T-Matrix approach to heavy quarks in the Quark-Gluon Plasma

Transcription

1 T-Matrix approach to heavy quarks in the Quark-Gluon Plasma Hendrik van Hees Justus-Liebig-Universität Gießen June 1, 28 with M. Mannarelli, V. Greco, and R. Rapp Institut für Theoretische Physik JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, 28 1 / 12

2 Outline 1 Heavy quarks in the sqgp 2 Heavy-quark diffusion: The Fokker-Planck Equation 3 Elastic scattering of heavy quarks in the sqgp Matrix elements from pqcd Static potentials from lqcd The T-matrix approach 4 Non-photonic electron observables at RHIC 5 Transport properties of the sqgp 6 Summary and Outlook Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, 28 2 / 12

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 Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, 28 3 / 12

4 correct equil. lim. Einstein relation: B 1 (t, p) = T (t)e p A(t, p) Hendrik Relativistic van Hees (JLU Gießen) Langevin simulation Heavy-Quark Kinetics for flowing the QGP medium June 1, 28 4 / 12 Heavy-Quark diffusion Fokker Planck Equation f(t, p) t = p i [ p i A(t, p) + ] B ij (t, p) f(t, p) p j drag (friction) and diffusion coefficients p i A(t, p) = p i p i B ij (t, p) = 1 (pi p 2 i)(p j p j) ( = B (t, p) δ ij p ) ip j p 2 + B 1 (t, p) p ip j p 2 transport coefficients defined via M X( p ) = 1 1 d 3 q d 3 q d 3 p γ c 2E p (2π) 3 2E q (2π) 3 2E q (2π) 3 2E p M 2 (2π) 4 δ (4) (p + q p q ) ˆf( q)x( p )

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 Kinetics in the QGP June 1, 28 5 / 12

6 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 Kinetics in the QGP June 1, 28 6 / 12

7 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 a Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, 28 7 / 12

8 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] 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 Kinetics in the QGP June 1, 28 8 / 12

9 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 Kinetics in the QGP June 1, 28 9 / 12

10 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 explanation of data increases both, R AA and v 2 momentum kick from light quarks! Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, 28 1 / 12

11 Transport properties of the sqgp measure for coupling strength in plasma: η/s relation to spatial diffusion coefficient η s 1 2 T D s (AdS/CFT), η s 1 5 T D s (wqgp) η/s T-mat + pqcd reso + pqcd pqcd KSS bound T (GeV) [Lacey 6] Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, / 12

12 Summary and Outlook Summary Heavy quarks in the sqgp non-perturbative interactions via lqcd potentials parameter free resonance formation at T > T c strong coupling res. melt at higher temperatures consistency betw. R AA and v 2! also provides natural mechanism for quark coalescence uncertainties extraction of V from lattice data potential approach at finite T : F, V or combination? Outlook include inelastic heavy-quark processes (gluon-radiation processes) other heavy-quark observables like charmonium (and bottomonium) suppression/regeneration Hendrik van Hees (JLU Gießen) Heavy-Quark Kinetics in the QGP June 1, / 12