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Transport models versus observables

Transport models versus observables. Lecture III:. E lena Bratkovskaya 27-31 Aug. 2008 , 20th Indian-Summer School of Physics & 4th HADES Summer School ‚ Hadrons in the Nuclear Medium ‘. Our ultimate goals:. Search for the critical point. The phase diagram of QCD.

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Transport models versus observables

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  1. Transport models versus observables Lecture III: Elena Bratkovskaya 27-31 Aug. 2008 , 20th Indian-Summer School of Physics& 4th HADES Summer School ‚Hadrons in the Nuclear Medium‘

  2. Our ultimate goals: • Search for the critical point The phase diagram of QCD • Study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma • Study of the in-medium properties of hadrons at high baryon density and temperature

  3. Lecture II: Dynamics of heavy-ion collisions –> complicated many-body problem! Correct way to solve the many-body problem including all quantum mechanical features  Kadanoff-Baym equations for Green functions S<(from 1962) e.g. for bosons Greens functions S / self-energies S : retarded (ret), advanced (adv) (anti-)causal (a,c ) • do Wigner transformation consider only contribution up tofirst order in the gradients = astandard approximationof kinetic theory which is justified if the gradients in the mean spacial coordinate X are small

  4. Lecture II:From Kadanoff-Baym equations to transport equations Generalized transport equations = first order gradient expansion of the Wigner transformed Kadanoff-Baym equations: Operator <> - 4-dimentional generalizaton of the Poisson-bracket drift term Vlasov term backflow term Backflow term incorporates the off-shell behavior in the particle propagation ! vanishes in the quasiparticle limit collision term =‚loss‘ term -‚gain‘ term The imaginary part of the retarded propagator is given by the normalized spectral function: For bosons in first order gradient expansion: GXP – width of spectral function = reaction rate of particle (at phase-space position XP) Greens function S< characterizes the number of particles (N) and their properties (A – spectral function ) W. Cassing et al., NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

  5. Lecture II: 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 iS<XP - insert in generalized transport equations and determine equations of motion ! General testparticle off-shell equations of motion: with Note:the common factor 1/(1-C(i)) can be absorbed in an ‚eigentime‘ of particle (i) !

  6. Basic concept of HSD • HSD – Hadron-String-Dynamics transport approach: • for each particle species i (i = N, R, Y, p, r, K, …) the phase-space density fi followsthe transport equations • with collision termsIcoll describing: • elastic and inelastic hadronic reactions: baryon-baryon, meson-baryon, meson-meson • formation and decay of baryonic and mesonicresonances • string formation and decay (for inclusive particle production: BB -> X , mB ->X, X =many particles) • implementation of detailed balance on the level of 1<->2 • and 2<->2 reactions (+ 2<->n multi-particle reactions in HSD !) • off-shell dynamics for short-lived states BB <-> B´B´, BB <-> B´B´m mB <-> m´B´, mB <-> B´ Baryons: B=(p, n, D(1232), N(1440), N(1535), ...) Mesons: m=(p, h, r, w, f, ...)

  7. (only 1<->2, 2<->2 reactions indicated here) E.g., Nucleon transport in N,p,D system : DfN=Icoll Full collision term consists of ~10000 different particle combinations • => set of transport equations coupled via Icoll and mean field

  8. (Collision term) Description of elementary reactions in HSD • Low energy collisions: • binary 2<->2 and • 2<->3 reactions • formation and • decay of baryonic and mesonic resonances • BB <-> B´B´ • BB <-> B´B´m • mB <-> m´B´ • mB <-> B´ • mm <-> m´m´ • mm <-> m´ • . . . • Baryons: • B=(p, n, D(1232), • N(1440), N(1535), ...) • Mesons: • m=(p, h, r, w, f, ...) High energy collisions: (above s1/2~2.5 GeV) Inclusive particle production: BB -> X , mB ->X X =many particles described by strings (= excited color singlet states q-qq, q-qbar) formation and decay p+p pp

  9. Degrees of freedom in HSD • hadrons - baryons and mesons including excited states (resonances) • pre-hadrons = hadrons under formation time tF~0.8 fm/c ( e > eC~1 GeV/fm3 ) • strings – excited color singlet states • (qq - q) or (q – qbar) • Based on the LUND string model • &perturbative QCD via PYTHIA • leading quarks(q, qbar) & diquarks • (q-q, qbar-qbar) •  NOT included : • no explicit parton-parton interactions (i.e. between quarks and gluons) outside strings! • no explicit phase transition from hadronic to partonic degrees of freedom • QCD EoS for partonic phase PHSD –Parton-Hadron-String-Dynamics

  10.  ! 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 <->mreactions: is Pauli-blocking or Bose-enhancement factors; h=1 for bosons and h=-1 for fermions is a transition probability

  11. W. Cassing, NPA 700 (2002) 618 Anti-barion production in heavy-ion reactions Multi-meson fusion reactions m1+m2+...+mn B+Bbar (m=p,r,w,..) important for antiproton, antilambda dynamics ! 2<->3

  12. AGS NA49 BRAHMS HSD – a microscopic model for heavy-ion reactions • very good description of particle production in pp, pA reactions • unique description of nuclear dynamicsfrom low (~100 MeV) to ultrarelativistic (~20 TeV) energies HSD 1999 predictions

  13. Our ultimate goals: • Search for the critical point The phase diagram of QCD • Study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma • Study of the in-medium properties of hadrons at high baryon density and temperature

  14. Aim I. Study of in-medium effects within transport approaches • In-medium models: • chiral perturbation theory • chiral SU(3) model • coupled-channel G-matrix approach • chiral coupled-channel effective field theory predict changes of the particle properties in the hot and dense medium, e.g. broadening of the spectral function R. Rapp: r meson spectral function • Accounting of in-medium effects with medium dependent spectral functions requires off-shell transport models ! •  cf. Lecture II

  15. Study of in-medium K+ and K- properties in heavy-ion collisions within dynamical transport models Theory (status: last millenium < 2000) : Implementation of in-medium K+ and K-scenarios (= ‚dropping‘ of K-mass and ‚enhancement‘of K+mass) in on-shelltransport models: BUU (Texas) (1994), HSD (or RBUU) (1997), QMD (Tübingen) (1998), IQMD (Nantes) (2000), ... • Baryon-Baryon collisions: Strangeness production at low energy • meson-Baryon collisions: • meson-meson collisions: Dominant channel for low energy K-production!

  16. p p p p p Off-shell transport => In-medium transition rates: G-matrix approach Need to know in-medium transition amplitudes G and their off-shell dependence L. Tolos et al., NPA 690 (2001) 547 Coupled channel G-matrix approach Transition probability : • with G(p,r,T) - G-matrix from the solution of coupled-channel equations • with pion dressing, i.e. including the pion self-energy in the intermediate pL, pS states • without pion dressing W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59

  17. K- production in A+A within the off-shell transport approach Updated plot‘07 Au+Au (and Ni+Ni) data at 1.5 (and 1.93) AGeV are consistent with the ‚pion dressing‘ scenario, whereas C+C at 1.8 AGeV are underestimated even without pion dressing  new ‚strange‘ puzzle for HADES ?! W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59

  18. K-/K+ ratio in Au+Au at 1.5 A GeV within the off-shell transport approach • Data are consistent with the ‚pion dressing‘ scenario W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59

  19. Dileptons from transport models • Theory (status: last millenium < 2000) : • Implementation of in-medium vector mesons (r,w) scenarios (= ‚dropping‘ mass and ‚collisional broadening‘) in on-shelltransport models: • BUU/AMPT (Texas) ( > 1995) • HSD ( > 1995) • UrQMD v. 1.3 (1998) • RQMD (Tübingen) (2003), but NO explicit propagation of vector mesons • IQMD (Nantes) (2007), but NO explicit propagation of vector mesons Theory (status: this millenium > 2000) : Implementation of in-medium vector mesons (r,w,f) scenarios (= ‚dropping‘ mass and ‚collisional broadening‘) in off-shelltransport models: • HSD (>2000) • BRoBUU (Rossendorf) (2006)

  20. Modelling of in-medium spectral functions for vector mesons In-medium scenarios: dropping mass collisional broadening dropping mass + coll. broad. m*=m0(1-a r/r0) G(M,r)=Gvac(M)+GCB(M,r) m* & GCB(M,r) Collisional width GCB(M,r) = g r <u sVNtot> r-meson spectral function: • Note:for a consistent off-shell transport one needs not only in-medium spectral functions but also in-medium transition rates for all channels with vector mesons, i.e. the full knowledge of the in-medium off-shell cross sections s(s,r) E.L.B., NPA 686 (2001), E.L.B. &W. Cassing, NPA 807 (2008) 214

  21. Dilepton channels in HSD all particles decaying to dileptons are firstly produced in BB, mB or mm collisions ‚Factorization‘ of diagramm in the transport approach: The dilepton spectra are calculated perturbatively with the time integration method.

  22. Bremsstrahlung – a new view on an ‚old‘ story • New OBE-model (Kaptari&Kämpfer, NPA 764 (2006) 338): • pn bremstrahlung is larger by a factor of 4 than it has been • calculated before (and used in transport calculations before)! • pp bremstrahlung is smaller than pn, however, not zero; consistent with the 1996 calculations from F.de Jong in a T-matrix approach 2007 ‚DLS puzzle‘ : Experiment: HADES = DLS ! Theory: the DLS puzzle is solved by accounting for a larger pn bremsstrahlung !

  23. HSD: Dileptons from C+C at 1 and 2 A GeV - HADES • HADES data show exponentially decreasing mass spectra • Data are better described by in-medium scenarios with collisional broadening • In-medium effects are more pronounced for heavy systems such as Au+Au E.B., Cassing, NPA807 (2008) 214

  24. HSD: Dileptons from A+A at 1 A GeV - DLS • bremsstrahlung and D-Dalitz are the dominant contributions in A+A for 0.15 < M < 0.55 GeV at 1 A GeV ! E.B., Cassing, NPA807 (2008) 214

  25. Dileptons at SPS: NA60 • NA60 data are better described by in-medium scenario with collisional broadening E.B., Cassing, O. Linnyk, arXiv:0808.1504 [nucl-th]

  26. Dileptons at SPS: CERES • CERS data are better described by in-medium scenario with collisional broadening E.B., Cassing, O. Linnyk, arXiv:0808.1504 [nucl-th]

  27. Dileptons at RHIC PHENIX: pp PHENIX: Au+Au • HSD provides a good description of pp data • Standard in-medium effects of vector mesons -- compatible with the NA60 and CERES data at SPS – do not explain the large enhancement observed by PHENIX in the invariant mass from 0.2 to 0.5 GeV in Au+Au collisions at s 1/2=200 GeV (relative to pp collisions) E.B., Cassing, O. Linnyk, arXiv:0808.1504 [nucl-th]

  28. Our ultimate goals: • Search for the critical point The phase diagram of QCD • Study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma • Study of the in-medium properties of hadrons at high baryon density and temperature

  29. The QGP in Lattice QCD • Quantum Cromo Dynamics : • predicts strong increase of • the energy density e at critical temperature TC ~170 MeV • Possible phase transition fromhadronic to partonic matter (quarks, gluons) at critical energy densityeC~1 GeV/fm3 Lattice QCD: energy density versus temperature Tc= 170 MeV Critical conditions - eC~1 GeV/fm3 , TC ~170 MeV -can be reached in heavy-ion experiments at bombarding energies > 5 GeV/A

  30. Dense and hot matter – average quantities Time evolution of the baryon density and energy density huge energy and baryon densities are reached (e > ecrit=1 GeV/fm3) at FAIR energies (> 5 A GeV)

  31. Hadron-string transport models versus observables - I • Strangeness signals of QGP ‚horn‘ in K+/p+ ‚step‘ in slope T Exp. data are not reproduced in terms of the hadron-string picture => evidence for nonhadronic degrees of freedom

  32. Hadron-string transport models versus observables - II • Collective flow signals of QGP: • RHIC: v2 of charged hadrons at mid-rapidity (PHOBOS) • Collective flow from hadronic interactions is too low at midrapidity ! • Charm signals of QGP: STAR experiment at RHIC observed strong collective flow v2 of charm D-mesons => evidence for strong nonhadronic interactions in the very early phase of the reaction

  33. Hadron-string transport models versus observables - III • High pT suppression signals of QGP: The attenuation of high pT-hadrons(RAA) iswell reproduced in the hadron-string approach for non-central Au+Au collisions at top RHIC energies, however, the hadron-string model doesn‘t provideenough high pT suppression for central Au+Au ! HSD with Cronin eff. • Jet suppression signals of QGP: STAR observed very strong far-side jetsuppression which is NOT reproduced in the hadron-string picture => evidence for strong nonhadronic interactions in the early phase of the reaction !

  34. From hadrons to partons • In order to study of the phase transition from • hadronic to partonic matter – Quark-Gluon-Plasma – • we need a consistent transport model with • explicit parton-parton interactions (i.e. between quarks and gluons) outside strings! • explicit phase transition from hadronic to partonic degrees of freedom • QCD EoS for partonic phase Transport theory: off-shell Kadanoff-Baym equations for the Green-functions G<h(x,p) in phase-space representation; with the partonic and hadronic phase Parton-Hadron-String-Dynamics (PHSD) QGP phase described by input from the Dynamical QuasiParticle Model(DQPM)

  35. T = 3 Tc T = 1.053 Tc T = 1.35 Tc The Dynamical QuasiParticle Model (DQPM) • Interacting quasiparticles : • massive quarks and gluons • with spectral functions Gluon‘s r(w): • DQPM well matches lQCD • DQPM provides mean-fields for gluons and quarks as well as effective 2-body interactions • and gives transition rates for the formation of hadrons  PHSD Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)

  36. PHSD - basic concepts Initial A+A collisions – HSD: string formation and decay to pre-hadrons Fragmentation of pre-hadrons into quarks: using the quark spectral functions from the Dynamical QuasiParticle Model (DQPM) approximation to QCD DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) • Partonic phase: quarks and gluons (= ‚dynamical quasiparticles‘) withoff-shell spectral functions (width, mass) defined by DQPM • elastic and inelastic parton-parton interactions:using the effective cross sections from the DQPM • q + qbar (flavor neutral) <=> gluon(colored) • gluon+ gluon<=> gluon(possible due to large spectral width) • q + qbar (color neutral) <=> hadron resonances Hadronization: based on DQPM - massive, off-shell quarks and gluons with broad spectralfunctions hadronize tooff-shell mesons and baryons: gluons  q + qbar;q + qbar  meson (or string); q + q +q  baryon(or string) (strings act as ‚doorway states‘ for hadrons) Hadronic phase: hadron-string interactions – off-shell HSD

  37. PHSD: hadronization E.g.time evolution of the partonic fireballat temperature 1.7 Tcwith initialized at mq=0 • Consequences: • Hadronization: q+qbar or 3q or 3qbar fuse to a color neutral hadrons (or strings)which furtheron decay to hadrons in amicrocanonical fashion, i.e.obeying all conservation laws (i.e. 4-momentum conservation, flavor current conservation)in each event • Hadronization yieldsan increase in total entropy Sand not a decrease as in the simple recombination model ! • Off-shell parton transport roughly leads a hydrodynamic evolution • of the partonic system Cassing, E.B. arXiv:0808.0022 [hep-ph] Cassing, arXiv:0808.0715 [nucl-th]

  38. Time-evolution of parton density Time-evolution of hadron density Expanding fireball Expanding grid: Δz(t) = Δz0(1+0.75 t) !

  39. R. Arnaldi et al., PRL 100 (2008) 022302 PHSD results: Dilepton radiation from the sQGP Dilepton spectra vs. NA60 Inverse slope parameter Tefffor dilepton spectra – NA60 sQGP:Drell-Yan process: q+qbarm+ + m- Conjecture: spectrum from sQGP is softer than from hadronic phase since quark-antiquark annihilation occurs dominantly before the collective radial flow has developed! Conjecture: the sQGP shows up already at SPS energies !

  40. PHSD Summary Accounting of in-medium effects requires off-shell transport models ! • Last millenium:on-shell transport models (QMD, BUU, ...) • This millenium: development of a new generation of • transport theories/codes • A first step: off-shell transport approaches • now default version of HSD • also taken up by other groups (e.g. Rossendorf BUU) Present developments: modeling of parton/hadron phase transition based on QCD EoS and off-shell parton transport  Parton-Hadron-String-Dynamics (PHSD)

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