Photon production in heavy-ion collisions Elena Bratkovskaya Institut für Theoretische Physik & FIAS, Uni. Frankfurt EMMI Workshop ‚Ab initio approaches in many-body QCD confront heavy-ion experiments‘ Heidelberg, December 2014

Elena Bratkovskaya (Uni. Frankfurt)2 Electromagnetic probes: photons and dileptons  Advantages: dileptons and real photons are emitted from different stages of the reaction and not effected by final- state interactions dileptons and real photons are emitted from different stages of the reaction and not effected by final- state interactions provide undistorted information about their production channels provide undistorted information about their production channels promising signal of QGP – ‚thermal‘ photons and dileptons promising signal of QGP – ‚thermal‘ photons and dileptons  Disadvantages:  low emission rate  production from hadronic corona  many production sources which cannot be individually disentangled in experimental data  Requires theoretical models which describe the dynamics of heavy-ion collisions during the whole time evolution!  Requires theoretical models which describe the dynamics of heavy-ion collisions during the whole time evolution! Feinberg (76), Shuryak (78)

3 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 hydrodynamical equations for fluid  assumption of local equilibrium  EoS with phase transition from QGP to HG  initial conditions (e-b-e, fluctuating)

Elena Bratkovskaya (Uni. Frankfurt)4 Production sources of photons in p+p and A+A  Decay photons (in pp and AA): m   + X, m =    ‘, a 1, …  Direct photons: (inclusive(=total) – decay) – measured experimentally  hard photons: (large p T, in pp and AA)  thermal photons: (low p T, in AA)  jet-  -conversion in plasma (large p T, in AA)  jet-medium photons (large p T, in AA) - scattering of hard partons with thermalized partons q hard +g QGP   +q, q hard + QGP   +q  jet-medium photons (large p T, in AA) - scattering of hard partons with thermalized partons q hard +g QGP   +q, q hard +qbar QGP   +q QGP QGP Hadron gas Hadron gas prompt (pQCD; initial hard N+N scattering) prompt (pQCD; initial hard N+N scattering) jet fragmentation (pQCD; qq, gq bremsstrahlung) (in AA can be modified by parton energy loss in medium) jet fragmentation (pQCD; qq, gq bremsstrahlung) (in AA can be modified by parton energy loss in medium) hardsoft PHENIX

(1) secondary mesonic interactions:  +    +    +K    +  … Production sources of thermal photons  Thermal QGP: Compton scattering q-qbar annihilation  Hadronic sources: Models: chiral OBE, soft-photon approximation (SPA) …  used in PHSD Photon rates from QGP:  pQCD LO: ‘AMY’ Arnold, Moore, Yaffe, JHEP 12, 009 (2001)  used in hydro !  pQCD NLO: Gale, Ghiglieri (2014)  resummed QCD: off-shell massive q, g O. Linnyk, JPG 38 (2011)  used in PHSD + soft … Elena Bratkovskaya (Uni. Frankfurt) 5 HG rates from massive Yang-Mills approach (TRG) Turbide, Rapp, Gale, PRC 69, (2004) Effective Lagrangian cross sections Kapusta et al PRC 69, (2004)  used in PHSD Turbide et al., PRC 69, (2004) TRG  used in hydro (2) meson-meson and meson-baryon bremsstrahlung: m+m  m+m+  m+B  m+B+  m=  *,…, B=p, ,…

Elena Bratkovskaya (Uni. Frankfurt)6 2010: Direct photon spectra for Au+Au at s 1/2 =200 GeV PHENIX, Phys. Rev. C81 (2010) Lesson 1: Variety of model predictions: fireball, 2+1 Bjorken hydro, 3+1 ideal hydro with different initial conditions and EoS  in order to be conclusive on photon production, the models must reproduce the final hadronic spectra, i.e. to pass the basic check (Step 1) for the adequate dynamical description of the HIC! Models: assume formation of a hot QGP with initial temperature T init at thermalization time  0  Huge variations in T init and  0 !  Photon spectra show sensitivity to the dynamical evolution

Elena Bratkovskaya (Uni. Frankfurt)7 PHENIX: Photon v 2 puzzle  PHENIX (also now ALICE): strong elliptic flow of photons v 2 (  dir )~ v 2 (  )  Result from a variety of models: v 2 (  dir ) << v 2 (  )  Problem: QGP radiation occurs at early times when flow is not yet developed  expected v 2 (  QGP )  0 v 2 = weighted average  a large QGP contribution gives small v 2 (  QGP ) Linnyk et al., PRC 88 (2013) PHENIX Challenge for theory – to describe spectra, v 2, v 3 simultaneously !  NEW (QM’2014): PHENIX, ALICE experiments - large photon v 3 !

Elena Bratkovskaya (Uni. Frankfurt)8 Photon production in hydrodynamical models  Step 2:  From smooth Glauber initial conditions to event-by-event hydro with fluctuating initial conditions  Lesson 2: effect of fluctuating initial conditions: slight increase at high p T for yield and v 2  small effect, but right direction! R. Chatterjee et al., PRC 88, (2013) Jyväskylä ideal hydro  Step 3:  From ideal to viscous hydro Thermal photons: QGP +HG RHIC energy (3+1)D MUSIC (McGill) M. Dion et al., PRC84 (2011) (2+1)D VISH2+1 (Ohio State) : C. Shen et al., arXiv: , arXiv:  Lesson 3: effect of shear viscosity: * small enhancement of the photon yield * suppression of photon v 2 * effect on v 2 for photons is stronger than for hadrons

Elena Bratkovskaya (Uni. Frankfurt)9 Step 4: Hydro with pre-equilibrium flow  pre-equilibrium flow in (2+1)D VISH : C. Shen et al., arXiv: , arXiv: ;  viscous QGP and HG fluid (  /s=0.18)  Initial: ‚bumpy‘ e-b-e from MC Glauber /KLN  EoS: lQCD  QGP photon rate: AMY  HG photon rate: TGR for meson gas with viscous corrections Generation of pre-equilibrium flow: using free-streaming model to evolve the partons right after the collisions to 0.6 fm/c Generation of pre-equilibrium flow: using free-streaming model to evolve the partons right after the collisions to 0.6 fm/c + Landau matching to switch to viscous hydro  quick development of momentum anisotropy with saturation near T C Warning: results can be considered as upper limit for the pre-equilibrium flow effect! ALICE (preliminary) Au+Au, 2760 GeV  Lesson 4: Pre-equilibrium flow:  small effect on photon spectra  slight increase of v 2  ‚Initial‘ flow: rapid increase in bulk v 2 in fireball model van Hees, Gale, Rapp, PRC84 (2011)

Elena Bratkovskaya (Uni. Frankfurt)10 What else?!  Further improvements of hydro models ?  Bulk viscosity  Modeling of initial pre-equlibrium effects  … From hydro to non-equilibrium microscopic transport models : use PHSD as a ‚laboratory‘ for that Non-equilibrium dynamics ? Non-equilibrium dynamics ? Missing strength related to hadronic stage in hydro ? Missing strength related to hadronic stage in hydro ?

 QGP phase is described by the Dynamical QuasiParticle Model DQPM  QGP phase is described by the Dynamical QuasiParticle Model (DQPM) Elena Bratkovskaya (Uni. Frankfurt) Quark Matter  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 which provides the microscopic description of the full collision evolution Basic ideas:  explicit phase transition from hadrons to partons  lQCD EoS (cross over) for the partonic phase  explicit parton-parton interactions - between quarks and gluons  dynamical hadronization  off-shell hadronic collision dynamics in the final reaction phase  Transport theory: generalized off-shell transport equations based on 1st order gradient expansion of Kadanoff-Baym equations (applicable for strongly interacting systems!) A. Peshier, W. Cassing, PRL 94 (2005) ; A. Peshier, W. Cassing, PRL 94 (2005) ; W. Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, E. B., PRC 78 (2008) ; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3  Spectral functions:  DQPM matches well lattice QCD

! sizeable contribution of hadronic sources, dominant – meson-meson (mm) and meson- Baryon (mB) bremsstrahlung ! sizeable contribution of hadronic sources, dominant – meson-meson (mm) and meson- Baryon (mB) bremsstrahlung Elena Bratkovskaya (Uni. Frankfurt)12 PHSD: photon spectra at RHIC: QGP vs. HG ?   Direct photon spectrum (min. bias) Linnyk et al., PRC88 (2013) ; PRC 89 (2014) Linnyk et al., PRC88 (2013) ; PRC 89 (2014) PHSD:  QGP gives up to ~50% of direct photon yield below 2 GeV/c m+m  m+m+   m+B  m+B+    m=  *,… B=p  !!! mm and mB bremsstrahlung channels can not be subtracted experimentally ! Measured Teff > ‚true‘ T ,blue shift‘ due to the radial flow! Measured Teff > ‚true‘ T ,blue shift‘ due to the radial flow! Cf. Hydro: Shen et al., PRC89 (2014)

Elena Bratkovskaya (Uni. Frankfurt)13 Bremsstrahlung – theoretical uncertainties  Uncertainties in the Bremsstrahlung channels in the previous PHSD results : C. Gale, J. Kapusta, Phys. Rev. C 35 (1987) 2107  Soft Photon Approximation (SPA): m 1 +m 2  m 1 +m 2  m 1 +m 2  m 1 +m 2  2) no experimental constraints on m+m and m+B differential elastic cross sections  Bremsstrahlung: seen at SPS - WA98 1) based on the Soft-Photon-Approximation (SPA) (factorization = strong x EM) Firebal model: Liu, Rapp, Nucl. Phys. A 96 (2007) 101  effective chiral model for      bremsstrahlung gives larger contribution than SPA HSD: E. B., Kiselev, Sharkov, PR C78 (2008) using SPA  mm and mB Bremsstrahlung is an important source of soft photons at SPS energies! ( used  el mm =10mb )

Elena Bratkovskaya (Uni. Frankfurt)14 Bremsstrahlung – theoretical uncertainties Beyond the Soft-Photon Approximation:  Effective chiral Lagrangian with , , and  ‘ exchange for  +  (chiral OBE model) : Linnyk et al., in preparation Linnyk et al., in preparation  Tensor meson  ‘ important at higher sqrt(s) and p T (  )  Strong angular dependence of elastic cross section elastic  cross sections from OBE: elastic  cross sections from OBE: total differential total differential

Elena Bratkovskaya (Uni. Frankfurt)15 PHSD: new photon spectra at RHIC beyond SPA   Direct photon spectrum (min. bias) Linnyk et al., in preparation Linnyk et al., in preparation Linnyk et al., PRC88 (2013) ; PRC 89 (2014) Linnyk et al., PRC88 (2013) ; PRC 89 (2014)  m+m bremsstrahlung based on the Soft-Photon-Approximation (SPA)  m+m bremsstrahlung based on the chiral OBE model  enhancement of low p T yield  reduction of high p T yield from m+m bremsstrahlung  m+m (and m+B) bremsstrahlung dominates photon spectra at low p T

Elena Bratkovskaya (Uni. Frankfurt)16 Photon p T spectra at RHIC for different centralities PHSD predictions: O. Linnyk et al, Phys. Rev. C 89 (2014) PHENIX data - arXiv: from talk by S. Mizuno at QM‘2014  mm and mB bremsstrahlung is dominant in peripheral collisions in the PHSD calculations PHSD  PHSD approximately reproduces the centrality dependence of photon spectra  How to separate hadronic and partonic contributions ?  Look at the centrality dependence of photon yield!

Elena Bratkovskaya (Uni. Frankfurt)17 Centrality dependence of the ‚thermal‘ photon yield  PHSD: scaling of the thermal photon yield with N part  with  ~1.5  similar results from viscous hydro: (2+1)d VISH2+1:  (HG) ~1.46,  (QGP) ~2,  (total) ~1.7 O. Linnyk et al, Phys. Rev. C 89 (2014) PHSD predictions:  Hadronic channels scale as ~ N part 1.5  Partonic channels scale as ~N part 1.75 (‘Thermal’ photon yield = direct photons - pQCD) PHENIX (arXiv: ): scaling of thermal photon yield vs centrality: dN/dy ~ N part  with  ~  What do we learn? Indications for a dominant hadronic origin of thermal photon production?!

Elena Bratkovskaya (Uni. Frankfurt)18 1) v 2 (  incl ) = v 2 (   ) - inclusive photons dominanty stem from   decays  HSD (without QGP) underestimates v 2 of hadrons and inclusive photons by a factor of 2, wheras the PHSD model with QGP is consistent with exp. data Are the direct photons a barometer of the QGP? PHSD: Linnyk et al., PRC88 (2013) ; PRC 89 (2014) ) v 2 (  dir ) of direct photons in PHSD underestimates the PHENIX data : v 2 (  QGP ) is very small, but QGP contribution is up to 50% of total yield  lowering flow v 2 (  QGP ) is very small, but QGP contribution is up to 50% of total yield  lowering flow  Do we see the QGP pressure in v 2 (  ) if the photon productions is dominated by hadronic sources? HSD(no QGP)  PHSD: v 2 (  dir ) comes from mm and mB bremsstrahlung ! Direct photons (inclusive(=total) – decay) :  The QGP causes the strong elliptic flow of photons indirectly, by enhancing the v 2 of final hadrons due to the partonic interactions

Elena Bratkovskaya (Uni. Frankfurt)19 Photons from PHSD at LHC  Is the considerable elliptic flow of direct photons at the LHC also of hadronic origin as for RHIC?!  The photon elliptic flow at LHC is lower than at RHIC due to a larger relative QGP contribution / longer QGP phase. PHSD: v 2 of inclusive photons Preliminary Preliminary PHSD- preliminary: Olena Linnyk PHSD: direct photons  LHC (similar to RHIC): hadronic photons dominate spectra and v 2

Elena Bratkovskaya (Uni. Frankfurt)20 Towards the solution of the v 2 puzzle ?  Is hadronic bremsstrahlung a ‚solution‘?  Pseudo-Critical Enhancement of thermal photons near T C ? H. van Hees, M. He, R. Rapp, NPA 933 (2014) 256 Other scenarios:  Early-time magnetic field effects ? Basar, Kharzeev, Skokov, PRL109 (2012) ; Basar, Kharzeev, Shuryak, PRC 90 (2014) „ … a novel photon production mechanism from the conformal anomaly of QCD-QED and the existence of strong (electro)-magnetic fields in heavy- ion collisions.“ Exp. checks: v 3, centrality dependence of photon yield (PHENIX: arXiv: )  Glasma effects ? L. McLerran, B. Schenke, arXiv: „ … Photon distributions from the Glasma are steeper than those computed in the Thermalized Quark Gluon Plasma (TQGP). Both the delayed equilibration of the Glasma and a possible anisotropy in the pressure lead to a slower expansion and mean times of photon emission of fixed energy are increased.“  non-perturbative effects - semi-QGP Y. Hidaka, S. Lin, R. Pisarski et al., NPA931 (2014) 681 Y. Hidaka, S. Lin, R. Pisarski et al., NPA931 (2014) 681  ???

21 Messages from the photon study  sizeable contribution from hadronic sources - at RHIC and LHC hadronic photons dominate spectra and v 2  meson-meson (mm) and meson-Baryon (mB) bremsstrahlung are important sources of direct photons  mm and mB bremsstrahlung channels can not be subtracted experimentally !  The QGP causes the strong elliptic flow of photons indirectly, by enhancing the v 2 of partons and final hadrons due to partonic interactions Photons – one of the most sensitive probes for the dynamics of HIC! Elena Bratkovskaya (Uni. Frankfurt)

22 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

23 Thank you ! Elena Bratkovskaya (Uni. Frankfurt)

24 V 3 at RHIC

25 Properties of parton-hadron matter: electric conductivity  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 : W. Cassing et al., PRL 110(2013)  Photon (dilepton) rates at q 0  0 are related to electric conductivity  0  Probe of electric properties of the QGP Elena Bratkovskaya (Uni. Frankfurt)

26 LPM effect

Elena Bratkovskaya (Uni. Frankfurt)27 Are thermal photons a QGP thermometer?  Measured Teff > ‚true‘ T ,blue shift‘ due to the radial flow!  only ~1/3 at LHC and ~1/4 at RHIC of total photons come from hot QCD (T>250 MeV)  (2+1)d viscous hydro VISH2+1 (Ohio) C. Shen et al., PRC89 (2014) ; arXiv:  Contour plots of differential photon yield vs. time and temperature T and T eff :  T eff = -1/slope vs. local fluid cell temperature T  Time evolution of the effective temperature Exp. Data:  RHIC: T eff = MeV  LHC: T eff = MeV

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) ; A. Peshier, W. Cassing, PRL 94 (2005) ; 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 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 28 Elena Bratkovskaya (Uni. Frankfurt)

29 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) ; DQPM: Peshier, Cassing, PRL 94 (2005) ; 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: width:  gluons:  quarks: lQCD: pure glue  Modeling of the quark/gluon masses and widths  HTL limit at high T

30 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) ; NPA831 (2009) 215; EPJ ST 168 (2009) 3; NPA856 (2011) 162.

Transverse mass spectra from SPS to RHIC Central Pb + Pb at SPS energies  PHSD gives harder m T spectra and works better than HSD (wo QGP) at high energies – 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 Elena Bratkovskaya (Uni. Frankfurt)

Elliptic flow v 2 vs. collision energy for Au+Au 32 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) Elena Bratkovskaya (Uni. Frankfurt)

33 p T spectra at LHC Mean p T of charged hadrons vs N ch p+p at s 1/2 =7 TeV p+Pb at s 1/2 =5.02 TeV, Pb+Pb at s 1/2 =2.76 TeV V. Konchakovski, W. Cassing, V. Toneev, arXiv: p T spectra of charged hadrons and pions central Pb+Pb at s 1/2 =2.76 TeV  PHSD reproduces ALICE data Elena Bratkovskaya (Uni. Frankfurt)

34 V n (n=2,3,4,5) at LHC V. Konchakovski, W. Cassing, V. Toneev, arXiv:  PHSD: increase of v n (n=2,3,4,5) with p T  v 2 increases with decreasing centrality  v n (n=3,4,5) show weak centrality dependence symbols – ALICE PRL 107 (2011) lines – PHSD Elena Bratkovskaya (Uni. Frankfurt)