Olena Linnyk Parton-hadron matter in and out of equilibrium

‚Little Bangs‘ in the Laboratory Equilibrium QGP? Initial State Hadronization Au quarks and gluons hadrons Parton Hadron String Dynamics (PHSD)

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 interactions between quarks and gluons (beyond strings)  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) ; A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3 From hadrons to partons

(First order gradient expansion of the Wigner-transformed Kadanoff-Baym equations) drift term Vlasov term collision term = ‚loss‘ term - ‚gain‘ term backflow term 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 = 2   (p 2 -M 2 ) ! vanishes in the quasiparticle limit A XP = 2   (p 2 -M 2 ) Propagation of the Green‘s function iS < XP =A XP f XP, which carries information not only on the number of particles, but also on their properties, interactions and correlations W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 4451 Boltzmann equation  off-shell transport GENERALIZATION  XP – width of spectral function = reaction rate of a particle (at phase-space position XP)

Lattice QCD  The Dynamical QuasiParticle Model (DQPM) 5 T C =160 MeV  C =0.5 GeV/fm 3 equation of state N f =3 lQCD: Fodor & Katz, (2009) lQCD: M. Cheng et al., PRD 77 (2008) S. Borsanyi et al., JHEP 1009, 073 (2010); JHEP 1011, 077 (2010) E.L.Bratkovskaya, W. Cassing, V.P. Konchakovski, O. Linnyk, NPA856 (2011) 162 interaction measure: Quasiparticle properties:  large width and mass for gluons and quarks Lorentzian spectral function, HTL limit at high T

DQPM describes QCD properties in terms of „resumed“ single-particle Green‘s functions in the sense of a two-particle irreducible (2PI) approach.  2PI framewark guaranties a consistent description of the system in- and out-of equilibrium on the basis of Kadanoff-Baym equations  the resumed properties are specified by complex self-energies which depend on temperature; the real part of self-energies describes a dynamically generated mass; the imaginary part describes the interaction width of partons  space-like part of energy-momentum tensor defines the potential energy density and the mean-field potential (1PI) for quarks and gluons  3 parameters of the model (for the resumed coupling) are fitted to QCD thermodynamics from the lattice A. Peshier, W. Cassing, PRL 94 (2005) ; A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) PHSD: Summary of the ideas

PHSD for HIC (highlights) PHSD for HIC (highlights) PHSD provides a consistent description of HIC dynamics

Properties of equilibrium QGP using PHSD

Shear viscosity T=T C :  /s shows a minimum ( ~0.1) close to the critical temperature   T=T C :  /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  /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 in PHSD = strongly-interacting liquid  /s using Kubo formalism and the relaxation time approximation (‚kinetic theory‘) V. Ozvenchuk et al., PRC 87 (2013) ; V. Ozvenchuk et al., arXiv: (accepted to PRC)

Electric conductivity W. Cassing et al., Phys.Rev.Lett. 110 (2013)  the QCD matter even at T~ T c is a much better electric conductor than Cu or Ag (at room temperature ) by a factor of 500 !  The response of the strongly-interacting system in equilibrium to an external electric field eE z defines the electric conductivity  0 :  Note: pQCD result at leading order :  additional force from external electric field eE z :

Dileptons from dynamical off-shell quark and gluon interactions, LO and NLO in the coupling Qualitative agreement of dynamical quasiparticels, lattice QCD, HTL Qualitative agreement of dynamical quasiparticels, lattice QCD, HTL O. Linnyk et al. Phys.Rev. C87 (2013) Thermal dilepton rates

Dileptons

Dileptons - an ideal probe to study the properties of the hot and dense medium Dileptons - an ideal probe to study the properties of the hot and dense medium Dilepton sources: 1) from the QGP via partonic (q,qbar, g) interactions: 2) from hadronic sources: direct decay of vector direct decay of vector mesons (  J  ‘) Dalitz decay of mesons Dalitz decay of mesons and baryons (  0, , ,…) radiation from secondary meson interaction: ,  + a1 radiation from secondary meson interaction: ,  + a1 correlated semi-leptonic decays of D- and B-mesons correlated semi-leptonic decays of D- and B-mesons **** g **** **** q l+l+ -l--l- **** q q q q q q g g q + qq

Dileptons at SPS: NA60  Mass region above 1 GeV is dominated by partonic radiation O. Linnyk, E. Bratkovskaya, V. Ozvenchuk, W. Cassing and C.M. Ko, PRC 84 (2011) , O. Linnyk, J.Phys.G38 (2011) , NA60 Collaboration, Eur. Phys. J. C 59 (2009) 607; CERN Courier 11/2009 NA60 data at low M are well described by an in- medium scenario with collisional broadening

PHENIX: dileptons from QGP The partonic channels fill up the discrepancy between the hadronic contributions and the data for M>1 GeV The partonic channels fill up the discrepancy between the hadronic contributions and the data for M>1 GeV The excess over the considered mesonic sources for M= GeV is not explained by the QGP radiation as incorporated presently in PHSD The excess over the considered mesonic sources for M= GeV is not explained by the QGP radiation as incorporated presently in PHSD O. Linnyk, W. Cassing, J. Manninen, E.Bratkovskaya and C.M. Ko, PRC 85 (2012)

STAR: dilepton mass spectra  STAR data are well described by the PHSD predictions O. Linnyk, W. Cassing, J. Manninen, E.Bratkovskaya and C.M. Ko, PRC 85 (2012)  Confirmed by the extended data set at QM2012

Predictions for LHC D-, B-mesons energy loss from Pol-Bernard Gossiaux and Jörg Aichelin JPsi and Psi’ nuclear modification from Che-Ming Ko and Taesoo Song O. Linnyk et al. Phys.Rev. C87 (2013) QGP(qbar-q) dominates at M>1.2 GeV QGP(qbar-q) dominates at M>1.2 GeV p T cut enhances the signal of QGP(qbar-q) p T cut enhances the signal of QGP(qbar-q)

Photons

Photons from the hot and dense QCD medium Photons from the hot and dense QCD medium 2) From hadronic sources decays of mesons: decays of mesons: secondary meson interactions: secondary meson interactions:  g q l+l+ -l--l- **** q q q q q q g g q Photon sources 1) From the QGP via partonic interactions: O. Linnyk et al. arXiv:

Photons from the QGP Photons from the QGP  Strong elliptic flow of photons seen by PHENIX is surprising, if the origin is the QGP O. Linnyk et al. arXiv:

 PHSD: PHENIX data are well described, including the T eff  QGP sources mandatory to explain the spectrum, but hadronic sources of ‘direct’ photons are considerable, too Photon spectrum Photon spectrum O. Linnyk et al. arXiv:

Photon spectrum Photon spectrum

Inclusive photon elliptic flow Inclusive photon elliptic flow  Pion elliptic flow is well under control in the PHSD.  Also the inclusive photon v 2 is reproduced, because the inclusive photons are dominate by those from the pion decay O. Linnyk et al. arXiv:

Direct photon elliptic flow Direct photon elliptic flow  Strong direct photon v 2 is reproduced by the PHSD calculations  QGP contribution is very small; v 2 of photons from hadronic sources is large  Observed elliptic flow of direct photons is reproduced, if the same calculation procedure as in the experiment is used PHENIX, Adare et al., Phys.Rev.Lett. 109 (2012) ; O. Linnyk et al., arXiv:

Parton-Hadron-String-Dynamics (PHSD) transport model provides a consistent description of the phase transition to the QGP in heavy-ion collisions. The dynamical quasiparticle model (DQPM) defines the partonic phase in line with lattice QCD. Parton-Hadron-String-Dynamics (PHSD) transport model provides a consistent description of the phase transition to the QGP in heavy-ion collisions. The dynamical quasiparticle model (DQPM) defines the partonic phase in line with lattice QCD. Distributions and the collective flow of particles produced in heavy ion collisions are reproduced from AGS to LHC energies. Distributions and the collective flow of particles produced in heavy ion collisions are reproduced from AGS to LHC energies. The properties of the sQGP in equilibrium are calculated: sheer viscosity, bulk viscosity, electric conductivity, thermal dilepton rate. The properties of the sQGP in equilibrium are calculated: sheer viscosity, bulk viscosity, electric conductivity, thermal dilepton rate. Dilepton data provide evidence for off-shell dynamics of vector mesons. Yield of dilepton pairs at masses above 1 GeV is described by the q+q interaction in the QGP. Dilepton data provide evidence for off-shell dynamics of vector mesons. Yield of dilepton pairs at masses above 1 GeV is described by the q+q interaction in the QGP. The enhanced yield and the elliptic flow of produced photons (inclusive and direct) are explained by the combination of partonic and hadron sources. The enhanced yield and the elliptic flow of produced photons (inclusive and direct) are explained by the combination of partonic and hadron sources. Conclusions

PHSD Team Wolfgang Cassing (Giessen U) Elena Bratkovskaya (FIAS & ITP Frankfurt U) Volodya Konchakovski (Giessen U) Thorsten Steinert (Giessen U) Vitalii Ozvenchuk (FIAS & ITP Frankfurt U) Rudy Marty (FIAS, Frankfurt U) Hamza Berrehrah (FIAS, Frankfurt U) Daniel Cabrera (ITP&FIAS, Frankfurt U) Taesoo Song (FIAS, Frankfurt U) Che-Ming Ko Jörg Aichelin Pol Bernard Gossiaux Christoph Hartnack Mark I. Gorenstein Viatcheslav D. Toneev Vadym Voronyuk Laura Tolos Angel Ramos Sergei Voloshin Collaboration

Back up slides

Flow harmonics (v 1, v 2, v 3, v 4 ) Increase of v 2 with impact parameter but flat v 3 and v 4 E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162; V. P. Konchakovski et al., PRC 85 (2012) Expected since η/s is very small in the DQPM and PHSD. v 2 /ε = const, indicates near ideal hydrodynamic flow ! v 2 /ε = const, indicates near ideal hydrodynamic flow !

Electro-magnetic fields Generalized transport equations: Magnetic field evolution in HSD/PHSD : Magnetic field evolution in HSD/PHSD : V. Voronyuk et al., Phys.Rev. C83 (2011) PHSD - transport model with electromagnetic fields.

The lowest and highest mass bins are described very well The lowest and highest mass bins are described very well Underestimation of p T data for 100<M<750 MeV bins consistent with dN/dM Underestimation of p T data for 100<M<750 MeV bins consistent with dN/dM The ‘missing source’(?) is located at low p T ! The ‘missing source’(?) is located at low p T ! PHENIX: p T spectra O. Linnyk, W. Cassing, J. Manninen, E.B. and C.-M. Ko, PRC 85 (2012)

Centrality dependent NA60 data PHSD predictions versus preliminary data Dominant rho-channel at low and quark annihilation at intermediate masses ! O. Linnyk, E. Bratkovskaya, V. Ozvenchuk, W. Cassing and C.M. Ko, PRC 84 (2011)

PHENIX: mass spectra  Peripheral collisions (and pp) are well described, however, central fail! O. Linnyk, W. Cassing, J. Manninen, E.B. and C.-M. Ko, PRC 85 (2012)

Parton-Hadron-String Dynamics (PHSD) Description of heavy-ion collisions as well as p+p, p+A, d+A,  +A reactions. Features: AGS to LHC Unified description of collisions at all energies from AGS to LHC. Non-equilibrium Non-equilibrium approach: applicable to far from equilibrium configurations as explosion-like heavy-ion collisions as well as to equilibrated matter („in the box“). Dynamics Dynamics: mean fields (hadronic and partonic), scattering (elastic, inelastic, 2  2, 2  n), resonance decays, retarded electro-magnetic fields. Phase transition Phase transition (cross over) according to the lattice QCD equation of state, hadronic and partonic degrees of freedom, spacial co-existance, dynamical hadronisation. Off-shell Off-shell transport: takes into account 2-particle correlations beyond the one- particle distributions.

Can we go back in time ?

Goal: microscopic transport description of the partonic and hadronic phase Problems:  How to model a QGP phase in line with lQCD data?  How to solve the hadronization problem? Ways to go: ‚Hybrid‘ models:  QGP phase: hydro with QGP EoS  hadronic freeze-out: after burner - hadron-string transport model  Hybrid-UrQMD  microscopic transport description of the partonic and hadronic phase in terms of strongly interacting dynamical quasi-particles and off-shell hadrons  PHSD pQCD based models:  QGP phase: pQCD cascade  hadronization: quark coalescence  BAMPS, AMPT, HIJING

Parton-Hadron-String Dynamics Main goal – description of heavy-ion collisions and properties of matter at high temperature and density as well as of p+p and p(d)+A reactions. AGS to LHC Unified description of collisions at all energies from AGS to LHC. Non-equilibrium Non-equilibrium: applicable to far from equilibrium configurations as explosion- like heavy-ion collisions as well as to equilibrated matter („in the box“). Universal: dileptons, charm, flow (v1, v2, v3, v4), chiral magnetic effect, spin, … Universal: dileptons, charm, flow (v1, v2, v3, v4), chiral magnetic effect, spin, … Dynamics Dynamics: mean fields (hadronic and partonic), scattering (elastic, inelastic, 2   2, 2  n), resonance decays, retarded electro-magnetic fields. Microscopic phase transition Microscopic phase transition (cross over) according to the lattice QCD equation of state, hadronic and partonic degrees of freedom, spacial co-existance, dynamical hadronisation. Off-shell Off-shell transport: takes into account 2-particle correlations beyond the one- particle distributions.

testparticle Ansatz 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: with W. Cassing, S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445 Off-shell equations of motion Off-shell equations of motion

Hadronization happens when the effective interactions | v | become attractive, approx. for parton densities 1 <  P < 2.2 fm -3 <= from DQPM gluons  q + qbar q + qbar  meson gluons  q + qbar q + qbar  meson q + q +q  baryon q + q +q  baryon Based on DQPM; massive, off-shell quarks and gluons with broad spectral functions hadronize to off-shell mesons and baryons: W. Cassing, E.L. Bratkovskaya, PRC 78 (2008) ; W. Cassing, EPJ ST 168 (2009) 3 Parton-parton recombination rate = W m - Gaussian in phase space with PHSD: hadronization

RHIC:Dileptons in pp and in heavy ions PHENIX: Au+Au PHENIX: pp Dilepton cocktail provides a good description of pp data as well as peripheral Au+Au data, however, fails in describing the central bins! ‚excess‘ Phys.Rev.C81 (2010)

PHSD Initial A+A collisions: Initial A+A collisions: string formation and decay to pre-hadrons Fragmentation Fragmentation of pre-hadrons into quarks using the quark spectral functions from the Dynamical Quasi-Particle Model Partonic phase: Elastic and inelastic parton-parton interactions Partonic phase: quarks and gluons with constituent mass and broad spectral functions defined by DQPM. Elastic and inelastic parton-parton interactions q + qbar gluon s + sbar gluon + gluon gluon q + qbar (color neutral) hadron resonances Hadronization: to off-shell hadrons: Hadronization: massive, off-shell quarks and gluons with broad spectral functions hadronize to off-shell hadrons: gluons  q + qbar; q + qbar  off-shell meson or ‚string‘; q + q +q  baryon or ‚string‘; Hadronic phase: Hadronic phase: hadron-hadron interaction, propagation and decays W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; EPJ ST 168 (2009) 3; NPA856 (2011) 162 Unified transport description of partonic and hadronic phases

Interacting quasiparticles Entropy density of interacting bosons and fermions (G. Baym 1998): gluons quarks antiquarks with d g = 16 for 8 transverse gluons and d q = 18 for quarks with 3 colors, 3 flavors and 2 spin projections Bose distribution function: Bose distribution function: Fermi distribution function: Fermi distribution function: 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 Simple approximations  DQPM: (scalar) (2PI)

The Dynamical QuasiParticle Model (DQPM) Properties of interacting quasi-particles - massive quarks and gluons (g, q, q bar ) with spectral functions : - massive quarks and gluons (g, q, q bar ) with spectral functions : DQPM: Peshier, Cassing, PRL 94 (2005) ; DQPM: Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) N c = 3, N f =3 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)  quasiparticle properties (mass, width)  quasiparticle properties (mass, width) 44 mass: mass: width:  gluons:  running coupling (pure glue):  quarks lQCD: pure glue

 N j (x,p) is the phase-space density of parton j at space-time position x and 4- momentum p  W m is the phase-space distribution of the formed ‚pre-hadrons‘: (Gaussian in phase space)   is the effective quark-antiquark interaction from the DQPM PHSD: Hadronization details Local covariant off-shell transition rate for q+qbar fusion => meson formation => meson formation using Cassing, Bratkovskaya, PRC 78 (2008) ; Cassing, EPJ ST 168 (2009) 3 45

Goal: microscopic transport description of the partonic and hadronic phase Problems:  How to model a QGP phase in line with lQCD data?  How to solve the hadronization problem? Ways to go: ‚ Hybrid‘ models:  QGP phase: hydro with QGP EoS  hadronic freeze-out: after burner - hadron-string transport model  Hybrid-UrQMD  microscopic transport description of the partonic and hadronic phase in terms of strongly interacting dynamical quasi-particles and off-shell hadrons  PHSD pQCD based models:  QGP phase: pQCD cascade  hadronization: quark coalescence  AMPT, HIJING, BAMPS

Bulk viscosity (mean-field effects)  bulk viscosity in relaxation time approximation with mean-field effects: Chakraborty, Kapusta, Phys. Rev.C 83, (2011). use DQPM results for masses for  q =0:  significant rise in the vicinity of critical temperature  in line with the ratio from lQCD calculations lQCD: Meyer, Phys. Rev. Lett. 100, (2008); Sakai,Nakamura, Pos LAT2007, 221 (2007). PHSD using the relaxation time approximation: V. Ozvenchuk et al., arXiv:

Bulk to shear viscosity ratio and specific sound   without mean-field effects  almost temperature independent behavior  with mean-field effects  strong increase close to the critical temperature (  +3  /4)/s: both the shear and bulk viscosities contribute to the damping of sound waves in the medium and provide a further constraint on the viscosities  (  +3  /4)/s: both the shear and bulk viscosities contribute to the damping of sound waves in the medium and provide a further constraint on the viscosities Specific sound channel (  +3  /4)/s as a function of temperature T Bulk to shear viscosity ratio  as a function of temperature T lQCD: H. Meyer V. Ozvenchuk et al., arXiv:

Scaled variance  scaled variance: where μ is the mean value of the observable x averaged over N events: σ 2 is the sample variance:  scaled variances reach a plateau in time for all observables  equilibrium values are less than 1 (as in GCE) for all   MCE  particle number fluctuations are flavor blind V. Ozvenchuk et al., PRC 87 (2013) , arXiv:

Skewness  skewness  skewness characterizes the asymmetry of the distribution function with respect to its average value V. Ozvenchuk et al., PRC 87 (2013) , arXiv:

Kurtosis  kurtosis:   2 is equal to 3 for normal distribution  excess kurtosis lQCD: Ejiri, Karsch, Redlich, Phys. Lett. B 633, 275 (2006) PHSD  Kurtosis as a probe of deconfinement:  Kurtosis in PHSD is compatible with lQCD for QGP V. Ozvenchuk et al., PRC 87 (2013) , arXiv:

Data vs. models Large discrepances between the models and PHENIX data in the invariant mass region from 0.2 to 0.7 GeV in central Au+Au collisions.  PHENIX dilepton puzzle?  PHENIX dilepton puzzle? Phys.Rev.C81 (2010) Hydro model – Dusling/ Zahed Fireball model – Rapp/Hees PHSD model, in-medium effects: coll. broadening ‚Cocktail‘

Bulk properties

Application to nucleus-nucleus collisions energy balance  Dramatic decrease of partonic phase with decreasing energy  Pb+Pb, 160 A GeV: only about 40% of the converted energy goes to partons; the rest is contained in the large hadronic corona and leading partons! (hadronic corona effect, cf. talk by J. Aichelin) Cassing & Bratkovskaya, NPA 831 (2009) partonic energy fraction vs energy

PHSD: Transverse mass spectra Central Pb + Pb at SPS energies 55  PHSD gives harder m T spectra and works better than HSD at high energies – RHIC, SPS (and top FAIR, NICA) – RHIC, SPS (and top FAIR, NICA)  however, at low SPS (and low FAIR, NICA) energies the effect of the partonic phase decreases due to the decrease of the partonic fraction Central Au+Au at RHIC W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215 E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162

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) from S. A. Voloshin, arXiv: x z

Collective flow: v 2 excitation functions Collective flow: v 2 excitation functions The excitation function for v 2 of charged particles from string-hadron transport models – UrQMD: PHSD Influence of hadron potentials  EoS QGP

Excitation function of elliptic flow Excitation function of elliptic flow is not described by hadron-string or purely partonic models (hadronic corona effect, cf. talk by J. Aichelin) !

Elliptic flow v 2 vs. collision energy for Au+Au 59 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)

Development of azimuthal anisotropies in time 60 Flow coefficients reach their asymptotic values by the time of 6–8 fm/c after the beginning of the collision  Flow coefficients reach their asymptotic values by the time of 6–8 fm/c after the beginning of the collision V. Konchakovski, E. Bratkovskaya, W. Cassing, V. Toneev, V. Voronyuk, Phys. Rev. C 85 (2012) Time evolution of v n for Au + Au collisions at s 1/2 = 200 GeV with impact parameter b = 8 fm.

Scaling properties: quark number scaling 61 The mass splitting at low p T is approximately reproduced as well as the meson-baryon splitting for p T > 2 GeV/c !  The mass splitting at low p T is approximately reproduced 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 at RHIC. E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162

NA60: differential spectrum O. Linnyk, E.Bratkovskaya, V. Ozvenchuk, W. Cassing and C.M. Ko, PRC 84 (2011) Acceptance corrected NA60 data Parton dominance at M>1 GeV and rho broadening confirmed by the differencial data

 meson E.L. Bratkovskaya, W. Cassing, V. P. Konchakovski, O. Linnyk, NPA856(2011) 162; E.L. Bratkovskaya, W. Cassing, NPA 807 (2008) 214; Off-shell propagation The off-shell spectral function becomes on-shell in the vacuum dynamically! gluon