Three-fluid hydrodynamics based event simulation for collisions at NICA and FAIR energies

Transcription

1 model Model Phy. Input output oberv. Three-fluid hydrodynamic baed event imulation for colliion at NICA and FAIR energie P. Batyuk, D. Blachke, M. Bleicher, Yu.B. Ivanov, Iu. Karpenko, S. Mert, M. Nahrgang, H. Peteren, O. Rogachevky Vekler and Baldin LHEP, Dubna, Dubna, Ruia Intitute of Theoretical Phyic, Univerity of Wroclaw, Wroclaw, Poland Bogoliubov Laboratory of Theoretical Phyic, Dubna, Dubna, Ruia National Reearch Nuclear Univerity "MEPhI", Mocow, Ruia Frankfurt Intitute for Advanced Studie (FIAS), Frankfurt am Main, Germany National Reearch Centre "Kurchatov Intitute", Mocow, Ruia Bogolyubov Intitute for Theoretical Phyic, Kiev, Ukraine INFN - Sezione di Firenze, Seto Fiorentino (Firenze), Italy Department of Phyic, Duke Univerity, Durham, North Carolina, USA SUBATECH, Univerité de Nante, France Goethe Univerität, Frankfurt am Main, Germany GSI Helmholtzzentrum für Schwerionenforchung GmbH, Darmtadt, Germany Meeting of the working group on theory of hadronic matter under extreme condition, Dubna, October 31-November 3, 2016

2 Exploring Nuclear Phae Diagram model Model Phy. Input output oberv. At which incident energy doe onet of deconfinement happen? What i the order of the deconfinement tranition at high baryon denitie? I there a critical end point in the phae diagram?

3 Hydrodynamic veru Kinetic model Model Phy. Input output oberv. Why we are not atified with kinetic or hybrid model? Only croover tranition into QGP i acceible in kinetic A Multi-Phae Tranport (AMPT) model [Lin, Ko and Pal, PRL 89, (2002)] Parton-Hadron-String Dynamic [Caing, Bratkovkaya, arxiv: (2009)] In hybrid model (Kinetic-Hydro-Kinetic), tranition into QGP i inacceible at the early (nonequilibrium) tage of the colliion 3-Fluid Hydrodynamic directly addree Equation of State (EoS)! 1t-order phae tranition into QGP i acceible through EoS Tranition into QGP i acceible alo at the early (nonequilibrium) tage of the colliion However, all thi require certain approximation

4 Aumption model Model Ditribution are eparated in momentum pace different fluid Leading particle carry baryon charge 2 baryon-rich fluid: projectile-like and target-like Phy. Input output oberv. At high incident energie (E lab > 10A GeV) Produced particle populate mid-rapidity fireball fluid Thi a minimal extenion of hydrodynamic required by heavy-ion dynamic

5 Hitory model Model Phy. Input output oberv. Kurchatov Int : 2-fluid hydro with free-treaming radiation of pion Mihutin, Rukikh, and Satarov Frankfurt Univerity : 3-fluid hydrodynamic with intant formation of fireball Brachmann, Katcher, Dumitru, Richke, Maruhn, Stöcker, Greiner, Mihutin, Satarov, et al. GSI 2003 now: 3-fluid hydrodynamic with delayed formation of fireball Ivanov, Rukikh, Toneev

6 Equation of Motion model Model Phy. Input output oberv. Produced particle populate mid-rapidity fireball fluid Target-like fluid: µ J µ t =0 µ T µν = Ftp ν + F ν Leading particle carry bar. charge Projectile-like fluid: µ J µ p =0, µ T µν p Fireball fluid: J µ f =0, µ T µν =Fpt ν + F ν t f t exchange/emiion = F ν pt + F ν f p f tp F ν Baryon-free fluid Source term Exchange The ource term i delayed due to a formation time τ f p F f ν t Total energy-momentum conervation: µ (T p µν + T µν t + T µν f ) = 0

7 Hydrodymanic denitie model Model Phy. Input output oberv. Baryon current: J µ α = n α u µ α n α = baryon denity of α-fluid u µ α = 4-velocity of α-fluid Energy-momentum tenor: T α µν = (ε α + P α )u αu µ α ν g µν P α ε α = energy denity P α = preure + Equation of tate: P = P(n, ε) Final Aim: To find a proper EoS, which reproduce all data

8 Phyical Input I model Model Phy. Input output oberv. I. Equation of State Hadronic EoS Galitky&Mihutin (1979) 1t-order tranition to QGP (2-phae EoS ) croover EoS [Khvorotukhin, Skokov, Redlich, Toneev, (2006)] P/(n 0 m N ) Phae tranition = EoS oftening T=10, 100, 200 MeV hadr. EoS 2-phae EoS croover EoS n/n 0

9 Phyical Input II and III model Model Phy. Input output oberv. II. Friction wa fitted to reproduce the baryon topping Hadronic EoS Friction in hadronic phae wa etimated by Satarov (SJNP 1990) Thi friction had to be enhanced. 2-phae EoS and croover EoS Phenomenological friction in QGP phae. Advantage of deconfinement cenario: Satarov friction in hadronic phae need no modification III. Freeze-out When ytem become dilute, hydro ha to be topped Freeze-out energy denity ε frz = 0.4 GeV/fm 3

10 Output model Model Phy. Input output oberv. Output at the freeze-out tage All fluid are frozen out in mall droplet characterized by proper volume V pr, temperature T, baryon, µ B, and trange, µ S, chemical potential collective flow velocity u µ, T, µ B and µ S are determined from baryon ρ B, trangene ρ S and energy ε denitie uing hadronic-ga EoS.

11 obervable model Model Phy. Input output oberv. directed flow = v 1 (y) = Hadron phae pace, p 0 d 3 N i d 3 p = α g i Vα pr p 0 (2π) 3 exp [ ] (p 0 µ αi )/T α ± 1 µ αi = B i µ αb + S i µ αs i the chemical potential of hadron i with baryon number B i and trangene S i, α ummation run over droplet from all (p, t and f) fluid, denote momentum in the droplet ret frame. Obervable are integral of function d 2 p T (p x /p T ) (p 0 d 3 N/d 3 p )/(d 3 N/dy) rapidity = dn/dy = d 2 p T p 0 d 3 N/d 3 p

12 model Model Phy. Input output In order to ue the a an event generator, the output hould be in term of oberved particle. Monte Carlo ampling procedure: oberv. Hadron are ampled according to their phae pace, p 0 d 3 N i d 3 p = α g i Vα pr p 0 (2π) 3 exp [(p 0 µ αi )/T α ] ± 1 denote momentum in the droplet ret frame µ αi = B i µ αb + S i µ αs i the chemical potential of hadron i with baryon number B i and trangene S i, α ummation run over droplet from all (p, t and f) fluid.

13 Sampling model Model Phy. Input output oberv. The ampling i run a a loop over all droplet: average multiplicitie of all hadron pecie are calculated according to N i,α = Vα pr n i,th (T, µ i ), together with their um N tot,α = i N i,α; total (integer) number of hadron from each droplet i ampled according to Poion with mean N tot,α. If the number i greater than zero, ort of hadron i randomly choen baed on probabilitie N i,α / N tot,α; hadron momentum p i ampled according to it phae pace, which i iotropic in momentum pace; momentum i Lorentz booted to the global frame of the colliion. Particle multiplicitie fluctuate from event to event according to the compoition of grand canonical enemble.

14 UrQMD imulation of final tate interaction model Model : Phy. Input output oberv. The Ultra-relativitic Quantum Molecular Dynamic (UrQMD) i ued to treat the interaction during the late non-equilibrium hadronic tage of heavy ion reaction, i.e. after particlization. + + Three-fluid Hydrodynamic-baed Event Simulator Extended by UrQMD final State interaction (THESEUS)

15 model Model Phy. Input output oberv. ] -2 dy) [GeV dp p N/(2 π 2 d T T pion THESEUS w/o UrQMD THESEUS m T -m [GeV] ] -2 dy) [GeV dp p N/(2 π 2 d T T kaon E lab =30 A GeV two-phae EoS m T -m [GeV] Figure: Tranvere momentum pectrum for pion (left panel) and kaon (right panel) for central Au+Au colliion (b = 2 fm) at E lab = 30 A GeV for the 2-phae EoS. and THESEUS without UrQMD how excellent agreement. UrQMD lead to a light teepening of the pion.

16 model Model Phy. Input output oberv. dn/dy pion THESEUS w/o UrQMD THESEUS y dn/dy kaon 10 two-phae EoS 5 E lab =30 A GeV y Figure: for pion (left panel) and kaon (right panel) for central Au+Au colliion (b = 2 fm) at E lab = 30 A GeV for the 2-phae EoS. and THESEUS without UrQMD how excellent agreement. UrQMD hadronic recattering meare out the double-peak tructure in the kaon rapidity pectrum.

17 Directed-Flow for emicentral Au+Au model Model Phy. Input output oberv. Figure: dv 1 /dy of proton Figure: dv 1 /dy of pion

18 for Au+Au colliion model Model Phy. Input output oberv. : Shadowing of pion by baryonic matter. S. A. Ba, et al., Phy. Lett. B 302, 381 (1993).

19 model Model Phy. Input output oberv. A new Three-fluid Hydrodynamic-baed Event Simulator Extended by UrQMD final State interaction (THESEUS) i developed + + (UrQMD) it can be ued for imulation of experimental event at NICA and FAIR it can decribe a hadron-to-quark matter tranition which proceed in the baryon topping regime THESEUS without UrQMD well reproduce reult afterburner ha little effect on the proton flow obervable afterburner reult in a qualitative change of the pion emiion pattern: from flow to antiflow

20 model Model Phy. Input output oberv. Thank for attention

21 model Model Phy. Input output oberv. ε m N n N [GeV/fm 3 ] ymbol paced 1 fm/c apart 2-phae EoS Au(4A GeV)+Au, b=2 fm Au(10A GeV)+Au, b=2 fm Pb(20A GeV)+Pb, b=2.4 fm e(t=0)-m N n B mixed phae inacceible region n B [fm -3 ] ε m N n B [GeV/fm 3 ] croover EoS Au(4A GeV)+Au, b=2 fm Au(10A GeV)+Au, b=2 fm Pb(20A GeV)+Pb, b=2.4 fm e(t=0)-m N n B W QGP =0.1 1 ymbol paced 1 fm/c apart W QGP =0.5 inacceible region n B [fm -3 ] Croover tranition by Khvorotukhin et al. i too mooth Lattice QCD predict a fat croover. Dynamical trajectorie of matter in the central box of colliding nuclei (4fm 4fm γ cm 4fm) Therefore, a true EoS i omewhere in between the Khvorotukhin et al. -croover and Khvorotukhin et al. -2-phae EoS. Onet of deconfinement happen at top-ags low-sps energie.

22 model Model Phy. Input output oberv. afterburner doe not eentially affect the