Heavy-Quark Transport in the QGP
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1 Heavy-Quark Transport in the QGP Hendrik van Hees Goethe-Universität Frankfurt November 9, 211 Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
2 Motivation Fast equilibration of hot and dense matter in heavy-ion collisions: collective flow (nearly ideal hydrodynamics) sqgp Heavy quarks as calibrated probe of QGP properties produced in early hard collisions: well-defined initial conditions not fully equilibrated due to large masses heavy-quark diffusion probes for QGP-transport properties Langevin simulation drag and diffusion coefficients T -matrix approach with static lattice-qcd heavy-quark potentials resonance formation close to T c mechanism for non-perturbative strong interactions Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
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 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 (GU Frankfurt) Heavy-Quark Transport November 9, / 19
4 Relativistic Langevin process Langevin process: friction force + Gaussian random force in the (local) rest frame of the heat bath d x = p dt, E p 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 Einstein dissipation-fluctuation relation B 1 = E p T A. flow via Lorentz boosts between heat-bath frame and lab frame A and B from microscopic models for qq, gq scattering Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
5 Microscopic model: Static potentials from lattice QCD V lqcd Kaczmarek et al color-singlet free energy from lattice 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 of Coulomb part for other color channels; confining part color blind [F. Riek, R. Rapp, Phys. Rev. C 82, 3521 (21)]. V 3 = 1 2 V 1, V 6 = 1 4 V 1, V 8 = 1 8 V 1 Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
6 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 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 (GU Frankfurt) Heavy-Quark Transport November 9, / 19
7 T-matrix results -Im T (GeV -2 ) T=1.2 T c T=1.5 T c T=2 T c c quarks T-Matrix with V=U Kac color-singlet channel E cm (GeV) resonance formation at lower temperatures T T c melting of resonances at higher T model-independent assessment of elastic Qq, Q q scattering! Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
8 Transport coefficients.4.3 c quarks T=1. T c T=1.5 T c T=2. T c gluons, T=1. T c gluons, T=1.5 T c gluons, T=2. T c c quarks T=1. T c T=1.5 T c T=2. T c gluons, T=1. T c gluons, T=1.5 T c gluons, T=2. T c A (1/fm).2 U Kac + pqcd gluons F Kac + pqcd gluons p (GeV) p (GeV) from non-pert. interactions reach A non pert 1/(7 fm/c) 4A pqcd results for free-energy potential, F considerably smaller Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
9 Bulk evolution and initial conditions bulk evolution as elliptic thermal fireball isentropic expansion with QGP Equation of State 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 (GU Frankfurt) Heavy-Quark Transport November 9, / 19
10 Spectra and elliptic flow for c-quarks R AA F Kac + pqcd gluons U Kac + pqcd gluons F Pet + pqcd gluons U Pet + pqcd gluons v 2 (%) 15 1 F Kac + pqcd gluons U Kac + pqcd gluons F Pet + pqcd gluons U Pet + pqcd gluons Au-Au s=2 GeV (b=7 fm), c-quarks.5 5 Au-Au s=2 GeV (b=7 fm), c-quarks Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
11 Spectra and elliptic flow for b-quarks R AA Au-Au s=2 GeV (b=7 fm), b-quarks v 2 (%) F Kac + pqcd gluons U Kac + pqcd gluons F Pet + pqcd gluons U Pet + pqcd gluons Au-Au s=2 GeV (b=7 fm), b-quarks.5 F Kac + pqcd gluons U Kac + pqcd gluons F Pet + pqcd gluons U Pet + pqcd gluons Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
12 Implementation in UrQMD Langevin simulation easily implemented into any bulk background UrQMD (hybrid cascade/hydro mode) more realistic fireball evolution possibility to study effects of fluctuations [T. Lang, J. Steinheimer, HvH, work in progress] Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
13 Non-photonic electrons at RHIC here: fireball model! quark coalescence+fragmentation D/B e + X R AA PHENIX (-1% central) STAR (-5% central) U Kac U Pet F Kac F Pet Au-Au s=2 GeV v PHENIX (min bias) U Kac Au-Au s=2 GeV U Pet F Kac F Pet 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 [L. Ravagli, R. Rapp, Phys. Lett. B 655, 126, (27); L. Ravagli, HvH, R. Rapp, Phys. Rev. C 79, 6492 (29)] Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
14 Resonance-Recombination Model transport approach for hadronization by q + q meson resonance t f M(t, p) = Γ f M (t, p) + g(p) f (eq) M γ (p) = γ p p Γ g(p) d 3 p 1 d 3 p 2 g(p) = (2π) 6 d 3 xf q (x, p 1 )f q (x, p 2 )σ(s)v rel δ (3) (p p 1 p 2 ) 4π (Γm) 2 σ(s) = g σ kcm 2 (s m 2 ) 2 + (Γm) T=18 MeV, β =.55 E dn/d 3 p (GeV -2 ) resonance recombination 1-5 blast wave [L. Ravagli, R. Rapp, Phys. Lett. B 655, 126, (27); L. Ravagli, HvH, R. Rapp, Phys. Rev. C 79, 6492 (29)] Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
15 Constituent-quark number scaling (p T ).2 J/ψ.2 φ v 2.1 v v D J/ψ scaled quark D scaled quark (a) scaled quark (b) φ meson scaled quark Scaling relations ( pt ) ( pt ) (a) v 2,M (p T ) v 2,q1 + v 2,q2 ( 2 ) 2 mq1 p T (b) v 2,M (p T ) v 2,q1 m q1 + m q2 ( ) mq2 p T + v 2,q2 m q1 + m q2 Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
16 KE T scaling of quarks usual coalescence models: factorization ansatz f q (p, x, ϕ) = f q (p, x)[1 + 2v q 2 (p T ) cos(2ϕ)] CQNS usually not robust with more realistic parametrizations of v 2 here: q input from relativistic Fokker-Planck-Langevin simulation v charm strange light KE t (GeV) Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
17 Constituent-quark number scaling (KE T ) usual coalescence models: factorization ansatz f q (p, x, ϕ) = f q (p, x)[1 + 2v q 2 (p T ) cos(2ϕ)] CQNS usually not robust with more realistic parametrizations of v 2 here: q input from relativistic Fokker-Planck-Langevin simulation (a) π + +π - (PHENIX) + - K +K (PHENIX) KS (STAR) p+p (PHENIX) Λ+Λ (STAR) + Ξ - +Ξ (STAR) (b) v 2.1 v 2 /n q.5.5 J/ψ φ D KE T (GeV) p T /n q (GeV/c) KE T /n q (GeV) Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
18 Meson spectra q- q input: Fokker-Planck-Langevin meson output: resonance-recombination model E dn/d 3 p (GeV -2 ) φ T=18 MeV 1-4 PHENIX STAR 1-5 STAR (new) E dn/d 3 p (GeV -2 ) J/ψ T=18 MeV 1-7 PHENIX Data from [A. Adare et al. (PHENIX) PRL 98, (27); S. S. Adler et al. (PHENIX) PRC 72, 1493 (25); J. Adams et al. (STAR) PLB 612, 181 (25) B. I. Abelev et al. (STAR) PRL 99, (27)] Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
19 Summary and Outlook Heavy quarks in the sqgp non-perturbative interactions mechanism for strong coupling: resonance formation at T T c lattice-qcd potentials parameter free resonances melt at higher temperatures consistency betw. R AA and v 2! also provides natural mechanism for quark coalescence resonance-recombination model 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 implementation of RRM in transport models (BAMPS) as a consistent hadronization model study QCD phase transition(s) fluctuations; finite µ B ; cross-over 1st order; CEP(!?!) Hendrik van Hees (GU Frankfurt) Heavy-Quark Transport November 9, / 19
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