1. 1 Theory and HPC Elena Bratkovskaya Institut für Theoretische Physik & FIAS, Uni. Frankfurt HIC for FAIR Physics Day: HPC Computing, FIAS, Frankfurt am Main 11 November 2014 11 November 2014

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

3. Physics at FAIR FAIR energies are well suited to study dense and hot nuclear matter :  a phase transition to QGP  in-medium effects of hadrons  chiral symmetry restoration Way to study: Experimental energy scan of different observables in order to find an ‚anomalous‘ behavior by comparing with theory  Dynamical models of HIC!

4. 4 Dynamical models for HIC Macroscopic Microscopic Macroscopic Microscopic ‚Hybrid‘ QGP phase: hydro with QGP EoS ‚Hybrid‘ QGP phase: hydro with QGP EoS  hadronic freeze-out: after burner - hadron-string transport model (‚hybrid‘-UrQMD, EPOS, …) (‚hybrid‘-UrQMD, EPOS, …) fireball models:  no explicit dynamics: parametrized time evolution (TAMU) ideal (Jyväskylä,SHASTA, TAMU, …) Non-equilibrium microscopic transport models – based on many-body theory Hadron-string models (UrQMD, IQMD, HSD, QGSM …) Partonic cascades pQCD based (Duke, BAMPS, …) Parton-hadron models:  QGP: pQCD based cascade  massless q, g  hadronization: coalescence (AMPT, HIJING) (AMPT, HIJING)  QGP: lQCD EoS  massive quasi-particles (q and g with spectral functions) in self-generated mean-field (q and g with spectral functions) in self-generated mean-field  dynamical hadronization  HG: off-shell dynamics (applicable for strongly interacting systems) viscous (Romachkke,(2+1)D VISH2+1, (3+1)D MUSIC,…) hydro-models: hydro-models:  description of QGP and hadronic phase by hydrodanamical equations for fluid  assumption of local equilibrium  EoS with phase transition from QGP to HG  initial conditions (e-b-e, fluctuating)

5. 5 Theoretical description of ‘in-medium effects’ Many-body theory: Strong interaction  large width = short life-time  broad spectral function  quantum object  broad spectral function  quantum object  How to describe the dynamics of broad strongly interacting quantum states in transport theory? Barcelona / Valencia group  (1783)N -1 and  (1830)N -1 exitations  semi-classical BUU  generalized transport equations first order gradient expansion of quantum Kadanoff-Baym equations In-medium effects = changes of particle properties in the hot and dense baryonic medium; example – vector mesons, strange mesons

6. 66 Semi-classical BUU equation Boltzmann-Uehling-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: is the single particle phase-space distribution function - probability to find the particle at position r with momentum p at time t  self-generated Hartree-Fock mean-field potential: Ludwig Boltzmann collision term: elastic and inelastic reactions Probability including Pauli blocking of fermions: Gain term: 3+4  1+2 Loss term: 1+2  3+4 Collision term for 1+2  3+4 (let‘s consider fermions) :  Collision term for 1+2  3+4 (let‘s consider fermions) : 1 2 3 4

7. 77 Dynamical description of strongly interacting systems  Semi-classical on-shell BUU: applies for small collisional width, i.e. for a weakly interacting systems of particles  Quantum field theory  Kadanoff-Baym dynamics for resummed single-particle Green functions S < (1962) Leo Kadanoff Gordon Baym Green functions S < /self-energies  : Integration over the intermediate spacetime How to describe strongly interacting systems?!

8. 88 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: Backflow term incorporates the off-shell behavior in the particle propagation Backflow term incorporates the off-shell behavior in the particle propagation ! vanishes in the quasiparticle limit A XP   (p 2 -M 2 ) ! vanishes in the quasiparticle limit A XP   (p 2 -M 2 )  Spectral function: – ‚width‘ of spectral function = reaction rate of particle (at space-time position X) – ‚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  GTE: Propagation of the Green‘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 ) drift term Vlasov term collision term = ‚gain‘ - ‚loss‘ term backflow term Generalized transport equations (GTE):  Life time

9. 99 General testparticle off-shell equations of motion  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 W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

10. 10 Collision term in off-shell transport models Collision term for reaction 1+2->3+4: Collision term for reaction 1+2->3+4: with The trace over particles 2,3,4 reads explicitly for fermions for bosons The transport approach and the particle spectral functions are fully determined once the in-medium transition amplitudes G are known in their off-shell dependence! additional integration ‚loss‘ term ‚gain‘ term ‚gain‘ term

11. In-medium transition rates: G-matrix approach Need to know in-medium transition amplitudes G and their off-shell dependence dependence Coupled channel G-matrix approach Transition probability : with G(p, ,T) - G-matrix from the solution of coupled-channel equations: G Baryons: Pauli blocking and potential dressing Baryons: Pauli blocking and potential dressing Meson selfenergy and spectral function Meson selfenergy and spectral function  For strangeness: D. Cabrera, L. Tolos, J. Aichelin, E.B., arXiv:1406.2570; W. Cassing, L. Tolos, E.B., A. Ramos, NPA727 (2003) 59

12. Collision width in off-shell transport model ! Assumptions used in transport calculations for V-mesons (to speed up calculations): Collision width in low density approximation:  coll =  VN tot  Collision width in low density approximation:  coll =  VN tot  replace  VN tot  by averaged value G=const:  coll =  G replace  VN tot  by averaged value G=const:  coll =  G (Works well – cf. low density approximation vs. the full dynamical calculation of  Coll in Ref. E.B., NPA696 (2001) 761)  Collision width is defined by all possible interactions in the local cell  Example: Collision width  coll for 1+2->3+4 process – defined from the loss term of the collision integral I coll :  Total width  collision width  decay width  =  coll +  dec In the vacuum:  =  dec In the vacuum:  =  dec (similar for the n m reactions!) (similar for the n m reactions!)

13. Mean-field potential in off-shell transport model Interacting relativistic particles have a complex self-energy:  By dispersion relation we get a contribution to the real part of self-energy: that gives a mean-field potential U XP via:  Many-body theory: to the inverse livetime of the particle  ~1/ . to the inverse livetime of the particle  ~1/ .  The collision width  coll is determined from the loss term of the collision integral I coll  =  coll +  dec The neg. imaginary part is related via the complex self-energy relates in a self-consistent way to the self-generated mean-field potential and collision width (inverse lifetime)  the complex self-energy relates in a self-consistent way to the self-generated mean-field potential and collision width (inverse lifetime)

14. 1414 Detailed balance on the level of 2 n: treatment of multi-particle collisions in transport approaches Detailed balance on the level of 2 n: treatment of multi-particle collisions in transport approaches W. Cassing, NPA 700 (2002) 618 Generalized collision integral for n m reactions: is Pauli-blocking or Bose-enhancement factors;  =1 for bosons and  =-1 for fermions is a transition probability  huge CPU!

15. 1515 Antibaryon production in heavy-ion reactions Antibaryon production in heavy-ion reactions W. Cassing, NPA 700 (2002) 618 Multi-meson fusion reactions m 1 +m 2 +...+m n  B+Bbar (m=   important for antiproton, antilambda dynamics ! 2<->3  approximate equilibrium of annihilation and recreation

16. 16 From hadrons to partons In order to study the phase transition from hadronic to partonic matter – Quark-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 Parton-Hadron-String-Dynamics (PHSD) QGP phase described by Dynamical QuasiParticle Model DQPM Dynamical QuasiParticle Model (DQPM) Transport theory: off-shell Kadanoff-Baym equations for the Green-functions S < h (x,p) in phase-space representation for the partonic and hadronic phase A. Peshier, W. Cassing, PRL 94 (2005) 172301; A. Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3

17. 17 DQPM describes QCD properties in terms of ‚resummed‘ single-particle Green‘s functions – in the sense of a two-particle irreducible (2PI) approach: A. Peshier, W. Cassing, PRL 94 (2005) 172301; A. Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) Dynamical QuasiParticle Model (DQPM) - Basic ideas:  the resummed properties are specified by complex self-energies which depend on temperature: -- the real part of self-energies (Σ q, Π) describes a dynamically generated mass (M q,M g ); -- the imaginary part describes the interaction width of partons (  q,  g ) -- the real part of self-energies (Σ q, Π) describes a dynamically generated mass (M q,M g ); -- the imaginary part describes the interaction width of partons (  q,  g )  space-like part of energy-momentum tensor T  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-off equilibrium on the basis of Kadanoff-Baym equations with proper states in equilibrium Gluon propagator: Δ -1 =P 2 - Π gluon self-energy: Π=M g 2 -i2  g ω Quark propagator: S q -1 = P 2 - Σ q quark self-energy: Σ q =M q 2 -i2  q ω

18. 18 The Dynamical QuasiParticle Model (DQPM) Properties of interacting quasi-particles: massive quarks and gluons (g, q, q bar ) with Lorentzian spectral functions : DQPM: Peshier, Cassing, PRL 94 (2005) 172301; DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) with 3 parameters: T s /T c =0.46; c=28.8; =2.42 (for pure glue N f =0)  fit to lattice (lQCD) results (e.g. entropy density)  running coupling (pure glue): N c = 3, N f =3 mass: mass: width:  gluons:  quarks: lQCD: pure glue  Modeling of the quark/gluon masses and widths  HTL limit at high T

19. 19 The Dynamical QuasiParticle Model (DQPM) Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)  Quasiparticle properties:  large width and mass for gluons and quarks DQPM matches well lattice QCD DQPM matches well lattice QCD DQPM provides mean-fields (1PI) for gluons and quarks DQPM provides mean-fields (1PI) for gluons and quarks as well as effective 2-body interactions (2PI) DQPM gives transition rates for the formation of hadrons  PHSD DQPM gives transition rates for the formation of hadrons  PHSD  fit to lattice (lQCD) results (e.g. entropy density) * BMW lQCD data S. Borsanyi et al., JHEP 1009 (2010) 073 T C =158 MeV  C =0.5 GeV/fm 3 19

20. 20 Initial A+A collisions: - string formation in primary NN collisions - strings decay to pre-hadrons (B - baryons, m – mesons) 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 (  ) and widths  q (  ) + mean-field potential U q at given  – local energy density ( related by lQCD EoS to T - temperature in the local cell) 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 (  ) and widths  q (  ) + mean-field potential U q at given  – local energy density ( related by lQCD EoS to T - temperature in the local cell) Parton Hadron String Dynamics I. From hadrons to QGP: QGP phase:  >  critical II. Partonic phase - QGP: quarks and gluons (= ‚dynamical quasiparticles‘) with off-shell spectral functions (width, mass) defined by the DQPM 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 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) 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 (quasi-) elastic and inelastic parton-parton interactions: using the effective cross sections from the DQPM IV. Hadronic phase: hadron-string interactions – off-shell HSD 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) 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) III. Hadronization: based on DQPM W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; EPJ ST 168 (2009) 3; NPA856 (2011) 162.

21. PHSD – ‚femto‘ accelerator

22. 22 PHSD code: structure over B, ISUBS NUM NUM NUM NUM PHSD is the parallel ensembles code!!! loop over NUM – parallel ensembles or ‚events‘:  needed for the smooth description of the mean-field properties as energy density or baryon density  possible parallelization HSD mode

23. 23 PHSD running time  HPC PHSD mode: Au+Au/Pb+Pb, central, t final = 40 fm/c PHSD mode: Au+Au/Pb+Pb, central, t final = 40 fm/c Elab, AGeV S 1/2, GeV CPU time, h NUM CPU time/NUM 10.74.860.25014.4sec 408.860.7510027sec 8012.41.1510041.4sec 15817.30.85057.6sec 213002001.75157min 406000027601.8521.6min NUM – the number of parallel ensembles/events PHSD is the open source code for the FAIR experiments: http://fias.uni-frankfurt.de/~brat/PHSD/index4.html  CPU time per event grows with energy  PHSD mode (for RHIC, LHC) – more time consuming than HSD from V. Konchakovski

24. 24 PHSD for HIC (highlights) PHSD for HIC (highlights)  PHSD provides a consistent description of p+A and HIC dynamics

25. 25 The most CPU costly observables (some examples)

26. (Multi-)strange particles in Au+Au

27. 27 Multi-strange baryon production Multi-strange hyperons (Ξ, Ω) are promising probes to study: in-medium effects at low bombarding energy in-medium effects at low bombarding energy QGP properties at high energy density QGP properties at high energy density  Elementary production:  In heavy-ion reactions: sub-threshold channels, e.g. Production through these channels highly depends on baryon density (and it‘s fluctuations) Production through these channels highly depends on baryon density (and it‘s fluctuations) (E beam > 3.7 GeV) (E beam > 7.0 GeV) CBM

28. Centrality dependence of (multi-)strange (anti-)baryons  enhanced production of (multi-) strange antibaryons in PHSD strange antibaryons _ _  +  0 multi-strange antibaryon _  + multi-strange baryon   - strange baryons  +  0 Cassing & Bratkovskaya, NPA 831 (2009) 215

29. Exitation function of (multi-)strange (anti-)baryons

30. Collective flow: anisotropy coefficients (v 1, v 2, v 3, v 4 ) in A+A x z

31. 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 indicates in-plane emission of particles v 2 < 0 corresponds to a squeeze-out perpendicular to the reaction plane (out-of-plane emission) v 2 > 0 from S. A. Voloshin, arXiv:1111.7241

32. 32 Directed flow signals of the Quark–Gluon Plasma H. Stöcker, Nucl. Phys. A 750, 121 (2005) Early hydro calculation predicted the “softest point” at E lab = 8 AGeV Early hydro calculation predicted the “softest point” at E lab = 8 AGeV A linear extrapolation of the data (arrow) suggests a collapse of flow at E lab = 30 AGeV A linear extrapolation of the data (arrow) suggests a collapse of flow at E lab = 30 AGeV

33. 33 Color scale: baryon number density Black levels: QGP- parton density 0.6 and 0.01 fm -3 Red arrows: local velocity of baryon matter Color scale: baryon number density Black levels: QGP- parton density 0.6 and 0.01 fm -3 Red arrows: local velocity of baryon matter t = 3 fm/c t = 6 fm/c PHSD: snapshot of the reaction plane V. Konchakovski, W. Cassing, Yu. Ivanov, V. Toneev, PRC(2014), arXiv:1404.2765 Directed flow v 1 is formed at an early stage of the nuclear interaction Directed flow v 1 is formed at an early stage of the nuclear interaction Baryons are reaching positive and mesons – negative value of v 1 Baryons are reaching positive and mesons – negative value of v 1

34. 34 STAR Collaboration, arXiv:1401.3043 PHSD/HSD and 3D-fluid hydro: V. Konchakovski, W. Cassing, Yu. Ivanov, V. Toneev, PRC(2014), arXiv:1404.2765 Hybrid/UrQMD/Hydro: J. Steinheimer, J. Auvinen, H. Petersen, M. Bleicher, H. Stöcker, PRC 89 (2014) 054913 Excitation function of v 1 slopes The slope of v 1 (y) at midrapidity: The slope of v 1 (y) at midrapidity: Models:  HSD, PHSD  3D-Fluid Dynamic approach (3FD)  UrQMD  Hybrid-UrQMD  1FD-hydro with chiral cross-over and Bag Model (BM) EoS crossover?!  smooth crossover?!

35. Elliptic flow v 2 vs. collision energy for Au+Au v 2 in PHSD is larger than in HSD due to the repulsive scalar mean-field potential U s (ρ) for partons  v 2 in PHSD is larger than in HSD due to the repulsive scalar mean-field potential U s (ρ) for partons  v 2 grows with bombarding energy due to the increase of the parton fraction V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, Phys. Rev. C 85 (2012) 011902

36. Flow coefficients versus centrality at RHIC increase of v 2 with impact parameter but flat v 3 and v 4  increase of v 2 with impact parameter but flat v 3 and v 4 V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, Phys. Rev. C 85 (2012) 044922

37. Fluctuations and correlations

38. Lattice QCD: Critical Point Fluctuations of the quark number density (susceptibility) at  q >0 [F. Karsch et al.] Lattice QCD  predictions:  (quark number density fluctuations) will diverge at the critical chiral point =>  q (quark number density fluctuations) will diverge at the critical chiral point => Experimental observation – look for non-monotonic behavior of the observables near the critical point non-monotonic behavior of the observables near the critical point :  baryon number fluctuations  charge number fluctuations  multiplicity fluctuations  particle ratio fluctuations (K/ , K/p,  )  mean p T fluctuations  2 particle correlations ...

39. Multiplicity fluctuations in p+p  Scaled variance - multiplicity fluctuations in some acceptance (charge, strangeness, etc.): The excitation functions of N ch and charge multiplicity fluctuations  ch from HSD are approximately in line with experimental data  The excitation functions of N ch and charge multiplicity fluctuations  ch from HSD are approximately in line with experimental data

40.  Multiplicity fluctuations for 1%MC practically do not depend on atomic mass for y>0 and only slightly grow with increasing collision energy. rapidity y>0 rapidity y>0  HSD (and UrQMD) show a plateau on top of which the SHINE Collaboration expects to find increasing multiplicity fluctuations as a "signal" for the critical point ! Multiplicity fluctuations in HSD: 1%MC 40 Konchakovski, Lungwitz, Gorenstein, Bratkovskaya, Phys. Rev. C78 (2008) 024906 Gazdzicki, PoS CPOD2006:016

41. Charge fluctuations 41  The decay of resonances strongly modifies the initial QGP fluctuations! HSD: Phys. Rev. C74 (2006) 64911 NA49: Phys. Rev. C70 (2004) 064903  sensitive to the EoS at the early stage of the collision and to its changes in the deconfinement phase transition region  net-charge fluctuations are smaller in QGP than in a hadron gas Jeon, Koch, PRL85 (2000) 2076 Asakawa, Heinz, Muller PRL85 (2000) 2072

42. K/  -ratio fluctuations: Transport models vs Data 42 Exp. data show a plateau from top SPS up to RHIC energies and an increase towards lower SPS energies  evidence for a critical point at low SPS energies ? but the HSD (without QGP!) results shows the same behavior  K/  -ratio fluctuation is driven by hadronic sources  No evidence for a critical point in the K/  ratio ? K/  ratio fluctuation is sensitive to the acceptance! HSD: Phys. Rev. C 79 (2009) 024907 UrQMD: J. Phys. G 30 (2004) S1381, PoS CFRNC2006,017 NA49: 0808.1237 STAR: 0901.1795  In GCE for ideal Boltzman gas:

43. 43 Outlook - Perspectives What is the stage of matter close to T c and large  :  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 a first-order phase transition in transport models? How to describe parton-hadron interactions in a ‚mixed‘ phase? How to describe parton-hadron interactions in a ‚mixed‘ phase? Lattice EQS for m=0  ‚crossover‘, T > T c

44. 44 FIAS & Frankfurt University Elena Bratkovskaya Rudy Marty Hamza Berrehrah Daniel Cabrera Taesoo Song Andrej Ilner Giessen University Wolfgang Cassing Olena Linnyk Volodya Konchakovski Thorsten Steinert Alessia Palmese 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 PHSD group

45. 45  strongly interacting quasi-particles - massive quarks and gluons (g, q, q bar ) with sizeable collisional widths in self-generated mean-field potential Parton-Hadron-String-Dynamics (PHSD) PHSD is a non-equilibrium transport model with  explicit phase transition from hadronic to partonic degrees of freedom  lQCD EoS for the partonic phase  explicit parton-parton interactions - between quarks and gluons  dynamical hadronization  QGP phase is described by the Dynamical QuasiParticle Model DQPM  QGP phase is described by the Dynamical QuasiParticle Model (DQPM)  Transport theory: generalized off-shell transport equations based on the 1st order gradient expansion of Kadanoff-Baym equations (applicable for strongly interacting system!) A. Peshier, W. Cassing, PRL 94 (2005) 172301; W. Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3  Spectral functions:

46. 46 Dileptons

47. 47 Dilepton sources  from the QGP via partonic (q,qbar, g) interactions:  from hadronic sources: direct decay of vector direct decay of vector mesons (  J  ‘) Dalitz decay of mesons Dalitz decay of mesons and baryons (  0, , ,…) correlated D+Dbar pairs correlated D+Dbar pairs radiation from multi-meson reactions (  + ,  + ,  + ,  + ,  +a 1 ) - ‚4  ‘ radiation from multi-meson reactions (  + ,  + ,  + ,  + ,  +a 1 ) - ‚4  ‘ hadronic bremsstrahlung hadronic bremsstrahlung **** g **** **** q l+l+ -l--l- **** q q q q q qgg q +qq Plot from A. Drees ‚thermal QGP‘

48. 48 Lessons from SPS: NA60 PHSD: Linnyk et al, PRC 84 (2011) 054917  Dilepton invariant mass spectra: Fireball model – Renk/Ruppert Fireball model – Rapp/vanHees Ideal hydro model – Dusling/Zahed Hybrid-UrQMD: Santini et al., PRC84 (2011) 014901 Message from SPS: (based on NA60 and CERES data) 1) Low mass spectra - evidence for the in-medium broadening of  -mesons 2) Intermediate mass spectra above 1 GeV - dominated by partonic radiation 3) The rise and fall of T eff – evidence for the thermal QGP radiation 4) Isotropic angular distribution – indication for a thermal origin of dimuons  Inverse slope parameter T eff : spectrum from QGP is softer than from hadronic phase since the QGP emission occurs dominantly before the collective radial flow has developed NA60: Eur. Phys. J. C 59 (2009) 607 QGP PRL 102 (2009) 222301

49. 49 cocktail HSD Ideal hydro Dusling/Zahed Fireball model Rapp/vanHees cocktail HSD Ideal hydro Dusling/Zahed Fireball model Rapp/vanHees Dileptons at RHIC: PHENIX Message: Models provide a good description of pp data and peripheral Au+Au data, however, fail in describing the excess for central collisions even with in-medium scenarios for the vector meson spectral function Models provide a good description of pp data and peripheral Au+Au data, however, fail in describing the excess for central collisions even with in-medium scenarios for the vector meson spectral function The ‘missing source’(?) is located at low p T The ‘missing source’(?) is located at low p T Intermediate mass spectra – dominant QGP contribution Intermediate mass spectra – dominant QGP contribution PHENIX: PRC81 (2010) 034911 Linnyk et al., PRC 85 (2012) 024910

50. 50 Dileptons at RHIC: STAR data vs model predictions Centrality dependence of dilepton yield (STAR: arXiv:1407.6788 ) Message: STAR data are described by models within a collisional broadening scenario for the vector meson spectral function + QGP Excess in low mass region, min. bias Models (predictions): Models (predictions):  Fireball model – R. Rapp  PHSD Low masses: collisional broadening of  collisional broadening of  Intermediate masses: QGP dominant

51. 51 Dileptons from RHIC BES: STAR Message: BES-STAR data show a constant low mass excess (scaled with N(   )) within the measured energy range BES-STAR data show a constant low mass excess (scaled with N(   )) within the measured energy range PHSD model: excess increasing with decreasing energy due to a longer  -propagation in the high baryon density phase PHSD model: excess increasing with decreasing energy due to a longer  -propagation in the high baryon density phase  Good perspectives for future experiments – CBM(FAIR) / MPD(NICA) (Talk by Nu Xu at QM‘2014) (Talk by Nu Xi at 23d CBM Meeting‘14)

52. 52 Dileptons at LHC Message:  low masses - hadronic sources: in-medium effects for  mesons are small  intermediate masses: QGP + D/Dbar  charm ‘background’ is smaller than thermal QGP yield  QGP(qbar-q) dominates at M>1.2 GeV  clean signal of QGP at LHC! O. Linnyk, W. Cassing, J. Manninen, E.B., P.B. Gossiaux, J. Aichelin, T. Song, C.-M. Ko, Phys.Rev. C87 (2013) 014905; arXiv:1208.1279 QGP