Resonance dynamics in the PHSD approach

Transcription

1 Resonance dynamics in the PHSD approach Elena Bratkovskaya Institut für f r Theoretische Physik & FIAS, Uni. Frankfurt Resonance Workshop in Catania 3-7 November 014 1

2 What do we learn from resonances? Resonances broad spectral function strongly interacting particles Low energies: produced during the whole time evolution probe high density hadronic matter in-medium effects (cf. talks by D. Cabrera, L. Tolos, E. Oset, A. Ilner) High energies: produced during hadronization at T C carry information about QGP strong hadronic interactions: : re-scattering, absorption, decay, regeneration Experimental observation of resonances: hadronic mode: strong final state interaction of daughter hadrons Plot from C. Markert leptonic mode: very rare process, hard to measure Only a small fraction of resonances can be reconstructed experimentally

3 Theoretical description of resonance dynamics Many-body theory: Strong interaction large width = short life-time broad spectral function quantum object How to describe the dynamics of broad resonances, i.e. strongly interacting quantum states in transport theory? Λ(1783)N -1 and Σ(1830)N -1 exitations semi-classical BUU first order gradient expansion of quantum Kadanoff-Baym equations Barcelona / Valencia group generalized transport equations 3

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

5 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 How to describe strongly interacting systems?! Quantum field theory Kadanoff-Baym dynamics for resummed single-particle Green functions S < (196) Green functions S < /self-energies energies Σ: is is is is < xy > xy c xy a xy = η {Φ = {Φ( = T = T c a + ( y )Φ( x ) } y )Φ + {Φ( x )Φ {Φ( x )Φ ( x ) } + + ( y ) } ( y ) } causal anticausal S S ret xy adv xy = S = S c xy c xy S S < xy > xy = S η = ± 1( bosons / T a (T c = S > xy < xy S S a xy a xy fermions ) retarded advanced ) ( anti )time ordering Integration over the intermediate spacetime operator 1 µ x Ŝ0 x ( x + M µ 0 ) Leo Kadanoff Gordon Baym 5

6 From Kadanoff-Baym equations to generalized transport equations After the first order gradient expansion of the Wigner transformed Kadanoff-Baym equations and separation into the real and imaginary parts one gets: g Generalized transport equations (GTE): drift term Vlasov term backflow term collision term = gain - loss term Backflow term incorporates the off-shell behavior in the particle propagation! vanishes in the quasiparticle limit A XP δ(p -M ) GTE: Propagation of the Green s s function is < XP =A XP N XP, which carries information not only on the number of particles (N XP ),, but also on their properties, interactions and correlations (via A XP ) Spectral function: Γ Σ 0Γ ret XP = Im XP = p width of spectral function = reaction rate of particle (at space-time position X) hc Life time τ = Γ 4-dimentional generalizaton of the Poisson-bracket: W. Cassing, S. Juchem, NPA 665 (000) 377; 67 (000) 417; 677 (000) 445 6

7 General testparticle off-shell equations of motion W. Cassing, S. Juchem, NPA 665 (000) 377; 67 (000) 417; 677 (000) 445 Employ testparticle Ansatz for the real valued quantity i S < XP - insert in generalized transport equations and determine equations of motion! General testparticle off-shell equations of motion for the time-like particles: with 7

8 Collision term in off-shell transport models Collision term for reaction 1+->3+4: gain term loss term with The trace over particles,3,4 reads explicitly for fermions for bosons additional integration 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! 8

9 In-medium transition rates: G-matrix G approach Need to know in-medium transition amplitudes G and their off-shell dependence Transition probability : Coupled channel G-matrix G approach with G(p,ρ,T),T) - G-matrix from the solution of coupled-channel channel equations: G Meson selfenergy and spectral function Baryons: Pauli blocking and potential dressing (cf. talks by D. Cabrera) For strangeness: D. Cabrera, L. Tolos, J. Aichelin, E.B., arxiv: ; W. Cassing, L. Tolos, E.B., A. Ramos, NPA77 (003) 59

10 Collision width in off-shell transport model Total width = collision width + decay width : Γ = Γ coll +Γ dec Example: Collision width Γ coll for 1+->3+4 process defined from the loss term of the collision integral I coll : (similar for the n<->m reactions!) I coll ( loss ) = Γ coll(x,p,m )N r XP M 3 3 r r r r r r Γcoll( X,P,M ) = TrTrTr 3 4 A( X,P,M )A( X,P,M )A( X,P 3,M3 )A( X,P 4,M r r r r (4 ) G((P,M ) + (P,M ) (P,M ) + (P,M )) δ (P+ P P P )N 4 4 Collision width is defined by all possible interactions in the local l cell ΑS In the vacuum: Γ = Γ dec r XP M ret = Im Σ = p Γ ΓXP XP 0 ) f r f XP 3M3 XP 4M4 r! Assumptions used in transport calculations for V-mesons V (to speed up calculations): Collision width in low density approximation: Γ coll replace replace < υ σ VN tot > by averaged value G=const: Γ coll VN tot coll = γ ρ <υ σ VN coll = γ ρ G tot VN > (Works well cf. low density approximation vs. the full dynamical calculation of Γ Coll E.B., NPA696 (001) 761) in Ref.

11 Mean-field potential in off-shell transport model Many-body theory: Interacting relativistic particles have a complex self-energy: energy: The neg. imaginary part Σ = ReΣ + i ImΣ ret XP ret XP ret = Im Σ = p Γ ΓXP XP 0 to the inverse livetime of the particle τ~1/ ~1/Γ. ret XP is related via Γ = Γ coll +Γ dec The collision width Γ coll is determined from the loss term of the collision integral I coll By dispersion relation we get a contribution to the real part of self-energy energy: ReΣ ret XP ( p 0 ret ImΣ XP(q) ) = Ρ dq (q p ) 0 0 that gives a mean-field potential U XP via: Re Σ ( p ) = p U ret XP 0 0 XP the complex self-energy energy relates in a self-consistent way to the self-generated mean-field potential and collision width (inverse lifetime)

12 Detailed balance on the level of <->n: treatment of multi-particle collisions in transport approaches Generalized collision integral for n <->m reactions: W. Cassing, NPA 700 (00) 618 is Pauli-blocking or Bose-enhancement enhancement factors; η=1 for bosons and η=-1 1 for fermions is a transition probability 1

13 Antibaryon production in heavy-ion reactions Multi-meson fusion reactions m 1 +m +...+m n B+Bbar (m=π,ρ,ω,..) important for antiproton, antilambda dynamics! W. Cassing, NPA 700 (00) 618 <->3 10 Pb+Pb, 160 A GeV dn/dt [arb. units] 10 1 central BB->X 3 mesons -> BB t [fm/c] approximate equilibrium of annihilation and recreation 13

14 Parton-Hadron-String-Dynamics (PHSD( 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 article Model (DQPM) strongly interacting quasi-particles - massive quarks and gluons (g, q, q bar with sizeable collisional widths in self-generated mean-field potential bar ) A. Peshier, W. Cassing, PRL 94 (005) 17301; W. Cassing, NPA 791 (007) 365: NPA 793 (007) Spectral functions: ρ ( ω,t ) = i ( i = q,q, g ) 4ωΓ (T) i v ( ω p M (T)) + 4ω Γ (T) i i Transport theory: generalized off-shell transport equations based on the 1st order gradient expansion of Kadanoff-Baym equations (applicable( for strongly interacting system!) W. Cassing, E. Bratkovskaya, PRC 78 (008) ; NPA831 (009) ) 15; W. Cassing, EPJ ST 168 (009) 3 14

15 PHSD for HIC (highlights) dn/dy y=0 / N wound Λ+Σ 0 NA57 NA Pb+Pb, 158 A GeV, mid-rapidity HSD PHSD Λ+Σ N wound N wound PHSD provides a consistent description of p+a and HIC dynamics 15

16 Dileptons 16

17 Dilepton sources from the QGP via partonic (q,qbar, g) interactions: q l + γ * q l - q g g q γ* q γ* q q g γ* q from hadronic sources: Plot from A. Drees direct decay of vector mesons (ρ,ω,φ, ρ,ω,φ,j/ψ,ψ /Ψ,Ψ ) thermal QGP Dalitz decay of mesons and baryons (π 0,η,, ) correlated D+Dbar pairs K + l νl D 0 c c D K + 0 l ν l +qq radiation from multi-meson meson reactions (π+π, π+ρ, π+ω, ρ+ρ, π+a 1 ) - 4π hadronic bremsstrahlung essen Joachim Stroth 17

18 Dileptons at SIS energies - HADES HADES: dilepton yield dn/dm dm scaled with the number of pions N π0 Dominant hadronic sourses at M>m π : η, Dalitz decays NN bremsstrahlung direct ρ decay ρ meson = strongly interecting resonance strong collisional broadening of the ρ width In-medium effects are more pronounced for heavy systems such as Ar+KCl then C+C The peak at M~0.78 GeV relates to ω/ρ mesons decaying in vacuum E.B., J. Aichelin,, M. Thomere,, S. Vogel, and M. Bleicher,, PRC 87 (013)

19 Dileptons at SIS energies: A+A vs. N+N ratio of AA/NN spectra (scaled by N π0 ) after subtracted η contribution HSD IQMD Strong enhancement of dilepton yield in A+A vs. NN is reproduced by HSD and IQMD for C+C at 1.0,.0 A Gev and Ar+KCl at 1.75 A GeV E.B., J. Aichelin,, M. Thomere,, S. Vogel, and M. Bleicher,, PRC 87 (013)

20 Dileptons at SIS (HADES): A+A vs NN Two o contributions to the enhancement of dilepton yield in A+A vs. NN 1) ) the pn bremsstrahlung which scales with the number of collisions and not with the number of participants, i.e. pions; ) ) the multiple regeneration dilepton emission from intermediate s which are part of the reaction cycles πn; πn and NN N ; N NNNN Enhancement of dilepton yield in A+A vs. NN increases with the system size! E.B., J. Aichelin,, M. Thomere,, S. Vogel, and M. Bleicher,, PRC 87 (013)

21 Dileptons at SIS (HADES): Au+Au HADES preliminary: Au+Au, 1.3 A GeV T. Galatyuk,, QM 014 HSD predictions (013) Strong in-medium enhancement of dilepton yield in Au+Au vs. NN measurement of regeneration by HADES! E.B., J. Aichelin,, M. Thomere,, S. Vogel, M. Bleicher,, PRC 87 (013)

22 Lessons from SPS: NA60 Dilepton invariant mass spectra: NA60: Eur. Phys. J. C 59 (009) 607 PHSD: Linnyk et al, PRC 84 (011) Hybrid-UrQMD: Santini et al., PRC84 (011) QGP Fireball model Renk/Ruppert Fireball model Rapp/vanHees Ideal hydro model Dusling/Zahed Inverse slope parameter T eff eff : spectrum from QGP is softer than from hadronic phase since the QGP Q emission occurs dominantly before the collective radial flow has developed Message from SPS: (based on NA60 and CERES data) 1) Low mass spectra - evidence for the in-medium broadening of ρ-mesons ) 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 PRL 10 (009) 301

23 Dileptons at RHIC: PHENIX PHENIX: PRC81 (010) cocktail cocktail Fireball model Fireball model Rapp/vanHees Rapp/vanHees Ideal hydro Dusling/Zahed HSD Linnyk et al., PRC 85 (01) 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 The missing source (?) is located at low p T Intermediate mass spectra dominant QGP contribution 3

24 Dileptons at RHIC: STAR data vs model predictions Centrality dependence of dilepton yield (STAR: arxiv: ) Excess in low mass region, min. bias Models (predictions): Fireball model R. Rapp PHSD Low masses: collisional broadening of ρ Intermediate masses: QGP dominant Message: STAR data are described by models within a collisional broadening scenario for the vector meson spectral function + QGP 4

25 Dileptons from RHIC BES: STAR (Talk by Nu Xu at QM ) (Talk by Nu Xi at 3d CBM Meeting 14 14) Message: BES-STAR STAR data show a constant low mass excess (scaled with N(π 0 )) within the measured energy range PHSD model: excess increasing with decreasing energy due to a longer ρ-propagation in the high baryon density phase Good perspectives for future experiments CBM(FAIR) / MPD(NICA) 5

26 Dileptons at LHC O. Linnyk, W. Cassing, J. Manninen, E.B., P.B. Gossiaux, J. Aichelin, T. Song, C.-M. Ko, Phys.Rev. C87 (013) ; ; arxiv: QGP Message: low masses - hadronic sources: in-medium effects for ρ mesons are small intermediate masses: QGP + D/Dbar Dbar charm background is smaller than thermal QGP yield QGP(qbar qbar-q) q) dominates at M>1. GeV clean signal of QGP at LHC! 6

27 Messages from dilepton data Low dilepton masses: Dilepton spectra show sizeable changes due to the in-medium effects modification of the properties of vector mesons (as collisional broadening) - which are observed experimentally In-medium effects can be observed at all energies from SIS to LHC Intermediate dilepton masses: The QGP (qbar-q) q) dominates for M>1. GeV Fraction of QGP grows with increasing energy; at the LHC it is dominant Outlook: * experimental energy scan * experimentale measurements of dilepton s higher flow harmonics v n +qq essen Joachim Stroth 7

28 Outlook - Perspectives What is the stage of matter close to T c and large µ: Lattice EQS for m=0 crossover, T > T c 1st order phase transition? Mixed phase = interaction of partonic and hadronic degrees of freedom? Open problems: How to describe a first-order phase transition in transport models? How to describe parton-hadron interactions in a mixed phase? 8

29 PHSD group FIAS & Frankfurt University Giessen University Elena Bratkovskaya Wolfgang Cassing Rudy Marty Olena Linnyk Hamza Berrehrah Volodya Konchakovski Daniel Cabrera Thorsten Steinert Taesoo Song Alessia Palmese Andrej Ilner Eduard Seifert External Collaborations SUBATECH, Nantes University: Jörg Aichelin Christoph Hartnack Pol-Bernard Gossiaux Vitalii Ozvenchuk Texas A&M University: Che-Ming Ko JINR, Dubna: Viacheslav Toneev Vadim Voronyuk BITP, Kiev University: Mark Gorenstein Barcelona University: Laura Tolos Angel Ramos 9