Covariant transport approach for strongl interacting partonic sstems Wolfgang Cassing Jamaica, 03.01.2010
Compressing and heating hadronic matter: sqgp Questions: What What are the transport properties of the sqgp? How How ma the hadronization (partons hadrons) occur? Where Where do we see traces of parton dnamics in HIC?
From hadrons to partons In order to stud of the phase transition from hadronic to partonic matter Quark-Gluon Gluon-Plasma we need a consistent dnamical description with explicit parton-parton interactions (i.e. between quarks and gluons) explicit phase transition from hadronic to partonic degrees of freedom QCD equation of state (EoS) for the partonic phase Transport theor: : off-shell Kadanoff-Bam equations for the Green-functions G < h(x,p) in phase-space space representation for the partonic and hadronic phase Parton-Hadron-String-Dnamics (PHSD( PHSD) QGP phase described b input from the Dnamical QuasiParticle article Model (DQPM)
The Dnamical QuasiParticle Model (DQPM) Spectral functions for partonic degrees of freedom (g, q, q bar ): gluon mass: gluon width: N c = 3 quark width: with E 2 (p)= p 2 + M 2 - γ 2 Peshier, PRD 70 (2004) 034016; Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)
The running coupling g 2 3 parameters: T s /T c =0.46; c=28.8; λ=2.42 α S (T) 2.5 2.0 1.5 1.0 0.5 N τ =8 lqcd: O. Kaczmarek et, PRD 72 (2005) 059903 fit to lattice (lqcd) entrop densit: quasiparticle properties (N f =3; T c = 0.185 GeV) 0.0 1 2 3 4 5 6 7 8 9 10 T/T C [GeV] 1.0 quarks 0.8 0.6 M 0.4 q large width for gluons and quarks! 0.2 γ q 0.0 0 1 2 3 4 5 T/T C
DQPM thermodnamics (N f =3) Thermodnamics: interaction measure: 20 15 10 5 0 N f = 3 entrop 200 400 600 800 1000 T [MeV] energ densit: s/t 3 ε/t 4 pressure P N f = 3 0.00 1 10 100 1000 DQPM gives a perfect description of lqcd results! p/ε 0.35 0.30 0.25 0.20 0.15 0.10 0.05 lqcd: M. Cheng et al., PRD 77 (2008) 014511 equation of state ε [GeV/fm 3 ] cf. V. D. Toneev, Heav Ion Phs. 8 (1998) 83
Transport properties of hot glue Wh do we need broad quasiparticles? shear viscosit ratio to entrop densit: 1 pqcd η/s 0.1 T = 2 T C N f =0 1/4π 0.0 0.1 0.2 0.3 0.4 0.5 0.6 γ g [GeV] otherwise η/s will be too high!
Time-like and space-like quantities some short-hand hand notations (useful for all single-particle quantities): gluons quarks antiquarks Time-like: Θ(+P 2 ): particles ma deca to real particles or interact q q e + e - Space-like: Θ(-P 2 ): particles are virtuell and appear as exchange quanta in interaction processes of real particles γ * e - e - Cassing, NPA 791 (2007) 365: NPA 793 (2007) q * q
Differential quark densit Example: Quarks: I(ω,p) 5 Quarks: I(ω,p) p=ω T=1.05 T C T=3 T C 1.5 time-like 4 time-like ω [GeV] 1.0 0.5 1E-5 2.8E-5 4.6E-5 6.4E-5 8.2E-5 1E-4 ω [GeV] 3 2 5E-4 1.4E-3 2.3E-3 3.2E-3 4.1E-3 5E-3 1 p=ω space-like 0.0 0.0 0.5 1.0 1.5 p [GeV/c] space-like 0 0 1 2 3 4 5 p [GeV/c] Large space-like contributions for broad quasiparticles! Cassing, NPA 791 (2007) 365: NPA 793 (2007)
Time-like and space-like densities densities : scalar densities: # * (T C / T) 3 2.0 1.5 1.0 0.5 N + g N g N + q N q ρ s g ρ s g 0.0 0 1 2 3 4 5 T/T C more virtuell (space-like) than time-like gluons but more time-like than virtuell quarks!
Time-like and space-like energ densities x: gluons, quarks, antiquarks 6 energ densit / T 4 5 4 3 2 1 0 T 00 T 00 g + g T 00 T 00 q + q 250 500 750 1000 T [MeV] space-like energ densit dominates for gluons; space-like parts are identified with potential energ densities!
Potential energ versus scalar parton densit potential energ: P = <P xx > - V s + V 0 ε = <p 0 > + V s + V 0 3.0 3.0 # [GeV] 2.5 2.0 1.5 1.0 V P /ρ S V 0 /ρ S V S /ρ S # [GeV] 2.5 2.0 1.5 1.0 U 0 U S 0.5 0.5 0.0 1 10 100 ρ S [fm -3 ] 0.0 1 10 100 ρ S [fm -3 ] mean fields: U s = dv s /dρ s U 0 = dv 0 /dρ 0 PHSD
Summar of part I The dnamical quasiparticle model (DQPM) well matches lqcd (with onl 3 parameters)! DQPM allows to extrapolate to finite quark chemical potentials DQPM separates lime-like like quantities from space-like (interaction) regions (needed for off-shell transport) DQPM provides mean-fields for gluons and quarks as well as effective 2-bod 2 interactions PHSD
I. PHSD: basic concepts 1. Initial A+A collisions off-shell HSD: string formation and deca to pre-hadrons Strings excited color singlet states time (qq - q) or (q qbar) (in HSD: pre-hadrons = hadrons under formation time τ F ~ 0.8 fm/c) q hadrons τ F color electric field hadrons qq z 2. Fragmentation of pre-hadrons into quarks: dissolve all new produced secondar hadrons to partons (and attribute a random color c) using the spectral functions from the Dnamical QuasiParticle Model (DQPM) approximation to lqcd -- 4-momentum, flavor and color conservation --
3. Partonic phase: II. PHSD: partonic phase Degrees of freedom: quarks and gluons (= dnamical quasiparticles ) (+ hadrons) Properties of partons: off-shell spectral functions (width, mass) defined b DQPM EoS of partonic phase: from lattice QCD (fitted b DQPM) elastic parton-parton interactions: using the effective cross sections from the DQPM inelastic parton-parton interactions: quark+antiquark (flavor neutral) <=> gluon (colored) gluon + gluon <=> gluon (possible due to large spectral width) quark + antiquark (color neutral) <=> hadron resonances Note: inelastic reactions are described b Breit-Wigner cross sections determined b the spectral properties of constituents (q,q bar,g)! parton propagation: with self-generated potentials U q, U g Cassing, Bratkovskaa, PRC 78 (2008) 034919 Cassing, EPJ ST 168 (2009) 3
III. PHSD: hadronization Based on DQPM: massive, off-shell quarks and gluons with broad spectral functions hadronize to off-shell mesons and barons: gluons q + qbar q + qbar meson q + q +q baron Hadronization happens: when the effective interactions become attractive for parton densities 1 < ρ P < 2.2 fm -3 : <= from DQPM Note: nucleon: parton densit ρ Ν P = N q / V N =3 / 2.5 fm 3 =1.2 fm -3 meson: parton densit ρ m P = N q / V m = 2 / 1.2 fm 3 =1.66 fm -3 Parton-parton recombination rate = probabilit to form bound state during fixed time-interval interval Δt t in volume ΔV: 4 d P 1 2 <= from DQPM flux V ( ρp ) qq ΔVΔt ΔV and recomb. model i,j ΔV ( ) 2 Matrix element V ρp q q increases drasticall for ρ P ->0 => => hadronization successful! 4 d P ΔVΔt ρ P 0
IV. PHSD: hadronization Conservation lows: 4-momentum conservation invariant mass and momentum of meson flavor current conservation quark-antiquark antiquark content of meson color + anticolor color neutralit large parton masses dominant production of vector mesons or baron resonances (of finite/large width) resonance state (or string) is determined b the weight of its spectral function at given invariant mass M hadronic resonances are propagated in HSD (and finall deca to the groundstates b emission of pions, kaons, etc.) Since the partons are massive the formed states are ver heav (strings) entrop production in the hadronization phase! 5. Hadronic phase: hadron-string interactions > off-shell transport in HSD
V. PHSD: Hadronization details Local off-shell transition rate: (meson formation) using W m : Gaussian in phase space Cassing, Bratkovskaa, PRC 78 (2008) 034919 Cassing, EPJ ST 168 (2009) 3
Application to nucleus-nucleus collisions energ balance central Pb + Pb at 158 A GeV particle balance 4000 Pb+Pb, 158 A GeV, b=1 fm 2000 Pb+Pb, 158 A GeV, b=1 fm 3000 E tot E p 1500 # [GeV] 2000 1000 E m E B Number 1000 500 partons mesons new B+Bbar 0 0 3 5 8 10 13 15 18 20 t [fm/c] 0 0 3 5 8 10 13 15 18 20 t [fm/c] onl about 40% of the converted energ goes to partons; the rest is contained in the large hadronic corona! W.C., E.L.B.: NPA 831 (2009) 215
Proton stopping at SPS dn/d 50 40 30 20 10 p Pb+Pb, 7% central NA49 HSD 40 A GeV 80 A GeV dn/d 50 40 30 20 10 _ p-p Pb+Pb 158 A GeV bin NA49 HSD 0 1 2 3 4 5 0-3 -2-1 0 1 2 3 0-3 -2-1 0 1 2 3 looks not bad in comparison to NA49, but not sensitive to parton dnamics! Cassing & Bratkovskaa, NPA 831 (2009) 215
Rapidit distributions of π,, K +, K - 250 200 150 π 40 A GeV, 7% central π Pb+Pb 80 A GeV, 7% central π 158 A GeV, 5% central 100 50 dn/d 0 30 25 20 15 10 5 0 20 15 10 5 K + K + K + K HSD K K PHSD 0-4 -3-2 -1 0 1 2 3-4 -3-2 -1 0 1 2 3-4 -3-2 -1 0 1 2 3 4 pion and kaon rapidit distributions become slightl narrower Cassing & Bratkovskaa, NPA 831 (2009) 215
PHSD: Transverse mass spectra at SPS 10 4 10 3 Central Pb + Pb at SPS energies 40 A GeV, 7% 10 4 10 3 Pb+Pb, mid-rapidit 80 A GeV, 7% 10 4 10 3 158 A GeV, 5% 1/m T dn/dm T d [(GeV) -2 ] 10 2 10 1 10 0 K + K *0.1 π 10 2 10 1 10 0 K + K *0.1 π 10 2 10 1 10 0 K + K *0.1 π 10-1 10-2 10-1 10-2 HSD PHSD 10-1 10-2 0.0 0.2 0.4 0.6 0.8 1.0 m T -m 0 [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 m T -m 0 [GeV] 0.0 0.2 0.4 0.6 0.8 1.0 m T -m 0 [GeV] PHSD gives harder spectra and works better than HSD at top SPS energies However, at low SPS (and FAIR) energies the effect of the partonic phase is NOT seen in rapidit distributions and m T spectra Cassing & Bratkovskaa, NPA 831 (2009) 215
Rapidit distributions of strange barons Pb+Pb 20 15 40 A GeV, 7% central Λ+Σ 0 80 A GeV, 7% central 158 A GeV, 10% central HSD PHSD dn/d 10 dn/d 5 0 2.0 1.5 1.0 0.5 0.0-3 -2-1 0 1 2 3 Ξ 40 A GeV, 7% central -3-2 -1 0 1 2 3 NA49, 5% NA49 NA49, 5% -3-2 -1 0 1 2 3-3 -2-1 0 1 2 3 Pb+Pb 80 A GeV, 7% central NA49-3 -2-1 0 1 2 3-3 -2-1 0 1 2 3 158 A GeV, 10% central HSD PHSD similar to HSD, reasonable agreement with data Cassing & Bratkovskaa, NPA 831 (2009) 215
Rapidit distributions of (multi-)strange antibarons dn/d 2.5 2.0 1.5 1.0 0.5 40 A GeV, 7% central Λ+Σ 0 NA49 NA49, 5% Pb+Pb 80 A GeV, 7% central 158 A GeV, 10% central HSD PHSD strange antibarons Λ+Σ 0 0.0 0.4-3 -2-1 0 1 2 3 40 A GeV, 7% central -3-2 -1 0 1 2 3-3 -2-1 0 1 2 3 Pb+Pb 80 A GeV, 7% central 158 A GeV, 10% central dn/d 0.3 0.2 0.1 Ξ + NA49 HSD PHSD multi-strange antibaron _ Ξ + 0.0-3 -2-1 0 1 2 3-3 -2-1 0 1 2 3-3 -2-1 0 1 2 3 enhanced production of (multi-) ) strange anti-barons in PHSD Cassing & Bratkovskaa, NPA 831 (2009) 215
Centralit distributions of (multi-)strange (anti-)barons strange barons Λ+Σ 0 dn/d =0 / N wound 0.06 0.05 0.04 0.03 0.02 0.01 Λ+Σ 0 NA57 NA49 0.00 0 100 200 300 400 Pb+Pb, 158 A 0.010 GeV, mid-rapidit HSD PHSD 0.008 0.006 0.004 0.002 Λ+Σ 0 0.000 0 100 200 300 400 strange antibarons Λ+Σ 0 N wound N wound multi-strange baron Ξ - dn/d =0 / N wound 10-2 10-3 Ξ NA57 NA49 HSD PHSD 10-4 0 100 200 300 400 Pb+Pb, 158 A GeV, mid-rapidit 10-3 10-4 Ξ + 0 100 200 300 400 multi-strange antibaron _ Ξ + N wound N wound enhanced production of (multi-) ) strange antibarons in PHSD Cassing & Bratkovskaa, NPA 831 (2009) 215
Number of s-bar s quarks in hadronic and partonic matter Number of s-bar s quarks in antibarons for central Pb+Pb collisions at 158 A GeV from PHSD and HSD 12 Pb+Pb, 158 A GeV, b=0.5 fm 10 N (time) 8 6 4 2 s-quarks in antibarons HSD PHSD 0 0 5 10 15 20 25 30 35 40 time [fm/c] significant effect on the production of (multi-)strange antibarons due to a slightl enhanced s-sbar s sbar pair production in the partonic phase from massive time-like gluon deca and a larger formation of antibarons in the hadronization process! Cassing & Bratkovskaa, NPA 831 (2009) 215
Perspectives at FAIR energies partonic energ fraction vs centralit and energ partonic energ fraction Pb+Pb, 158 A GeV 0.4 b [fm] 1 3 0.3 5 7 0.2 9 11 13 0.1 0.0 2 3 4 5 6 7 8 9 10 t [fm/c] partonic energ fraction 0.4 0.3 0.2 0.1 Pb+Pb, b=1 fm T kin [A GeV] 20 40 80 160 0.0 0 3 5 8 10 13 15 18 20 t [fm/c] Dramatic decrease of partonic phase with decreasing energ and centralit! Cassing & Bratkovskaa, NPA 831 (2009) 215
Summar of part II PHSD provides a consistent description of off-shell parton dnamics in line with lqcd; ; the repulsive mean fields generate transverse flow The dnamical hadronization in PHSD ields particle ratios close to the (GC) statistical model at a temperature of about 170 MeV The elliptic flow v 2 scales with the initial eccentricit in space as in ideal hdrodnamics The Pb + Pb data at top SPS energies are rather well described within PHSD including baron stopping, strange antibaron enhancement and meson m T slopes At FAIR energies PHSD gives practicall the same results as HSD (except for strange antibarons) when the lqcd EoS (where the phase transition is alwas a cross-over) over) is used
Open problems Is the critical energ/temperature provided b the lqcd calculations sufficientl accurate? How to describe a first-order phase transition in transport? How to describe parton-hadron interactions in a mixed phase?
Thanks in particular to Elena Bratkovskaa (dnamical hadronization and application to A+A reactions) Sascha Juchem (off-shell transport) Andre Peshier (DQPM) and the numerous theoretical and experimental friends and colleagues!