Heavy-Quark Diffusion in the Quark-Gluon Plasma - ResearchGate

Heavy-Quark Diffusionin the Quark-Gluon PlasmaHendrik van HeesTexas A&M UniversityFebruary 13, 2008withM. Mannarelli, V. Greco and R. RappHendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 1 / 11

Outline1 Heavy Quark interactions in the sQGP2 Heavy-Quark Diffusion in the Quark-Gluon Plasma3 Non-photonic electrons at RHIC4 Summary and OutlookHendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 2 / 11

Heavy Quarks in Heavy-Ion collisionscqghard production of HQsdescribed by PDF’s + pQCD (PYTHIA)c,b quarksQGPHQ rescattering in QGP: Langevin simulationdrag and diffusion coefficients fromnon-perturbative many-body T matrix (sQGP)¯qcHadronization to D,B mesons viaquark coalescence + fragmentationV. Greco, C. M. Ko, R. Rapp, PL B 595, 202 (2004)Ke ±semileptonic decay ⇒“non-photonic” electron observablesν eHendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 3 / 11

Static potentials from lattice QCD876543210−1−2−3F 1 (r,T)/T c[Kaczmarek et al 04]Rσ 1/2T/T c0.900.940.980 1 2 3 4 5 6 7color-singlet free energy from latticeuse internal energyU 1 (r, T ) = F 1 (r, T ) − T ∂F 1(r, T ),∂TV 1 (r, T ) = U 1 (r, T ) − U 1 (r → ∞, T )Casimir scaling for other color channels [Nakamura et al 05; Döring et al 07]V¯3 = 1 2 V 1, V 6 = − 1 4 V 1, V 8 = − 1 8 V 1Hendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 4 / 11

T-matrixBrueckner many-body approach for elastic Qq, Q¯q scatteringq, ¯qcT= V + VTΣ= Σ glu + Treduction scheme: 4D Bethe-Salpeter → 3D Lipmann-SchwingerS- and P wavessame scheme for light quarks (self consistent!)Relation to invariant matrix elements∑|M(s)| 2 ∝ ∑ (d a |Ta,l=0 (s)| 2 + 3|T a,l=1 (s)| 2 )cos θ cmqHendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 5 / 11

T-matrix-Im T (GeV -2 )12s waveT=1.1 T cs waveT=1.1 T c10T=1.2 Tcolor singletccolor tripletT=1.2 T cT=1.3 T cT=1.3 T c8T=1.4 T c2T=1.4 T cT=1.5 T cT=1.5 T c6T=1.6 T cT=1.6 T cT=1.7 T cT=1.7 T c4T=1.8 T c 1T=1.8 T c2000 1 2 3 4 0 1 2 3 4E cm (GeV)E cm (GeV)resonance formation at lower temperatures T ≃ T cmelting of resonances at higher T ! ⇒ sQGPP wave smallerresonances near T c : natural connection to quark coalescence[Ravagli, Rapp 07]model-independent assessment of elastic Qq, Q¯q scatteringproblems: uncertainties in extracting potential from lQCDin-medium potential V vs. F ?Hendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 6 / 11-Im T (GeV -2 )3

Elastic pQCD processesLowest-order matrix elements [Combridge 79]In-medium Debye-screening mass for t-channel gluon exchange:µ g = gT , α s = 0.4Hendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 7 / 11

correct equil. lim. ⇒ Einstein relation: B 1 (t, p) = T (t)E p A(t, p)Hendrik vanRelativistic Hees (Texas A&MLangevin University) simulation Heavy-Quark Diffusion for flowing the QGP medium February 13, 2008 8 / 11Heavy-Quark diffusionFokker Planck Equation∂f(t, ⃗p)∂t= ∂ [p i A(t, p) +∂ ]B ij (t, ⃗p) f(t, ⃗p)∂p i ∂p jdrag (friction) and diffusion coefficientsp i A(t, ⃗p) = 〈 p i − p ′ 〉iB ij (t, ⃗p) = 1 〈(pi − p ′2i)(p j − p ′ j) 〉(= B 0 (t, p) δ ij − p )ip jp 2 + B 1 (t, p) p ip jp 2transport 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 ′ )

Transport coefficients0.150.1T-matrix: 1.1 T cT-matrix: 1.4 T cT-matrix: 1.8 T cpQCD: 1.1 T cpQCD: 1.4 T cΑ (1/fm)0.05pQCD: 1.8 T c04030pQCD+T-matpQCD2πT D s201000 1 2 3 4 5p (GeV)0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34T (GeV)from non-pert. interactions reach A non-pert ≃ 1/(7 fm/c ≃ 4A pQCDA decreases with higher temperaturehigher density (over)compensated by melting of resonances!spatial diffusion coefficientincreases with temperatureD s =TmAHendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 9 / 11

Non-photonic electrons at RHICR AAv 2 (%)same model for bottomquark coalescence+fragmentation → D/B → e + X1.61.41.210.80.60.40.20105T-matrixpQCD, α s =0.4Au-Au √s=200 GeV (central)0 1 2 3 4 5p T (GeV)15T-matrixpQCD, α s =0.4Au-Au √s=200 GeVb=7 fmR AAv 21.81.61.41.210.80.60.40.20.150.10.05(a)Au+Au √s=200 AGeV(b)0-10% centralminimum biastheoryPHENIXSTARfrag. onlyPHENIXPHENIX QM0800 1 2 3 4 5p T (GeV)00 1 2 3 4 5p T[GeV]coalescence crucial for explanation of dataincreases both, R AA and v 2 ⇔ “momentum kick” from light quarks!“resonance formation” towards T c ⇒ coalescence natural [Ravagli, Rapp 07]Hendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 10 / 11

Summary and OutlookSummaryHeavy quarks in the sQGPnon-perturbative interactions via lQCD potentials parameter freeresonance formation at T > T c ⇒ strong couplingres. melt at higher temperatures ⇔ consistency betw. R AA and v 2 !also provides “natural” mechanism for quark coalescenceuncertaintiesextraction of V from lattice datapotential approach at finite T : F , V or combination?Outlookinclude inelastic heavy-quark processes (gluon-radiation processes)other heavy-quark observables like charmoniumsuppression/regenerationHendrik van Hees (Texas A&M University) Heavy-Quark Diffusion in the QGP February 13, 2008 11 / 11