gossiaux Vitalii Ozvenchuk Texas A&M University: Che-Ming Ko JINR, Dubna: Viacheslav Toneev Vadim Voronyuk BITP, Kiev University: Mark Gorenstein Barcelona University: Laura Tolos Angel Ramos 40