Hadronic equation of state and relativistic heavy-ion collisions

Transcription

1 Hadronic equation of state and relativistic heavy-ion collisions Pasi Huovinen J. W. Goethe Universität Workshop on Excited Hadronic States and the Deconfinement Transition Feb 23, 2011, Thomas Jefferson National Accelerator Facility in collaboration with P. Petreczky, H. Niemi and G. Denicol

2 Hadron properties, hydrodynamics, and relativistic heavy-ion collisions or Why we need to know hadron properties to learn about QGP P. JLab, Feb 23, /25

3 Nuclear phase diagram Temperature [MeV] K ~170 ǫ 0.7 GeV/fm 3 Quark gluon plasma? Tricritical point? Hadrons : baryons p,n,... mesons π,k,... SC phases? 0 Everyday world n 0 = /m 3 ǫ 0.16 GeV/fm 3 n 0 ~5 10 Baryon density 1 3 (n q n q ) P. JLab, Feb 23, /25

4 free streaming freeze-out fluid dynamics thermalization initial collision c Dirk H. Rischke P. JLab, Feb 23, /25

5 Ideal hydrodynamics local conservation of energy, momentum and baryon number: µ T µν (x) = 0 and µ N µ (x) = 0 localequilibrium, nodissipation: T µν = (e+p)u µ u ν Pg µν N µ = nu µ local, macroscopic variables: energy density e(x) pressure P(x) flow velocity u µ (x) matter characterized by: equation of state P = P(e,n) Unknowns: initial state, final state, equation of state P. JLab, Feb 23, /25

6 Elliptic flow spatial anisotropy final azimuthal momentum anisotropy ε x2 y 2 x 2 +y 2 v 2 p2 x p 2 y p 2 x+p 2 y sensitive to speed of sound c 2 s = p/ e and shear viscosity η P. JLab, Feb 23, /25

7 Pion gas EoS Sollfrank et al, PRC55, 392 (1997) E d σ/d 3 p (mb GeV 2 ) WA80 π 0 S + Au 200 A GeV 2.1 < y < m T m 0 (GeV) ideal pion gas EoS too stiff must have many hadronic d.o.f s in the EoS P. JLab, Feb 23, /25

8 Hagedorn states? (ε-3p)/t 4 BW HRG s95p p4, N τ =8 stout, cont. 1 0 T [MeV] BW: fit to Wuppertal results, Hagedorn states? s95p: hadrons up to 2 GeV mass below T c P. JLab, Feb 23, /25

9 have tiny effect ideal fluid Au+Au collision at RHIC, s = 200 GeV, b=7 fm T dec = 124 MeV; all EoSs! (2π) -1 dn/(dy p T dp T ) π p BW s95p p T (GeV) P. JLab, Feb 23, /25

10 have tiny effect ideal fluid Au+Au collision at RHIC, s = 200 GeV, b=7 fm T dec = 124 MeV; all EoSs! 0.2 BW s95p 0.15 v π p p T (GeV) P. JLab, Feb 23, /25

11 First order phase transition first order phase transition region with zero speed of sound P. JLab, Feb 23, /25

12 has an observable effect! ideal hydro, Au+Au at s NN = 200 GeV s95p: T dec = 140 MeV EoS Q: first order phase transition at T c = 170 MeV, T dec = 125 MeV P. JLab, Feb 23, /25

13 Thermal models - Hadronic phase: ideal gas of massive hadrons and resonances - in chemical equilibrium Ratios 1 p/p Λ/ Λ Ξ/ Ξ + Ω / Ω π - /π K /K K /π p/π K *0 - /h - φ/h - Λ/h - - Ξ /hω/π *10 p/p K /K K /π /π p Ω/h * STAR PHENIX PHOBOS BRAHMS s NN =130 GeV Model re-fit with all data T = 176 MeV, = 41 MeV µ b =200 GeV s NN Model prediction for T = 177 MeV, = 29 MeV µ b Particle ratios (approximately) correspond to a system in T MeV temperature Evolution to T MeV temperature In hydro particle ratios become wrong P. JLab, Feb 23, /25

14 Chemical non-equilibrium Treat number of pions, kaons etc. as conserved quantum numbers below T ch (Bebie et al, Nucl.Phys.B378:95-130,1992) P = P(ǫ,n b ) changes very little, but T = T(ǫ,n b ) changes... P. JLab, Feb 23, /25

15 Effect on flow ideal hydro, Au+Au at s NN = 200 GeV T chem = 150 MeV P. JLab, Feb 23, /25

16 Viscous hydrodynamics relativistic Navier-Stokes hydro: small corrections linear in gradients T µν NS = T µν ideal +η( µ u ν + ν u µ 2 3 µν α u α )+ζ µν α u α N µ NS = N µ ideal κ ( nt e+p ) 2 µµ T where µν u µ u ν g µν, µ = µν ν η, ζ shear and bulk viscosities, κ heat conductivity two problems: parabolic equations acausal Müller ( 76), Israel & Stewart ( 79)... instabilities Hiscock & Lindblom, PRD31, 725 (1985)... P. JLab, Feb 23, /25

17 Causal viscous hydro Müller, Israel & Stewart... T µν π µν +Π µν, N µ = n e+p qµ bulk pressure Π, shear stress π µν heat flow q µ treated as independent dynamical quantities that relax to their Navier-Stokes value on time scales τ Π (e,n), τ π (e,n), τ q (e,n) schematically Ẋ = X X NS τ X +F(X) restores causality (for not too small τ X ) P. JLab, Feb 23, /25

18 estimate for η/s Luzum & Romatschke, PRC78, (2008) η/s = 0.08 or η/s = 0.16 depending on initialization P. JLab, Feb 23, /25

19 η/s(t) Kapusta, McLerran and Csernai, nucl-th/ : Low T (Prakash et al.) using experimental data for 2-body interactions High T (Yaffe et al.) using perturbative QCD P. JLab, Feb 23, /25

20 η/s(t) Niemi et al., arxiv: η/s LH-LQ LH-HQ HH-LQ HH-HQ v 2 (p T ) LH-LQ LH-HQ HH-LQ HH-HQ STAR v 2 [4] RHIC 200 AGeV % charged hadrons T [GeV] p T [GeV] v 2 (p T ) mostly sensitive to hadronic η/s(t) at RHIC! P. JLab, Feb 23, /25

21 η/s? 25 Glauber STAR non-flow corrected (est.) STAR event-plane η/s= LH-LQ LH-HQ HH-LQ HH-HQ STAR v 2 [4] v 2 (percent) η/s=0.08 η/s=0.16 v 2 (p T ) RHIC 200 AGeV % p T [GeV] charged hadrons p T [GeV] small η/s at minimum, large in HRG or vice versa? P. JLab, Feb 23, /25

22 η/s(t) at LHC Niemi et al., arxiv: LH-LQ LH-HQ HH-LQ HH-HQ ALICE v 2 [4] 0.25 LH-LQ LH-HQ HH-LQ HH-HQ LHC 2760 AGeV LHC 5500 AGeV v 2 (p T ) 0.15 v 2 (p T ) % % charged hadrons 0.05 charged hadrons p T [GeV] p T [GeV] at the top LHC energy η/s of plasma dominates P. JLab, Feb 23, /25

23 Cooper-Frye description: Fluid to particles E dn dp 3 = f(x,p u) thermal ideal fluid dissipation requires f th f th (1+δf) Σ fo dσ µ p µ f(x,p u) Grad 14-moment approximation (Boltzmann distribution) Shear only, Landau matching gives δf = ǫ+ǫ µ p µ +ǫ µν p µ p ν δf = ǫ µν p µ p ν = 1 2T 2 (ǫ+p) πµν p µ p ν How to share π µν for each particle species? P. JLab, Feb 23, /25

24 δf TWO effects: - dissipative corrections to hydro fields u µ,t,n - dissipative corrections to thermal distributions f f 0 +δf η/s 1/(4π) (σ tr τ 2/3 ) δf = f 0 p µ p ν π µν 8nT 3 P. JLab, Feb 23, /25

25 δf for mixtures Denicol et al., work in progress: Analogous to single component system: At Navier-Stokes limit: δf i = p µp ν π µν i 2(ε i +P i )T 2 π µν = ησ µν = π µν i = η i σ µν Thus Using kinetic theory: δf i p µ p ν 2(ε i +P i )T 2 η i η πµν η i = F(T,{µ i },{m i },σ ij,) is a complicated integral over thermal distributions P. JLab, Feb 23, /25

26 Conclusions hadronic EoS has only a small observable effect once the hadronic # of d.o.f is large enough chemical non-equilibrium of hadron phase has large effect! hadronic viscosity dominates at RHIC less so at LHC η/s(t) of QGP cannot be constrained using RHIC v 2 data only δf a big uncertainty hadron cross sections required to evaluate it! P. JLab, Feb 23, /25