Heavy Quarks + Vector Mesons in Medium Ralf Rapp Cyclotron Institute + Physics Department Texas A&M University College Station, USA School of Collective Dynamics in High-Energy Collisions “Medium Properties, Chiral Symmetry and Astrophysical Phenomena” Lawrence Berkeley National Laboratory,

1.) Introduction: QGP + High-Energy Heavy-Ion Collisions  Achievements and Open Questions 2.) Heavy-Quark Probes (c,b)  Heavy-Quark Diffusion in the sQGP  RHIC Data 3.) Electromagnetic Radiation  Relation to Chiral Symmetry Restoration  In-Medium Vector Mesons  Dileptons: CERES/NA45 and NA60 4.) Conclusions Outline

1.1 The “Little Bang” in the Laboratory e + e - Questions: Thermalization? QGP Signatures?? Phase Transition???  c,b

1.2 Achievements at RHIC: Towards the QGP Hadron Spectra (↔ bulk matter properties) Momenta p t ≤ 2GeV : Hydrodynamic flow (v 0,v 2 )  early thermalization, QGP pressure  thermal medium, small viscosity, large opacity, partonic, T o ≈ 2 T c (indirect) [Shuryak, Heinz,…] p t ≥ 6GeV : pQCD energy-loss (factor ~5 suppression)  energy densities  0 ≈ 20 GeV fm -3 [Gyulassy, Vitev, Wang, …] 2 GeV ≤ p t ≤ 6 GeV : p/  ≈1, quark “scaling” in v 2  quark coalescence [Greco et al, Fries et al, Hwa et al, …]

1.3 Microscopic Probes: Understanding the QGP Questions: - prevalent interactions? - d.o.f. (resonances in sQGP)? - phase diagram + transition?  Advanced studies required: Heavy Quarks ► c- and b-quark energy loss, thermalization, “flow” ? ► Q-Q bound states (J/ , Y) in sQGP? Electromagnetic Emission ► photons: q 0 =q, thermal radiation? ► dileptons: (M ee ) 2 = q q 2 > 0 : Vector spectral functions in medium? Chiral Symmetry Restoration? -

p T [GeV] R AA = (AA) / (pp) [Gyulassy etal ’05] [Armesto et al ’05] substantial collectivity bottom “contamination”? Elliptic Flow Nuclear Modification Factor factor 4-5 suppression elastic E-loss, pQCD?! 2.) Heavy-Quark Probes at RHIC Radiative energy loss smaller for c+b quarks Elastic interactions? Collective flow? Heavy-quark diffusion? experimental tool: electron spectra D,B → eX c,b ?

Brownian Motion: scattering rate diffusion constant 2.1 Heavy-Quark Diffusion in the QGP Fokker Planck Eq. [Svetitsky ’88,…] Q e.g. T =300 MeV,  s =0.4:  therm ~15 fm/c slow! (  QGP ≤ 5 fm/c) Perturbative QCD g c dominated by t-channel gluon-ex.: Microscopic Calculations of Diffusion: qcqc [Svetitsky ’88, Mustafa et al ’98, Molnar et al ’04, Zhang et al ’04, Hees+RR ’04, Teaney+Moore‘04]

2.1.2 Open-Charm Resonances in QGP effective lagrangian with pseudo/scalar + axial/vector “D-mesons” “Light”-Quark Resonances 1.4T c [Asakawa+ Hatsuda ’03] parameters: m D =2GeV, G D, m c =1.5GeV, m q =0 no. of D-states (chiral+HQ symm.): 8 per u and d, 4 for s resonance cross section isotropic, pQCD forward [van Hees+ RR ’04] c “D” c _ q _ q

2.1.3 Thermal Relaxation of Heavy Quarks in QGP factor ~3 faster with resonance interactions! Charm: pQCD vs. Resonances pQCD “D”  c therm ≈  QGP ≈ 3-5 fm/c bottom does not thermalize Charm vs. Bottom

Relativistic Langevin Simulation: stochastic implementation of heavy-quark motion in expanding QGP- fireball with “hydrodynamic” evolution of bulk-matter  T, v Heavy-Quark Spectra at RHIC [van Hees,Greco+RR ’05] Nuclear Modification Factor resonances → large charm suppression+collectivity, not for bottom v 2 “leveling off”’ characteristic for transition thermal → kinetic Elliptic Flow

2.2.2 HQ Langevin Simulations: Hydro vs. Fireball [van Hees,Greco+RR ’05] Elastic pQCD (charm) + Hydrodynamics  s, g 1, , ,1.8 [Moore and Teaney ’04] T c =165MeV,  ≈ 9fm/c  s and  D ~gT independent (  D ≡1.5T)  gQ ~ (  s /  D ) 2  s =0.4 ↔ D(2  T) ≈ 20  hydro ≈ fireball expansion

2.3 Single-e ± at RHIC: Effect of Resonances hadronize output from Langevin HQs (  -fct. fragmentation, coalescence) semileptonic decays: D, B → e+ +X large suppression from resonances, elliptic flow underpredicted (?) bottom sets in at p T ~2.5GeV Fragmentation only

less suppression and more v 2 anti-correlation R AA ↔ v 2 from coalescence (both up) radiative E-loss at high p T ?! Single-e ± at RHIC: Resonances + Q-q Coalescence f q from , K Nuclear Modification Factor Elliptic Flow [Greco et al ’03]

2.4 Model Comparisons to Recent PHENIX Data Single-e ± Spectra [PHENIX ’06] coalescence essential for consistent R AA and v 2 other mechanisms: 3-body collisions, … [Liu+Ko’06, Adil+Vitev ‘06] pQCD radiative E-loss with 10-fold upscaled transport coeff. Langevin with elastic pQCD + resonances + coalescence Langevin with 2-6 upscaled pQCD elastic

2.5. Transport Properties of (s)QGP small spatial diffusion → strong coupling Spatial Diffusion Coefficient ‹x 2 ›-‹x› 2 =D x ·t, D x =2d·(T/m Q )/  D s =D x /2d E.g. strongly coupled gauge theory (AdS/CFT):  /s=1/4 , D HQ ≈1/2  T  resonances: D HQ ≈4-6/2  T, D HQ ~  /s ≈ (1-1.5)/  Charm-Quark Diffusion Viscosity-to-Entropy: Lattice QCD [Nakamura +Sakai ’04]

2.6 Potential Scattering in sQGP Lattice Q-Q Free Energy [Bielefeld Group ’04] Applications → Schröd.-Eq. → bound states (sQGP)! scattering states? imaginary parts? → Lippmann-Schwinger Equation [Shuryak,Zahed, Brown ’04]  solve numerically [Mannarelli+RR ’05] q-q T-Matrix -

2.6.2 Charm-light Cross Sections with Lat-QCD Potential Temperature Evolution Channel Decomposition interaction strength concentrated close to threshold meson and diquark channels dominant

2.6.3 Friction Coefficients (Relaxation Rate): Lat-QCD vs. Resonance Model uncertainty in potential extraction from lattice QCD potential scattering comparable to resonance model close to T c T ≈ 200 MeV T ≈ 250 MeV

2.6.4 Charm-Quark Spectra at RHIC Nuclear Suppression Factor Elliptic Flow nonperturbative effects stronger than elastic pQCD radiative (2↔3) scattering?

3.) Electromagnetic Radiation E.M. Correlation Function: e + e - γ Im Π em (M,q;  B,T) Im Π em (q 0 =q;  B,T) Radiation Sources: Relevance: Quark-Gluon Plasma: high mass + temp. qq → e + e , … M > 1.5GeV, T >T c Hot + Dense Hadron Gas: M ≤ 1 GeV     → e + e , … T ≤ T c - qqqq _ eeee  e+e-e+e-   qq _ e + e  → hadrons

3.2 EM Radiation and Chiral Symmetry Axial-/Vector in Vacuum pQCD continuum at T c : Chiral Restoration Im  em ~ [ImD  +ImD  /10+ImD  /5] Low-Mass Dilepton Rate:  -meson dominated! Axialvector Channel:  ±  invariant mass-spectra ~ Im D a1 (M) ?! ~ “  - a 1 (1260)” (chiral partners)

> >    B *,a 1,K 1... N, ,K … 3.3 Medium Effects: Hadronic Many-Body Theory D  (M,q;  B,T) = [M 2 - m  2 –   –   B -   M ] -1  -Propagator: [Chanfray et al, Herrmann et al, RR et al, Weise et al, Koch et al, Post et al, Eletsky et al, Oset et al, …] Constraints: - vacuum decays: B,M→  N,  - scattering data:  N,  A,  N→  N - QCD sum rules NANA  -ex Nuclei  N =0.8  0 [Urban et al ’98]   =   =  -Selfenergies:  [Ko et al ’92, Klingl et al ’97, Leupold et al ’98]

[RR+Gale ’99]  -Meson Spectral Functions at SPS  -meson “melts” in hot and dense matter (→ pQCD continuum) baryon density  more important than temperature reasonable agreement between models  B /  Hot+Dense Matter Hot Meson Gas [RR+Wambach ’99] [Eletsky etal ’01] Model Comparison [RR+Wambach ’99]

3.4 Pb-Au Collisions at SPS: CERES/NA45 T 0 ≈205MeV, T fo ≈110MeV QGP contribution small medium effects on  -meson! → Evolve dilepton rates over thermal fireball QGP+Mix+HG:

3.5 In-In at SPS: Dimuons from NA60 excellent mass resolution and statistics for the first time, dilepton excess spectra could be extracted! quantitative theory? [PRL ’06]

3.5.2 Dimuon Excess Spectra at SPS predicted ”melting”-  confirmed, average (   ) med ≈ 350MeV ≈ m  /2 relative strength of thermal sources fix, absolute yield ↔ fireball lifetime baryon effects essential; probing matter close to T c !? [van Hees +RR ‘06] Central In-In fireball: T 0-fo =195→120MeV, T c =175MeV,  FB =7fm Full Spectral Functions Switch off Medium Effects

3.6 Chiral Virial Approach vs. NA60 chiral reduction of scatt. ME’s + low-density expansion also: compare fireball vs. hydrodynamics good agreement fireball - hydro (p T -spectra!) lack of broadening [van Hees+RR ‘06] [Dusling,Teaney+Zahed ’06]

3.7 NA60 p T -Spectra freezeout-  :  -factor! good model agreement other fireball model: harder slopes, QGP dominant at M≥1GeV [Renk+ Ruppert ’06] Fireball + Many-Body Hydro + Chiral Virial theory slopes too soft ok with data hadronic emission prevalent [Dusling+Zahed ’06] [van Hees+RR ’06]

4.) Summary and Conclusions Heavy quarks probe the (s)QGP: strong suppression, collectivity Importance of elastic collisions; need explicit charm pQCD not enough, resonances in sQGP?! Microscopic description (lattice QCD potentials, correlators) Electromagnetic probes are becoming a precision tool Equilibrium radiation from QCD matter!? Average  -meson width  ≈ m  /2 (  →m  toward T c ) T- and  B -dependence of bare parameters in the Lagrangian? hard exp. p T -spectra

3.3 Dilepton Emission Rate: Hadron Gas vs. QGP “matching” of HG and QGP emission close to T c In-Medium Reduction of “Quark-Hadron Duality” Threshold ?!

4.3 NA60 p T -Spectra vs. Hadronic Many-Body improved freezeout-  (  -factor!) + Drell-Yan (p T >1.5GeV) approx. agreement (local slopes?!) See parallel talks by H.van Hees, J.Ruppert

3.2 Selfconsistent T-Matrix and Selfenergy [Mannarelli+RR ’05] assume m q (gluon)=0.1GeV transition from bound (1.2T c ) to resonance states! quark-width ≈0.3GeV ≈ (2/3fm) -1 (≈ mass ↔ liquid!?) colored states, equat. of state? q-q T-Matrices - Quark Self- Energy T=1.2T c T=1.5T c T=1.75T c T=1.5T c

5.) Electromagnetic Probes Thermal Photons I : SPS Expanding Fireball + pQCD pQCD+Cronin at q t >1.6GeV  T 0 =205MeV suff., HG dom. addt’l meson-Bremsstrahlung  →   K→  K  substantial at low q t [Liu+ RR’05] WA98 “Low-q t Anomaly” [Turbide,RR+Gale’04]

thermal radiation q t <3GeV ?! QGP window 1.5<q t <3GeV ?! Thermal Photons II: RHIC also:   -radiation off jets shrinks QGP window q t <2GeV ?! [Gale,Fries,Turbide,Srivastava ’04]

5.3.2 Dileptons II: RHIC low mass: thermal! (mostly in-medium  ) connection to Chiral Restoration: a 1 (1260)→ , 3  int. mass: QGP (resonances?) vs. cc → e + e - X (softening?) - [RR ’01] [R. Averbeck, PHENIX] QGP

4.2.4 NA60 Data: Chiral Virial Approach also compare fireball vs. hydrodynamics lack of broadening good agreement hydro - fireball [ van Hees+RR ‘06] [Dusling,Teaney+Zahed ‘06]