Beam energy scan using a viscous hydro+cascade model: an update

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1 Beam energy scan using a viscous hydro+cascade model: an update Iurii KARPENKO Frankfurt Institute for Advanced Studies/ Bogolyubov Institute for heoretical Physics ransport group meeting, December 17, 14 In collaboration with M. Bleicher, P. Huovinen, H. Petersen Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

2 Outline Motivation Model description Results 1: the first round of simulations Results : adjustment to the data Addition to Results 1: EoS dependence Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec. 14 / 15

3 Some lessons from Au-Au RHIC/ Pb-Pb LHC Hydrodynamic/hybrid approach works very well η/s 1/(4π) at top RHIC with Monte Carlo Glauber IC, and somewhat larger value for.76 ev PbPb LHC However, there are large uncertainties in η/s extraction from the initial state model, quantities to fit, model parameters. Figure: extracted η/s for top RHIC (grey bands),.76 ev LHC (green bands). aken from Huichao Song, QM1 proceedings arxiv: Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec. 14 / 15

4 Motivation: apply a hybrid for RHIC BES, FAIR/NICA to understand whether fluid is created at lower energies, find its transport properties (η/s,...) and constrain EoS. * plot provided by M. Gazdzicki For Beam energy scan, we need a more elaborate model: 1 D (non-boost-invariant) fluctuating initial state Baryon and electric charge densities obtained from an initial state model propagated in hydro phase and included in EoS taken into account in particlization procedure Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

5 he model Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

6 Initial conditions for hydro phase t hydro starting time vs collision energy cascade (UrQMD).5 hydro phase incoming nuclei pre-thermal phase (UrQMD) [fm/c] τ start.5 z s [GeV] Pre-thermal phase: UrQMD Hydro starts at τ = t z = τ (red curve): τ = γv R z At τ = τ we deposit the energy/momentum, baryon and electric charge from particle to fluid cells: ( ) 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 Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

7 Hydrodynamic phase he hydrodynamic equations: local energy-momentum and charge conservation ;ν µν = ν µν + Γ µ νλ νλ + Γ ν νλ µλ =, ;ν N ν = (1) where (we choose Landau definition of velocity) 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 π µν ;γ u γ (a) where < A µν >= ( 1 µ α ν β + 1 ν α µ β 1 µν αβ )A αβ * Bulk viscosity ζ =, charge diffusion= vhlle code, see arxiv: for the details of the code and its testing. Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

8 Equations of state for hydrodynamic phase Chiral model coupled to Polyakov loop to include the deconfinement phase transition good agreement with lattice QCD data at µb =, also applicable at finite baryon densities (current version) has crossover type P between hadron and quark-gluon phase at all µ B Hadron resonance gas + Bag Model (a.k.a. EoS Q) hadron resonance gas made of u,d quarks including repulsive meanfield the phases matched via Maxwell construction, resulting in 1 st order P.5 n B = HRG+BM EoS Chiral EoS.5 n B / /4 =. ] p [GeV/fm 1.5 ] p [GeV/fm [GeV/fm ] [GeV/fm ] refs: J. Steinheimer, S. Schramm and H. Stocker, J. Phys. G 8, 51 (11); P.F. Kolb, J. Sollfrank, and U. Heinz, Phys.Rev. C 6, 5499 (). Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

9 Fluid particle transition ε = ε sw =.5 GeV/fm (blue curve): { µ,n b,n q } of hadron-resonance gas = { µ,n b,n q } of fluid t Momentum distribution from Landau/Cooper-Frye prescription: cascade (UrQMD) hydro phase incoming nuclei pre-thermal phase (UrQMD) z p d n i d p = (fl.eq. (x,p) + δf (x,p) ) p µ dσ µ Cornelius subroutine is used to compute σ i on transition hypersurface. UrQMD cascade is employed after particlization surface. Huovinen P and Petersen H 1, Eur.Phys.J. A Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

10 Results 1 From the first round of simulations: fixed η/s, Chiral EoS he rest of the parameters are fixed to their reasonable values: R = R η = 1 fm, } τ = max{ R γvz,1fm/c ε sw =.5 GeV/fm Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

11 Results: E lab = 4 A GeV Pb-Pb (SPS) snn = 8.8 GeV, -5% central collisions (b =...4 fm) (Chiral EoS only) dn/dy E lab =4 A GeV, central ideal η/s=. pure UrQMD NA49, π NA49, K+ NA49, K dy) [GeV ] dm d N/(m E lab =4 A GeV, central ideal η/s=. pure UrQMD NA49, π NA49, K NA49, K y m m [GeV] viscous entropy production viscosity causes stronger transverse expansion Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

12 Going to s = 19.6 GeV interval Solid lines: η/s =. except for GeV where η/s =.1 7 dn ch /dη.1.9 p integrated v {EP} /dη ch dn 4 v.5.4 GeV, η/s=.1 6 GeV, η/s=. 9 GeV, η/s= GeV, η/s=. -% PHOBOS -6% PHOBOS...1 SAR v {EP} ideal η/s=. pure UrQMD η s [GeV] fine tuning is needed for every collision energy individually Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec. 14 / 15

13 Results : parameter adjustment to the data in BES region using Chiral EoS!!! Observables in the model strongly depend on the details of the initial state for hydrodynamic expansion, because the hydro phase is shorter compared to full RHIC/LHC energies Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec. 14 / 15

14 Parameter space exploration Response of the observables: ( ) dn eff from m dm dy = C exp m eff fit dn/dy in y <. p integrated elliptic flow v {EP} to the change of every individual parameter with respect to its default value. Defaults: η/s =, R = R η = 1 fm, ε crit =.5 GeV/fm. [GeV] eff eff change of R change of R η change of crit relative change of the parameter.1.9 v {EP}, s=19.6 GeV, -% central 1 5 dn/dy y= v SAR v {EP} change of R change of R η change of τ y= dn/dy change of R change of R η change of crit relative change of the parameter relative change of the parameter Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

15 par. R R z η/s τ ε crit eff dn/dy v adjusting to experimental data Energy dependent model parameters: s [GeV] τ [fm/c] R [fm] R z [fm] η/s 7.7/8.8./ /17. 1./ Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

16 Results for A GeV SPS 1 η/s=. Rt=1.4 Rz=.5 NA49, π NA49, K+ NA49, K E lab =4 A GeV, central η/s=. Rt=1.4 Rz=.5 NA49, π- NA49, K- NA49, K+ NA49, p 8 dn/dy dy) 6 4 dm N/(m d 1 E lab =4 A GeV (SPS), central y m -m [GeV] η/s=.15 Rt=1.4 Rz=.5 NA49, 158 GeV π- NA49, 158 GeV, K+ NA49, 158 GeV, K- E lab =158 A GeV (SPS), central η/s=.15 Rt=1.4 Rz=.5 NA49, 158 GeV, π- NA49, 158 GeV, K- NA49, 158 GeV, K+ NA49, 158 GeV, p 1 dy) dn/dy 8 dm N/(m d y 1 E lab =158 A GeV, central m -m [GeV] Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

17 Results for RHIC BES + top RHIC p spectra, s=6.4 GeV η/s=.8, Rt=1., Rz=.7 PHOBOS, c= 15%, π PHOBOS, c= 15%, K PHOBOS, c= 15%, p p spectra, s= GeV, 5% central η/s=.8, Rt=1., Rz=1. PHENIX, π PHENIX, K PHENIX, p dp dy) dy) dp d N/( π p 1 d N/( π p p [GeV] p [GeV] dn ch /dη s= GeV s=6.4 GeV s=9 GeV s=19.6 GeV -% PHOBOS -6% PHOBOS p integrated v {EP} SAR v {EP}, c=-% η/s( s), R( s) 5.6 dn ch /dη 4 v η s [GeV] Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

18 he Horn and the Step K+/π+, midrapidity.4. K-/π-, midrapidity s [GeV] s [GeV].45.4 eff variable η/s and R 1 1 dn/dy y=.5 p 1 [GeV] eff..5 K- (solid) K+ (dash) y= dn/dy π- 6 5 variable η/s 4.1 s [GeV] s [GeV] Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

19 HB(interferometry) measurements he only tool for space-time measurements at the scales of 15 m, s q = p p 1 Gaussian approximation of CFs (q ): 1 k = ( p 1 + p ) C(p 1,p ) = P(p 1,p ) P(p 1 )P(p ) = real event pairs mixed event pairs C( k, q) = 1+λ(k)e q out R out q side R side q long R long R out,r side,r long (HB radii) correspond to homogeneity lengths, which reflect the space-time scales of emission process In an event generator, BE/FD two-particle amplitude (anti)symmetrization must be introduced Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

20 Femtoscopic radii 8 Rout 8 Rside R [fm] 5 R [fm] SAR, c=-5%, p =.5 GeV η/s( s), R( s) s [GeV] s [GeV] 1.8 Ro/Rs 8 Rlong R [fm] s [GeV] s [GeV] Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

21 Addition to the Results 1: EoS dependence From the first round of simulations: fixed η/s, R = R η = 1 fm, } τ = max{ R γvz,1fm/c ε sw =.5 GeV/fm Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

22 Effects of the EoS Q compared to Chiral EoS? Yes: hydro phase in average lasts longer with EoS Q GeV, τ =1 Chiral GeV, τ =1 1P 9 GeV, τ =1 Chiral 9 GeV, τ =1 1P 19.6 GeV, Chiral 19.6 GeV, 1P 7.7 GeV Chiral 7.7 GeV, 1P GeV, τ =1 Chiral GeV, τ =1 1P 9 GeV, τ =1 Chiral 9 GeV, τ =1 1P 19.6 GeV, Chiral 19.6 GeV, 1P 7.7 GeV Chiral 7.7 GeV, 1P dn/dτ 4 dn/dτ 15 last interactions particlization τ [fm/c] τ [fm/c] Can we see it in femtoscopy (HB), or any other observables? Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

23 Femtoscopic radii: ideal hydro/chiral EoS, ideal hydro/eos Q, visc.hydro/chiral EoS R long R out/rside R out /R side ideal ideal, 1P EoS η/s=. SAR R [fm] s [GeV] s [GeV] 8 8 R out R side R [fm] 5 R [fm] s [GeV] s [GeV] Previous results for EoS dependence of HB in hybrid UrQMD, see Q. Li et al., Phys.Lett.B674:111,9 Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

24 EoS dependence of the elliptic flow ideal hydro/chiral EoS, ideal hydro/eos Q, visc.hydro/chiral EoS, pure UrQMD.1.9 p integrated v {EP} vs collision energy v s [GeV] SAR v {EP} fic, ideal fic, ideal, 1P EoS fic, η/s=. pure UrQMD Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15

25 Summary +1D EbE viscous hydro + UrQMD model: pre-termal stage: UrQMD +1D viscous hydrodynamics, EbyE treatment EoS at finite µ B : Chiral model, EoS Q Conclusions: Model applied for s NN = GeV A+A collisions. A fit to experimental data suggests η/s =..8 when s = GeV, modulo initial state (UrQMD) and EoS (Chiral model) used. his hints for µ B dependent η/s or η/(ε + p) being appropriate quantity. EoS Q is likely to be disfavored by the data (too small v + too small dn/dη, slightly worse for HB. Harder to compensate it by readjusting other model parameters) More experimental data and much more parameter space exploration is needed to extract η/s and other model parameters less ambiguously. Work in progress. hank you for your attention! Yuriy Karpenko (FIAS/BIP) Beam energy scan using visc.hydro+cascade ransport group meeting, 17 Dec / 15