Event-by-event distribution of azimuthal asymmetries in ultrarelativistic heavy-ion collisions

Transcription

1 Event-by-event distribution of azimuthal asymmetries in ultrarelativistic heavy-ion collisions Hannu Holopainen Frankfurt Institute for Advanced Studies in collaboration with G. S. Denicol, P. Huovinen, H. Niemi and D. H. Rischke VIII Workshop on Particle Correlations and Femtoscopy Frankfurt am Main WPCF H. Holopainen (FIAS) 1/21

2 Event-by-event hydrodynamics Why are we interested in ebye hydrodynamics? We can get correct v 2 in central collisions. Triangular flow! Fluctuations of v n. Higher harmonics and correlation between different harmonics. v (a) 0-5% charged v2{ep} v2{pp} v2{rp} v2{smooth} p T [GeV] HH, Niemi, Eskola PRC83 (2011) WPCF H. Holopainen (FIAS) 2/21

3 Event-by-event hydrodynamics Viscous ebye reproduces the data pretty well. v n v 2 v 3 v 4 v 5 PHENIX v 2 PHENIX v 3 PHENIX v 4 η/s= % v % v % v % v % PHENIX v 2 PHENIX v 3 PHENIX v 4 η/s= p T [GeV] p T [GeV] Schenke, Jeon, Gale, Phys. Rev. C85, (2012) If ebye hydro really works, one can apply hydro in each event we should be able to reproduce the v n distributions! WPCF H. Holopainen (FIAS) 3/21

4 Hydrodynamical model WPCF H. Holopainen (FIAS) 4/21

5 Our model Hydrodynamical model previously employed in Niemi, Denicol, Huovinen, Molnar, Rischke, Phys. Rev. Lett. 106, (2011) Niemi, Denicol, Huovinen, Molnar, Rischke, Phys. Rev. C86, (2012) 2+1D viscous hydrodynamics, Bjorken in beam direction No net-baryon number EoS: s95p-pce-v1 Huovinen, Petreczky, NPA837 (2010) Chemical freeze-out T c = 150 MeV Kinetical decoupling T f = 100 MeV Hadrons only up to mass 1.1 GeV, 2- and 3-particle decays Initial state from Monte Carlo Glauber Velocities and shear-stress tensor initialized to zero WPCF H. Holopainen (FIAS) 5/21

6 Initial states Nucleons are distributed into nuclei using Woods-Saxon. No finite size or NN-correlation effects included. Random impact parameter from dn/db b. Nucleons collide if (x i x j ) 2 +(y i y j ) 2 σ NN π σ NN = 42 mb for RHIC y [fm] HH, Niemi, Eskola PRC83 (2011) HH PhD thesis x [fm] WPCF H. Holopainen (FIAS) 6/21

7 Initial profiles from MCG We use sbc and swn profiles with Gaussian smearing, i.e s(x, y) = const. wn,bc where σ = 0.8 fm. We choose τ 0 = 1 fm. y [fm] T [MeV] x [fm] σ = 0.4 fm 1 [ 2πσ 2 exp (x x i) 2 +(y y i ) 2 ] 2σ 2, y [fm] T [MeV] x [fm] σ = 0.8 fm WPCF H. Holopainen (FIAS) 7/

8 Centrality classes Let s use the number of BC/WN to define the centrality classes. Impact parameter varies freely in each centrality class. N/N tot % Au+Au snn = 200 GeV 20-30% 10-20% 5-10% 0-5% N part Centrality N part range N part b [fm] 0-5 % % % % % Centrality N bin range N part b [fm] 0-5 % % % % % HH, Niemi, Eskola PRC83 (2011) WPCF H. Holopainen (FIAS) 8/21

9 v n determination We use event plane method v n = dφ cos[n(φ ψn )] dn dydφ dφ dn dydφ = cos[n(φ ψ n )] ψ n = (1/n) arctan ( p Ty / ptx ) We know the orientation of the event plane exactly! Remember this if comparing with the data. (e.g. Luzum, Ollitrault, The event-plane method is obsolete, arxiv: [nucl-ex]) WPCF H. Holopainen (FIAS) 9/21

10 Results WPCF H. Holopainen (FIAS) 10/21

11 Correlations v 2, ǫ 2 v c( 2,v 2) =0.979 C 2 =07 (a) v c( 2,v 2) =0.989 C 2 =0.147 (b) sbc /s = sbc /s = % % Clear linear correlation between ǫ 2 and v 2. c(a, b) = ( )( ) a a ev b b ev σ a σ b ev WPCF H. Holopainen (FIAS) 11/21

12 Correlations v 3, ǫ c( 3,v 3) =0.893 C 3 =0.176 (a) c( 3,v 3) =0.954 C 3 =0.087 (b) v v sbc /s = sbc /s = % 2030 % Clear linear correlation between ǫ 3 and v 3. c(a, b) = ( )( ) a a ev b b ev σ a σ b ev WPCF H. Holopainen (FIAS) 12/21

13 Correlations v 4, ǫ c( 4,v 4) =0.199 C 4 =0.109 (a) c( 4,v 4) =0.199 C 4 =0.032 (b) v 4 v sbc /s = % sbc /s = % For n = 4 there is basically no correlation. c(a, b) = ( )( ) a a ev b b ev σ a σ b ev WPCF H. Holopainen (FIAS) 13/21

14 Correlations v 4, ǫ 4 v c( 4,v 4) =0.511 C 4 =0.039 (b) v c( 4,v 4) =0.199 C 4 =0.032 (b) sbc /s = % sbc /s = % However, in central collisions we can see the correlation, why? WPCF H. Holopainen (FIAS) 14/21

15 Correlations v 4, ǫ 4 best est. v 4 rms Ε 4 Ε 6,4 Ε 2,4 2 Ε 4 andε 2 2 Ε centrality Gardim, Grassi, Luzum, Ollitrault Phys. Rev. C85, (2012) v 4 comes from ǫ 4 and ǫ 2 2. In central collisions contribution from ǫ 2 2 is weak we see ǫ 4, v 4 correlation In more peripheral collisions ǫ 2 2 is more important no ǫ 4, v 4 correlation WPCF H. Holopainen (FIAS) 15/21

16 v 2 distributions 1.2 <v 2 <v 2 > =0.061 ('/s =0.0) > =0.043 ('/s =0.16) sbc %/s =0.0 sbc %/s = <v 2 <v 2 > =0.039 (swn) > =0.043 (sbc) swn -/s =0.16 sbc -/s = sbc & swn. 2 sbc. 2 2) $##v2 ), P( 0.8 (a) 2),++v2 ), P( 0.8 (a) P( 0.4 P( (v 2! <v 2 >)/ <v 2 >, (" 2! <" 2 >)/ <" 2 > 0.0 (1.0 ( (v 2 ) <v 2 >)/ <v 2 >, (* 2 ) <* 2 >)/ <* 2 > Distributions are not sensitive to transport properties! sbc and swn initial states are similar since they come from the same Glauber model. WPCF H. Holopainen (FIAS) 16/21

17 v 3 distributions 1.2 <v 3 <v 3 > =0.023 (6/s =0.0) > =0.011 (6/s =0.16) sbc 4/s =0.0 sbc 4/s = <v 3 <v 3 > =0.012 (swn) > =0.011 (sbc) swn </s =0.16 sbc </s = sbc swn = 3 sbc = 3 3) 322v3 ), P( 0.8 (b) 3) ;::v3 ), P( 0.8 (b) P( 0.4 P( /1.0 / (v 3 0 <v 3 >)/ <v 3 >, (1 3 0 <1 3 >)/ <1 3 > (v 3 8 <v 3 >)/ <v 3 >, (9 3 8 <9 3 >)/ <9 3 > Distributions are not sensitive to transport properties! sbc and swn initial states are similar since they come from the same Glauber model. WPCF H. Holopainen (FIAS) 17/21

18 v 4 distributions 1.2 <v 4 <v 4 > =0.013 (E/s =0.0) > =0.004 (E/s =0.16) sbc C/s =0.0 sbc C/s = <v 4 <v 4 > =0.003 (swn) > =0.004 (sbc) swn K/s =0.16 sbc K/s = sbc D swn L 4 sbc L 4 4) BAAv4 ), P( 0.8 (c) 4) JIIv4 ), P( 0.8 (c) P( 0.4 P( >1.0 > (v 4? <v 4 >)/ <v 4 >, (@ 4? <@ 4 >)/ <@ 4 > 0.0 F1.0 F (v 4 G <v 4 >)/ <v 4 >, (H 4 G <H 4 >)/ <H 4 > Distributions are not sensitive to transport properties! Direct probe of the initial state fluctuations! WPCF H. Holopainen (FIAS) 18/21

19 Correlations between different harmonics sbc N/s =0.0 sbc Q/s = sbc S/s =0.0 (a) sbc N/s =0.16 swn N/s =0.16 (b) sbc Q/s =0.16 swn Q/s = (c) sbc S/s =0.16 swn S/s = R30 % T30 % c(v 2,v 3 ) O30 % c(v 3,v 4 ) c(v 2,v 4 ) M0.1 P p T [GeV] p T [GeV] p T [GeV] Only v 2 and v 4 have a linear correlation. This correlation is sensitive to initial conditions and transport properties. WPCF H. Holopainen (FIAS) 19/21

20 Correlations between different harmonics c(ǫ 2,ǫ 3 ) c(v 2, v 3 ) c(ǫ 2,ǫ 4 ) c(v 2, v 4 ) c(ǫ 3,ǫ 4 ) c(v 3, v 4 ) sbc η/s = sbc η/s = swn η/s = In the initial state the anisotropies are not correlated. Correlation between v 2 and v 4 builds up during the evolution. WPCF H. Holopainen (FIAS) 20/21

21 Summary There is a linear correlation between ǫ 2, v 2 and ǫ 3, v 3, but for ǫ 4, v 4 the correlation is weak. v n distributions probe the initial state fluctuations! Only the correlation between v 2 and v 4 probes both initial conditions and transport properties use this to study ebye hydrodynamics? WPCF H. Holopainen (FIAS) 21/21

22 Backup slides WPCF H. Holopainen (FIAS) 22/21

23 Viscous hydrodynamics Time evolution of the shear-stress tensor µν αβ τ π π αβ + π µν = 2ησ µν 4 3 πµν θ 10 7 µν αβ σα λ πβλ η µν αβ πα λ πβλ, Transport coefficients taken from massless limit, 14-moment approximation and relaxation time was assumed to be τ π = 5η/(ε+P) Denicol, Niemi, Molnar, Rischke, Phys. Rev. D85, (2012) Denicol, Koide, Rischke, Phys. Rev. Lett. 105, (2010) WPCF H. Holopainen (FIAS) 23/21