Hybrid Model of Heavy-Ion Collisions at BES Energies with Dynamical Sources

Transcription

1 Hybrid Model of Heavy-Ion Collisions at BES Energies with Dynamical Sources Lipei Du In collaboration with Gojko Vujanovic and Ulrich Heinz Department of Physics, The Ohio State University, USA May 14, 218 Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

2 QCD phase diagram and heavy-ion collisions 27 NSAC Long Range Plan C. Shen et al, Comput.Phys.Commun. 199 (216) Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

3 Hybrid models Fluidization features in different hybrid approaches [D. Oliinychenko and H. Petersen, Phys.Rev. C93 (216) 3495] The switching criteria: either constant proper time τ or constant time in the center-of-mass frame t CM, determined by geometrical criterion. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

4 Dynamical string model (Shen and Schenke, ) Chun Shen, Dynamical initialization and hydrodynamic modeling of relativistic heavy-ion collisions Š 16 May 218, 11:3 K. Kajantie and L. McLerran, Phys. Lett. B119, 23 (1982), Nucl. Phys. B214, 261 (1983). M. Okai et al, Phys.Rev. C95 (217) C. Shen et al, Nucl. Phys. A967 (217) 796, Phys.Rev. C97 (218) Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

5 Conservation laws and source terms The conservation laws are [ ] d µ T µν = d µ T µν fluid + T µν particle =, ] d µ N µ = d µ [N µ fluid + N µ particle =, from which we can get the source terms for the fluid as What is needed to get source terms: d µ T µν fluid = Jsource(x) ν d µ T µν particle (x), d µ N µ fluid = ρ Bsource (x) d µ N µ particle (x). Pre-equilibrium dynamics to give information of particles; Energy-momentum tensor and net baryon current constructed from particles. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

6 Pre-equilibrium dynamics Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

7 Our model: Dynamical initialization based on UrQMD Instead of rescattering after production, particles get thermalized after formation = [/] τ [/] - [] - - η t z plot of particles at production time τ η s plot of particles at formation time Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

8 Energy = τ [/] τ [/] Our model: η -5% Au+Au@19.6GeV τ (fm) τ (fm) ηs Lipei Du (The Ohio State University) η C. Shen and B. Schenke, Phys.Rev. C97 (218) 2497: Hybrid Model with Dynamical Sources -5% Au+Au@2GeV 4 2 ηs May 14, / 26

9 Baryon distribution τ = τ = / η τ (fm) % Au+Au@2GeV η s Our model (produced mesons not shown) C. Shen and B. Schenke, Phys.Rev. C97 (218) 2497 Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

10 Baryon distribution Particle formation time strongly affects the baryon distribution in space-time = τ = = τ = / - - τ [/] τ [/] - - η - - η Interesting question: how will this difference affect the final momentum distributions? Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

11 Baryon distribution in space-time rapidity (central 2 GeV) /η (/) τ = / τ = / τ = / / η () This model dnb/dηs (a) 5 nucleon decelerated τ =. 5 fm nucleon + rapidity loss fluct. valence quark decelerated τ =. 5 fm valence quark + rapidity loss fluct. -5% Au+Au@2 GeV η s C. Shen and B. Schenke, Phys.Rev. C97 (218) 2497 The initial spacetime distribution of net baryon number can be strongly model dependent, within our model on the value of the formation time. Similar rapidity distributions can correspond to very different space-time rapidity distributions, and different space-time rapidity distributions may lead to different hydrodynamic evolution. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

12 Baryon distribution in space-time rapidity (central 19.6 GeV) /η (/) τ = / τ = / τ = / / η () This model dnb/dηs % GeV (b) nucleon decelerated τ =. 5 fm nucleon + rapidity loss fluct. valence quark decelerated τ =. 5 fm valence quark + rapidity loss fluct η s C. Shen and B. Schenke, Phys.Rev. C97 (218) 2497 The initial spacetime distribution of net baryon number can be strongly model dependent, within our model on the value of the formation time. Similar rapidity distributions can correspond to very different space-time rapidity distributions, and different space-time rapidity distributions may lead to different hydrodynamic evolution. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

13 Source terms Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

14 Constructing the source terms Baryon current and energy-momentum tensor of the particles are given by [D. Oliinychenko and H. Petersen, Phys.Rev. C93 (216) 3495] T µν particle (t, r) = i N µ particle (t, r) = i p µ i pν i p i K(r r i (t), p i ), p µ i b i p K(r r i (t), p i ). i The smearing kernel in the rest frame is given by [ 1 (xrf r rf,i ) 2 ] K i (t rf, x rf, p i ) = γ i exp (2πσ 2 3/2 ) 2σ 2 Θ(t form,i t rf ), 1 γ i exp (2πσ 2 3/2 ) [ (x xi (t)) 2 (u i (x x i (t))) 2 2σ 2 ] Θ(t form,i t rf ). Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

15 Thermalization of particles Θ(t form t) = 1 2 [ tanh ( tform t τ th ) ] τ + 1 th θ(t form t). 1 tform,i-trf [tanh( 2 Δτth )+1] HeavisideTheta Θ(-) Δτ [/] Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

16 Dynamical sources (central 2 GeV) Energy-momentum source J τ source fm -5 Baryon number source ρ B source fm τ =.5 fm/c Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

17 Dynamical sources (central 2 GeV) Energy-momentum source J τ source fm Baryon number source ρ B source fm τ =.7 fm/c Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

18 Dynamical sources (central 2 GeV) Energy-momentum source J τ source fm -5 Baryon number source ρ B source fm τ =.9 fm/c Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

19 Dynamical sources (central 2 GeV) Energy-momentum source J τ source fm -5 Baryon number source ρ B source fm τ = 1.1 fm/c Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

20 Evolution in the transverse plane 2 GeV) fm-5 Our model 6 fm C. Shen, QM217 In our model, bumpiness of ρb is not correlated with that of e. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

21 Hydrodynamics with dynamical sources Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

22 Dissipative hydrodynamics The conservation law of energy momentum is d µ T µν fluid = d µ(eu µ u ν (p + Π) µν + π µν ) = J ν source. The dissipative transport equations are τ Π Π + Π = ζθ δππ Πθ + λ Ππ π µν σ µν l Πn n τ Πn n p λ Πn n τ π π µν + π µν = 2ησ µν + 2τ π π µ λ ω ν λ δ ππ π µν θ τ ππ π λ µ σ ν λ + λ πππσ µν τ πn n µ ν p + l πn µ n ν + λ πn n µ ν ( µ B T ), ( µb ), T D. Bazow et al, Comput.Phys.Commun. 225 (218) G. S. Denicol et al, Phys. Rev. D89, 745, Phys. Rev. C9, Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

23 Baryon evolution The conservation law of the net baryon number is d µ N µ fluid = d µ(ρ B u µ + n µ ) = ρ Bsource. The dissipative transport equation for the baryon diffusion current is ( τ n ṅ µ + n µ = κ B µ µ ) B τ n n ν ω νµ δ nn n µ θ λ nn n ν σ µν. T In the Navier-Stokes limit, the baryon diffusion current is ( n µ κ B µ µ ) B. T ρ Bu µ and n µ together control transportation of the net baryon number when there is no source. G. S. Denicol et al, Phys. Rev. D89, 745, Phys. Rev. C9, Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

24 Baryon diffusion coefficient Relaxation time approximation [G. S. Denicol et al, arxiv: [nucl-th]] µ CB ρb T 1 B κb = ρb coth T 3 T e+p Holographic model [R. Rougemont et al, Phys. Rev. Lett. 115, 2231] fm Holographic model smoothes out spatial fluctuations of κb. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

25 Initial longitudinal profiles and driving forces Initial longitudinal profiles: P. Bozek, et al, Phys. Rev. C91 (215) 54912, C. Shen, Quark Matter 217. [ - ] - - η ρ [ - ] - - η / / µ/ η [ - ] η η Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

26 Baryon diffusion coefficient ρ /η [ - ] / = = = /η [/ - ] / = = = - - η - - η Net baryon number is transported to midrapidity by diffusion, and to large rapidities by longitudinal expansion; energy density is insensitive to baryon diffusion. Consistent with C. Shen et al, Nucl. Phys. A967 (217) Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

27 Baryon evolution with dynamical sources η [ - ] ρ η [ - ] τ = / τ = / - - η /η = τ = / τ = / τ = / τ = / - - η In spite of the expansion of the fireball, net baryon number at large rapidity increases due to continued feeding by baryon number sources (dynamical sources cease at 4 fm/c). Net baryon number doesn t decrease strongly in midrapidity because the baryon diffusion is against the flow velocity. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

28 Conclusions Based on modified UrQMD, a dynamical source model for both the energy-momentum and net baryon current is constructed; A (3+1)D hydrodynamical code with baryon evolution has been developed which can handle dynamical sources; The initial space-time rapidity distribution of net baryon number is strongly model dependent even within a single model, on the value of the formation time in our model; its influence on the final momentum distributions is an interesting question under investigation. The baryon evolution in the longitudinal direction is studied and is consistent with previous studies when the same initial condition is used; how the evolution will be changed with the quite different initial conditions got from our dynamical source model needs to be studied. Study of final spectra from full (3+1)D hydrodynamics with dynamical sources for both the energy-momentum and net baryon current is upcoming. Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26

29 Thank you very much! Lipei Du (The Ohio State University) Hybrid Model with Dynamical Sources May 14, / 26