Title Perfect-fluid hydrodynamics for RHIC successes and problems Wojciech Florkowski with W. Broniowski, M. Chojnacki, A. Kisiel, Institute of Nuclear Physics, Kraków & Jan Kochanowski University, Kielce, Poland HIRSCHEGG 1: Strongly Interacting Matter under Extreme Conditions Jan. 17-3, 1 Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 1 / 3
RHIC at BNL RHIC at BNL Relativistic Heavy Ion Collider at Brookhaven National Laboratory Google Maps: http://maps.google.com/?ll=.8769,-7.87598&spn=.7118,.7983&z=1 Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 / 3
RHIC at BNL Four experiments RHIC at BNL Four experiments STAR PHENIX BRAHMS PHOBOS Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 3 / 3
Experimental data 1) transverse-momentum spectra Experimental data (soft hadronic sector) 1) transverse-momentum spectra, p T distributions ] / GeV N / dp dy [c T p T ) d (1/π 1 3 + π 1 + K p 1 1 1-1 1-1 -3 Positive ( - 5% central) Negative ( - 5% central) π - - K p ] / GeV N / dp T dy [c p T ) d (1/π 1 1 1-1 1-1 -3 1-1 -5 Positive (6-9% peripheral) Negative (6-9% peripheral) 1-6.5 1 1.5.5 3 3.5.5.5 1 1.5.5 3 3.5.5 p T [GeV/c] p T [GeV/c] PHENIX, Phys. Rev. C69, 399 () Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 / 3
Experimental data ) elliptic flow coefficient v Experimental data ) elliptic flow coefficient v v.3 -% pbar π K. ch -% -6%.1.3. -% p π + K + ch + -% -6%.1 http://www.phenix.bnl.gov/www/software/luxor/ani/ ellipticflow/ellipticsmall1-1.mpg Animation by Jeffery Mitchell (Brookhaven National Laboratory) p T (GeV/c) PHENIX, Phys.Rev.Lett.91,1831(3) Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 5 / 3
Experimental data 3) correlations of identical particles (HBT) Experimental data 3) correlations of identical particles (Hanbury-Brown, Twiss) three projections of the correlation source emitting particles functions SOURCE C 1.3 1. 1.1 qo; q s,q l < 3 MeV/c 1.3 1. 1.1 Raw C Standard CC C Standard fit Bowler-Sinyukov fit 1 1 two identical pions, π + π +, π π C 1. < 3 MeV/c q s; q o,q l q l ; q o,q s < 3 MeV/c 1. C p Μ 1 k Μ 1.1 1.1 Π 1 x Μ 1 t x q Μ x Μ p Μ Π 1.5.1.5.1.15 q (GeV/c) q (GeV/c) STAR, Phys.Rev.C71,96(5) 1 Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 6 / 3
Experimental data 3) source sizes (HBT radii) Experimental data 3) source sizes (HBT radii) HBT radii depend on k T "Fourier transform" HBT radii R side - spatial transverse extension R out - spatial transverse extension + emission time R long - longitudinal extension (fm) R o (fm) R s 6 6-5% 5-1% 1-% -3% 3-5% 5-8%..3..5.6..3..5.6 m T (GeV/c) m T (GeV/c) STAR, Phys.Rev.C71,96(5) 6 R l (fm) Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 7 / 3
Standard Model/Scheme of heavy-ion collisions Standard Model/Scheme of heavy-ion collisions main ingredients of the +1 models: initial conditions, short thermalization time, τ i 1 fm Glauber model, e.g., initial entropy/energy density is proportional to the linear combination of the wounded-nucleon density and binary-collision density, σ i(x ) or ε i(x ) ρ sr(x ) = 1 κ Color Glass Condensate w (x ) + κ n (x ) initial transverse flow, usually set equal to zero (?) HYDRODYNAMIC STAGE v data suggest that matter behaves like a perfect fluid main tool: perfect-fluid hydrodynamics (Shuryak, Heinz,... ) hadronization included in the equation of state freeze-out, Cooper-Frye formula freeze-out hypersurface, thermal description of hadron production transition hypersurface, change to a hadronic cascade Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 8 / 3
Motivation Motivation for our research an attempt to obtain a uniform description of soft observables (resolution of the HBT puzzle) 1/ π dn/dyp T dp T (GeV ) π ± PHENIX 1 p PHENIX p STAR π ± hydro 1 p hydro 1 most central 1 1 3 p T (GeV) v (%) 15 1 h +/ ewn swn 5 ebc sbc STAR.5 1 1.5.5 p T (GeV) R out (fm) R side (fm) 8 8 hydro w/o FS hydro with FS hydro, τ equ = τ form STAR π, π +...6.8 K (GeV) U.Heinz and P.Kolb, Nucl. Phys. A7, 69 () R long (fm) 1 8 hydro w/o FS hydro with FS hydro, τ equ = τ form STAR π, π +...6.8 K (GeV) at Y= [arb. units] dn dmtdy 1 πmt 1 1 1 1.1.1.1.1 π PHENIX π K (.6) PHENIX K p ( 3.5) 1e-5.5 1 1.5.5 3 3.5 mt [GeV/c ] PHENIX p.1..3..5 MT [GeV/c ] Rout [fm] Rlong [fm] 8 6 1 8 6 Hydro STAR Hydro STAR.1..3..5 MT [GeV/c ] Rside [fm] Rout/Rside 8 6 Hydro STAR.1..3..5 MT [GeV/c ] 1 Hydro STAR.1..3..5 MT [GeV/c ] T.Hirano, K.Morita, S.Muroya, and C.Nonaka, Phys. Rev. C65, 619 () Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 9 / 3
+1 Cracow hydrodynamic model +1 Cracow hydrodynamic model initial conditions, short thermalization time, τ i 1 fm Glauber and Gaussian initial conditions (including fluctuations) option: initial transverse flow obtained from free-streaming (Yu. Sinyukov) HYDRODYNAMIC STAGE perfect-fluid hydrodynamics implemented in the code LHYQUID (M. Chojnacki) hadronization included in the modern equation of state freeze-out, Cooper-Frye formula freeze-out hypersurface, thermal description of hadron production THERMINATOR (A. Kisiel et al.), complete set of resonances, single-freeze-out scenario assumed, two-particle method, with or without Coulomb, used to calculate the HBT radii: R side, R out, R long, R out/r side Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 1 / 3
Initial conditions Nuclear matter profiles Initial conditions Nuclear matter profiles play an important role, Phys. Rev. Lett. 11 (8) 31 most of the approaches use the Glauber model or Color Glass Condensate, we assume the Gaussian profile (Gaussian approximation to Glauber) dn dxdy exp x a y «b the widths a and b determined from GLISSANDO 1 Ρ.3.5..15.1.5 Φ gaussian fit to GLISSANDO optical Glauber Φ Π centrality class 3. 6 8 r fm 1 W. Broniowski, M. Rybczyński, P. Bożek arxiv:71.5731[nucl-th] Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 11 / 3
Initial conditions Free-streaming Initial conditions Free-streaming thermalization requires some time (τ.5 1. fm) two scenarios early thermalization free-streaming Τ fm Τ fm.5.5. 1.5. 1.5 hydrodynamics thermalization 1..5 Τ HYD.5 fm 1 1.5 model for early stage dynamics r fm - free streaming of particles, no interactions - sudden hermalization Landau s matching conditions. our results indicate that the two scenarios are equivalent 1. hydrodynamics Τ HYD 1. fm thermalization.5 free streaming Τ FS.5 fm r fm 1 1.5 Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 1 / 3
Thermodynamics phase diagrams Thermodynamics phase diagrams phase diagram for water Wojciech Florkowski (IFJ PAN & UJK Kielce) phase diagram for QCD Hydro description of heavy-ion collisions Jan. 19, 1 13 / 3
Thermodynamics modeling of the QCD EOS Thermodynamics modeling of the QCD EOS hadron gas model for low temparatures pliki inputowe z SHARE: Statistical hadronization with resonances G. Torrieri, S. Steinke, W. Broniowski, W. Florkowski, J. Letessier, J. Rafelski, Comput. Phys. Commun. 167, 9 (5) lattice QCD simulations for large temperatures based on: Y. Aoki, Z. Fodor, S. Katz, K. Szabo, JHEP 61, 89 (6) simple parameterization of pressure: T. Biro, J. Zimanyi, Phys.Lett.B65, 193 (7) cross-over phase transition thermodynamic variables change suddenly at T c but smoothly, the sound velocity does not drop to zero..3 Hadron Gas lattice QCD c S..1...5 1. 1.5. T T C Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 1 / 3
Hydrodynamics conservation laws Hydrodynamics energy-momentum conservation law µ T µν = energy-momentum of the perfect fluid T µν = (ɛ + P) u µ u ν Pg µν ɛ - energy density, P - pressure, u µ - fluid four-velocity mid-rapidity ( y 1) for RHIC µ B, temperature is the only independent parameter boost-invariance equations solved at z =, solutions for z obtained by Lorentz boosts EOS encoded in c s Baym, Friman, Blaizot, Soyeur, Czyz, Hydrodynamics of Ultrarelativistic Heavy Ion Collisions, Nucl. Phys. A7 (1983) 51 Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 15 / 3
Hydrodynamics results from LHYQUID results from LHYQUID relativistic HYdrodynamics of QUark-gluon fluid Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 16 / 3
Hydrodynamics freeze-out hypersurfaces Hydrodynamics freeze-out hypersurfaces freeze-out temperature T f = 15 MeV central collisions peripheral collisions t fm 1..1..3..5..1..3..5 8.6.5 6.5.5.. in plane.3 out of plane.3. c 5.1 T i 5 MeV.. Τ Τ.1. 6 8 1 r fm t fm 8.1..3..5..1..3. 6.6.5.5.. in plane out of plane.3.3 c 3. T i 6 MeV.1. Τ Τ.1 6 8 r fm because of the strong transverse flow, hadron do not reenter the medium space-like and time-like emission is similar. Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 17 / 3
THERMINATOR THERMal heavy-ion generator THERMINATOR THERMal heavy-ion generator primordial particles are emitted according to the Cooper-Frye formula Z dn = dσ µ p µf dy d eq (p u), p T dσ µ - element of the freeze-out hypersurface obtained from hydro u µ - four-velocity of the fluid all resonances included elliptic flow coefficient v dn dn = (1 + v dy d (p T ) cos(φ p) +...) p T dy πp T dp T A. Kisiel, T. Tałuć, W. Broniowski and W. Florkowski Comput. Phys. Commun. 17, 669 (6) Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 18 / 3
THERMINATOR results for the spectra and v THERMINATOR results for the spectra and v dn Π p T dp T dy 1 1 1 PHENIX s NN GeV c 5 1 Π Π K K p p.1 c 5 c 5 T i 33 MeV T i 5 MeV Τ 1. fm Τ Τ.1..5 1. 1.5. p T GeV.5 Π K Π K..15 p c T i 35 MeV Τ 1. fm p c T i 6 MeV Τ Τ dn Π p T dp T dy 1 1 1 PHENIX s NN GeV c 3 1 Π Π K K p p.1 c 3 c 3 T i 35 MeV T i 6 MeV Τ 1. fm Τ Τ.1..5 1. 1.5. p T GeV v.1.5 PHENIX s NN GeV c...5 1. 1.5. p T GeV Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 19 / 3
THERMINATOR femtoscopy THERMINATOR femtoscopy 3 two-particle method used to calculate the correlation functions (procedure mimics closely the experimental situation), the wave function calculated in the pair rest frame (PRF) includes Coulomb (option) correlation function fitted in the Bertsch-Pratt coordinates (k T, q out, q side, q long ) with Bowler-Sinyukov correction (option) C( q, h i k) = (1 λ)+λk coul (q inv) 1 + exp Rout qout Rsideq side Rlongq long, HBT radii (R out, R side, R long ) obtained from the fit and compared with data 3 A. Kisiel, W. Florkowski and W. Broniowski Phys. Rev. C73, 69 (6) Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 / 3
THERMINATOR HBT results THERMINATOR HBT results Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 1 / 3
THERMINATOR oscillations of the HBT radii THERMINATOR oscillations of the HBT radii, PRC 79 (9) 19 R out, R side, R long, 6 3 3 1 1 3 N part 1 1 3 N part 1 3 N part /R side, R out,.1 1 3 N part /R side, R side,.1 1 3 N part R out side, /R side,.1 1 3 N part Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 / 3
Conclusions Conclusions +1 Cracow hydrodynamical model correctly describes the soft-hadronic data, in our opinion, this is the first successful attempt to solve the RHIC HBT puzzle. the things which matter - realistic equation of state (no soft point!) - initial profile Gaussian approximation to Glauber, fluctuations of the eccentricity - all resonances included - two-particle algorithm for femtoscopy Wojciech Florkowski (IFJ PAN & UJK Kielce) Hydro description of heavy-ion collisions Jan. 19, 1 3 / 3