Beam energy scan using a viscous hydro+cascade model

Transcription

1 Beam energy scan using a viscous hydro+cascade model Iurii KARPENKO INFN sezione Firenze In collaboration with Marcus Bleicher, Pasi Huovinen and Hannah Petersen Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT 6-3 / 9

2 (cascade+)hydro+cascade framework for the Beam Energy Scan Hybrid model: initial state + hydrodynamic phase + hadronic cascade thermalization particlization Initial state: thick pancakes boost ivariance is not a good approximation need for 3 dimensional evolution CGC picture loses its applicability CGC picture needs revision Baryon and electric charges obtained from the initial state included in hydro phase taken into account at particlization Fluctuations in initial state, viscosity, afterburner Pictures taken from: Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT 6-3 / 9

3 The model Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT 6-3 / 9

4 Initial stage Pre-thermal evolution: UrQMD cascade, which involves PYTHIA for s GeV scatterings The scatterings are allowed until τ = t z = τ (red curve) The minimal value of τ is τ = R γv z, when two nuclei completely pass through each other. t cascade (UrQMD) minimal hydro starting time vs collision energy hydro phase incoming nuclei pre-thermal phase (UrQMD) τ [fm/c].5 z.5.5 s NN [GeV] Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

5 Thermalization (fluidization) The pre-thermal evolution does not lead to a thermalized state at τ. Therefore, τ = τ the energy, momentum and charges of initial state particles are mapped to hydro grid: (avic) Averaged initial state from many pre-thermal UrQMD evolutions + single-shot hydrodynamics 8 6 UrQMD, epsilon(x,y) r_y [fm] r_x [fm] y [fm] (fic) A single pre-thermal UrQMD event + Gaussian smearing + event-by-event hydrodynamics: energy density [GeV/fm 3 ] x [fm] y [fm/c] energy density [GeV/fm 3 ] x [fm/c] y [fm/c] energy density [GeV/fm 3 ] x [fm/c] Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

6 Hydrodynamic stage The hydrodynamic equations: local energy-momentum and charge conservation ;ν T µν = ν T µν + Γ µ νλ T νλ + Γ ν νλ T µλ =, ;ν N ν = () where (we choose Landau definition of velocity) T µν = εu µ u ν (p + Π)(g µν u µ u ν ) + π µν () Evolutionary equations for shear/bulk, coming from Israel-Stewart formalism: < u γ ;γ π µν > = π µν π µν NS τ π 4 3 π µν ;γ u γ (3a) * Bulk viscosity ζ =, charge diffusion= vhlle code: free and open source. Comput. Phys. Commun. 85 (4), Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

7 Equations of state in the fluid stage Chiral model J. Steinheimer, et al, J. Phys. G 38, 35 () good agreement with lattice QCD at µ B = crossover type PT between confined and deconfined phases at all µ B Hadron resonance gas + Bag Model P.F. Kolb, et al, Phys.Rev. C 6, 5499 () (a.k.a. EoS Q) hadron resonance gas made of u, d quarks including repulsive meanfield Maxwell construction resulting in st order PT p(, n ) Chiral EoS B p(, n ) HRG+Bag Model EoS B Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

8 Fluid particle transition and hadronic phase ε = ε sw =.5 GeV/fm 3 (blue curve), when the system is in hadronic phase: {T µ,n b,n q } of hadron-resonance gas = {T µ,n b,n q } of fluid t Momentum distribution from Landau/Cooper-Frye prescription: cascade (UrQMD) hydro phase p d3 n i d 3 p = (fl.eq. (x,p) + δf (x,p) ) p µ dσ µ incoming nuclei pre-thermal phase (UrQMD) z Cornelius subroutine is used to compute σ i on transition hypersurface. Hadron gas phase: UrQMD cascade is employed after particlization surface. Huovinen and Petersen, Eur.Phys.J. A 48 (), 7 Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

9 Results Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

10 T Averaged initial state + non-ebe hydro Parameters fixed to: η/s = or. ε sw =.5 GeV/fm 3 8 the model, ideal the model, η/s=. the model, η/s=. NA49, 4GeV π- NA49, 4GeV, K+ NA49, 4GeV, K- dn/dy 6 dn/dy and p are nicely reproduced for SPS energies (E lab = 3 58 GeV), but p -integrated v is not y dy) dm T 3 = 4 A GeV E lab ideal + UrQMD η/s=. + UrQMD η/s=. + UrQMD NA49 π- NA49 K- NA49 K+ v p -integrated v T, c=-3% N/(m.4 d.3.. STAR v {4} ideal + UrQMD η/s=. + UrQMD m T -m [GeV] s NN [GeV] Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

11 Fluctuating initial state + EbE hydro Gaussian smearing of energy, momentum and charges at fluidization: ( ) Pijk α = Pα C exp ( xi + yj )/R η k γ ητ /R η ( ) Nijk = N C exp ( xi + yj )/R η k γ ητ /R η R = R η = fm ε sw =.5 GeV/fm 3 v p -integrated v {EP} vs T s STAR v {EP} avic ideal + UrQMD avic η/s=. + UrQMD fic, ideal + UrQMD fic, η/s=. + UrQMD dashed: average IC solid: fluctuating IC s [GeV] v ( s NN ) trend is reproduced with fic! Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

12 Fluctuating initial state + EbE hydro: extending to full BES range } R = R η = fm, τ = max{ R γvz,fm/c, ε sw =.5 GeV/fm dn ch /dη (b)..8.6 v n {EP}, -3% central STAR v STAR v {EP} 3 {EP} ideal η/s=. pure UrQMD dn ch /dη 4 3 η/s=. ideal PHOBOS -6%: s= GeV s=6.4 GeV s=9.6 GeV η s= GeV s=6.4 GeV s=9.6 GeV v n.4. s NN [GeV] v v 3 Parameter tuning needed? Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT 6-3 / 9

13 Smearing matters energy density [GeV/fm^3] energy density [GeV/fm^3].5 "<awk R_eta=.7 '{if($==.) fm print $}' outd.dat" u :3:6 S = "<awk R_eta=. '{if($==.) fm print $}' outd.dat" u :3:6 S = eta eta x [fm] x [fm] energy density [GeV/fm^3] eta.5.5 "<awk R_eta=.4 '{if($==.) fm print $}' outd.dat" u :3:6 S = Same total energy: E = 473 GeV x [fm] Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT 6-3 / 9

14 Learning parameter dependence Response of the observables: T eff, inverse slope of p T spectrum dn/dy at midrapidity p T integrated v {EP} to the change of every parameter with respect to its default value. v v {EP}, s=9.6 GeV, -3% central STAR v {EP} change of R change of R η change of sw change of τ relative change of the parameter [GeV] T eff.34 T change of R eff change of R η.3 p change of sw.3 change of τ K π relative change of the parameter (b) dn/dy y= dn/dy y= change of R change of R η change of sw change of τ relative change of the parameter (a) Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT 6-3 / 9

15 Learning parameter dependence () par. R R z η/s τ ε crit T eff dn/dy v Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

16 Parameter values used to approach the data EoS: Chiral model, ε sw =.5 GeV/fm 3. s τ R R z η/s [GeV] [fm/c] [fm] [fm] * * *...8 *here we increase τ as compared to τ = γv R z. η/s effective η/s vs collision energy s NN [GeV] Green band: same v and ±5% change in T eff.! Actual error bar would require a proper χ fitting of the model parameters (and enormous amount of CPU time). Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

17 T A GeV PbPb SPS ( s = 8.8 and 7.3 GeV) 8 η/s=. NA49, π- NA49, K+ NA49, K- E lab =4 A GeV -5% central (c) dy) 3 η/s=. NA49, π- NA49, K- NA49, K+ NA49, p dn/dy 6 4 dm T T N/(m d (c) y - E lab =4 A GeV, -5% central m T -m [GeV] dn/dy η/s=.5 - NA49, π + NA49, K - NA49, K E lab =58 A GeV -5% central -4-4 y (b) dy) dm T N/(m d 3 - E lab =58 A GeV, -5% central η/s=.5 NA49, π- NA49, K- NA49, K+ NA49, p m T -m [GeV] (b) Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

18 T T RHIC BES + top RHIC dy) dp p N/( π d η/s=.8 - PHOBOS, π - PHOBOS, K PHOBOS, p (a) dy) T dp d N/( π p T 3 η/s=.8 PHENIX, π- PHENIX, K- PHENIX, p - s=6.4 GeV, -5% central - p spectra, s= GeV, -5% central T p [GeV] T p [GeV] T 7 dn ch /dη 6 dn ch /dη s= GeV s=6.4 GeV s=39 GeV s=9.6 GeV -6% PHOBOS η The rapidity/pseudorapidity and p T distributions from SPS/NA49 together with RHIC are reasonably reproduced. Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

19 Elliptic and triangular flows at RHIC BES + top RHIC v,v 3 vs collision energy v,v 3 vs centrality v n STAR v {EP} STAR v 3 {EP} v, η/s( s) and R( s) v 3, η/s( s) and R( s) s NN [GeV] v n {EP}, -3% central v v v {EP} and v 3 {EP}, s=39 GeV STAR v {EP} η/s=.8 ideal centrality percentage v v 3 EoS dependence, hyperon polarization and HBT: in my Workshop talk Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

20 Summary 3+D EbE UrQMD + viscous hydro + UrQMD model: pre-termal stage: UrQMD 3+D viscous hydrodynamics EoS at finite µ B : Chiral model, EoS Q Conclusions: The model is applied for Au+Au + Observables do depend on the way the initial state is constructed, and parameters of the fluidization procedure. Eyeball parameter adjustment results in a reasonable reproduction of basic hadronic observables. Much more rigorous analysis of the parameter space: see next talk by Jussi Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9

21 Outlook: At lower end of the BES, pre-hydro stage in a sandwich approach is too long: UrQMD 3.4, J. Auvinen, H. Petersen, Phys.Rev.C 88:6498,3 a) Charged hadrons, b = fm Charged hadrons, b = fm.3.8 Integrated v Event plane analysis Before hydro After hydro After hadronic rescattering s NN [GeV] b) Integrated v Event plane analysis Before hydro After hydro After hadronic rescattering s NN [GeV] This can be overcome with multi-fluid dynamics (with cold nuclear matter IC), or with an IC model allowing for dynamical fluidization. Iurii Karpenko (INFN) BES in a viscous hydro+cascade INT / 9