Heavy-Quark Transport in the QGP

Transcription

1 Heavy-Quark Transport in the QGP Hendrik van Hees Justus-Liebig Universität Gießen October 13, 29 Institut für Theoretische Physik JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 1 / 18

2 Outline 1 Heavy-quark interactions in the sqgp Heavy quarks in heavy-ion collisions Heavy-quark diffusion: The Langevin Equation Elastic pqcd heavy-quark scattering Non-perturbative interactions: Resonance Scattering 2 Non-photonic electrons at RHIC 3 Microscopic model for non-perturbative HQ interactions Static heavy-quark potentials from lattice QCD T-matrix approach 4 Summary and Outlook Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 2 / 18

3 Heavy Quarks in Heavy-Ion collisions c q g hard production of HQs described by PDF s + pqcd (PYTHIA) c,b quark sqgp HQ rescattering in QGP: Langevin simulation drag and diffusion coefficients from microscopic model for HQ interactions in the sqgp q c Hadronization to D,B mesons via quark coalescence + fragmentation V. Greco, C. M. Ko, R. Rapp, PLB 595, 22 (24) K ν e e ± semileptonic decay non-photonic electron observables R e+ e AA (p T), v e+ e 2 (p T ) Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 3 / 18

4 Relativistic Langevin process Langevin process: friction force + Gaussian random force in the (local) rest frame of the heat bath d x = p E p dt, d p = A p dt + 2dt[ B P + B 1 P ] w w: normal-distributed random variable A: friction (drag) coefficient B,1 : diffusion coefficients dependent on realization of stochastic process to guarantee correct equilibrium limit: Use Hänggi-Klimontovich calculus, i.e., use B /1 (t, p + d p) Einstein dissipation-fluctuation relation B = B 1 = E p T A. to implement flow of the medium use Lorentz boost to change into local heat-bath frame use update rule in heat-bath frame boost back into lab frame Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 4 / 18

5 Elastic pqcd processes Lowest-order matrix elements [Combridge 79] Debye-screening mass for t-channel gluon exch. µ g = gt, α s =.4 not sufficient to understand RHIC data on non-photonic electrons Hendrik [Moore, van Hees Teaney (JLU 25] Gießen) Heavy-Quark Transport October 13, 29 5 / 18

6 Non-perturbative interactions: Resonance Scattering General idea: Survival of D- and B-meson like resonances above T c elastic heavy-light-(anti-)quark scattering q c q c c D, D, D s s q c u D, D, D s q D- and B-meson like resonances in sqgp q D, D, D s D, D, D s parameters m D = 2 GeV, Γ D = GeV m B = 5 GeV, Γ B = GeV k c k Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 6 / 18

7 Cross sections σ [mb] Res. s-channel Res. u-channel pqcd qc scatt. pqcd gc scatt s [GeV] total pqcd and resonance cross sections: comparable in size BUT pqcd forward peaked resonance isotropic resonance scattering more effective for friction and diffusion Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 7 / 18

8 Time evolution of the fire ball Elliptic fire-ball parameterization fitted to hydrodynamical flow pattern [Kolb ] V (t) = π(z + v z t)a(t)b(t), a, b: semi-axes of ellipse, v a,b = v [1 exp( αt)] v[1 exp( βt)] Isentropic expansion: S = const (fixed from N ch ) QGP Equation of state: s = S V (t) = 4π2 9 T 3 ( n f ), n f = 2.5 obtain T (t) A(t, p), B (t, p) and B 1 = T EA for semicentral collisions (b = 7 fm): T = 34 MeV, QGP lifetime 5 fm/c. simulate FP equation as relativistic Langevin process Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 8 / 18

9 Initial conditions need initial p T -spectra of charm and bottom quarks (modified) PYTHIA to describe exp. D meson spectra, assuming δ-function fragmentation exp. non-photonic single-e ± spectra: Fix bottom/charm ratio 1/(2 πp T ) d 2 N/dp T dy [a.u.] d+au s NN =2 GeV STAR D STAR prelim. D * ( 2.5) c-quark (mod. PYTHIA) c-quark (CompHEP) p T [GeV] 1/(2πp T ) dn/dp T [a.u.] e ± σ bb /σ cc = 4.9 x1-3 STAR (prel, pp) STAR (prel, d+au/7.5) STAR (pp) D e B e sum p T [GeV] Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 9 / 18

10 Spectra and elliptic flow for heavy quarks 1.5 c, reso (Γ= GeV) c, pqcd, α s =.4 b, reso (Γ= GeV) 2 15 c, reso (Γ= GeV) c, pqcd, α s =.4 b, reso (Γ= GeV) R AA 1 v 2 [%] 1 Au-Au s=2 GeV (b=7 fm).5 Au-Au s=2 GeV (b=7 fm) p T [GeV] p T [GeV] µ D = gt, α s = g 2 /(4π) =.4 resonances c-quark thermalization without upscaling of cross sections Fireball parametrization consistent with hydro Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, 29 1 / 18

11 Comparison to single-electron RHIC R AA (a) 1% central Armesto et al. (I) van Hees et al. (II) 3/(2πT) Moore & 12/(2πT) Teaney (III) HF v s NN = 2 GeV (b) minimum bias π R AA, p T π v 2, p T e ± R, e ± vhf AA 2 > 4 GeV/c > 2 GeV/c PHENIX Collaboration PRL (27) p [GeV/c] T Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

12 Microscopic model: Static potentials from lattice QCD V lqcd Kaczmarek et al color-singlet free energy from lattice use internal energy U 1 (r, T ) = F 1 (r, T ) T F 1(r, T ), T V 1 (r, T ) = U 1 (r, T ) U 1 (r, T ) Casimir scaling for other color channels [Nakamura et al 5; Döring et al 7] V 3 = 1 2 V 1, V 6 = 1 4 V 1, V 8 = 1 8 V 1 Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

13 T-matrix Brueckner many-body approach for elastic Qq, Q q scattering q, q c T = V + V T Σ = Σ glu + T reduction scheme: 4D Bethe-Salpeter 3D Lipmann-Schwinger S- and P waves same scheme for light quarks (self consistent!) Relation to invariant matrix elements M(s) 2 ( d a Ta,l= (s) T a,l=1 (s) 2 ) cos θ cm q Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

14 T-matrix -Im T (GeV -2 ) s wave color singlet T=1.1 T c T=1.2 T c T=1.3 T c T=1.4 T c T=1.5 T c T=1.6 T c T=1.7 T c T=1.8 T c E cm (GeV) -Im T (GeV -2 ) s wave color triplet T=1.1 T c T=1.2 T c T=1.3 T c T=1.4 T c T=1.5 T c T=1.6 T c T=1.7 T c T=1.8 T c E cm (GeV) resonance formation at lower temperatures T T c melting of resonances at higher T! sqgp P wave smaller resonances near T c : natural connection to quark coalescence [Ravagli, Rapp 7; Ravagli, HvH, Rapp 8] model-independent assessment of elastic Qq, Q q scattering problems: uncertainties in extracting potential from lqcd in-medium potential V vs. F? Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

15 Transport coefficients.15.1 T-matrix: 1.1 T c T-matrix: 1.4 T c T-matrix: 1.8 T c pqcd: 1.1 T c pqcd: 1.4 T c pqcd: 1.8 T c 4 3 pqcd+t-mat pqcd Α (1/fm) 2πT D s p (GeV) T (GeV) from non-pert. interactions reach A non pert 1/(7 fm/c) 4A pqcd A decreases with higher temperature higher density (over)compensated by melting of resonances! spatial diffusion coefficient increases with temperature D s = T ma Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

16 Non-photonic electrons at RHIC same model for bottom quark coalescence+fragmentation D/B e + X R AA v 2 (%) T-matrix pqcd, α s =.4 Au-Au s=2 GeV (central) p T (GeV) 15 T-matrix pqcd, α s = Au-Au s=2 GeV b=7 fm R AA v % central Au+Au s=2 AGeV minimum bias theory [Wo] frag. only [Wo] theory [SZ] PHENIX STAR PHENIX PHENIX QM p T (GeV) p T [GeV] coalescence crucial for description of data increases both, R AA and v 2 momentum kick from light quarks! resonance formation towards T c coalescence natural [Ravagli, Rapp 7] Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

17 Transport properties of the sqgp spatial diffusion coefficient: Fokker-Planck D s = T measure for coupling strength in plasma: η/s η s 1 2 T D s (AdS/CFT), η s 1 5 T D s ma = T 2 D (wqgp) T-mat + pqcd reso + pqcd pqcd pqcd run. α s KSS bound η/s.5 charm quarks T (GeV) [Lacey, Taranenko (26)] Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18

18 Summary and Outlook Summary Heavy quarks in the sqgp non-perturbative interactions mechanism for strong coupling: resonance formation at T T c lqcd potentials parameter free res. melt at higher temperatures consistency betw. R AA and v 2! also provides natural mechanism for quark coalescence resonance-recombination model [L. Ravagli, HvH, R. Rapp, Phys. Rev. C 79, 6492 (29)] problems extraction of V from lattice data potential approach at finite T : F, V or combination? Outlook include inelastic heavy-quark processes (gluo-radiative processes) other heavy-quark observables like charmonium suppression/regeneration Hendrik van Hees (JLU Gießen) Heavy-Quark Transport October 13, / 18