HeavyFlavor Transport at FAIR Ralf Rapp Cyclotron Institute

Heavy-Flavor Transport at FAIR Ralf Rapp Cyclotron Institute + Dept of Phys & Astro Texas A&M University College Station, USA HICfor. FAIR Workshop “Heavy-Flavor Physics with CBM” FIAS (Frankfurt, Germany), 26. -28. 05. 14

1. ) Introduction: Why Heavy Quarks in URHICs? “Large” scale m. Q >> LQCD, T (Q = c, b): • pair production in primordial NN collisions → well defined initial condition, flavor conserved • thermal relaxation time t. Q~ m. Q/T ~ 5 -20 ≥ tfireball → incomplete thermalization, “gauge” of interaction strength • simplifications in theoretical treatment → diffusion: Brownian markers of QGP → access to soft interactions in QGP / hadronization → potential theory → quantitative connections to lattice QCD → direct window on QGP transport coefficient

1. 2 Heavy-Quark Evolution in URHICs 0 | 0. 5 | t [fm/c] c • initial cond. (shadowing, • c-quark diffusion Cronin), in QGP liquid pre-equil. fields 5 | 10 | D • c-quark hadronization • D-meson diffusion in hadron liquid • Consistency - weak coupling: p. QCD + fragmentation - strong coupling: non-pert. diffusion + recombination

1. 3 Matter Evolution at CBM mqch[Me. V] 5 80 130 150 • significant time around (even above) Tc • need to control: - Q interactions with quarks - D, D and Lc interactions in hadronic matter

Outline 1. ) Introduction 2. ) Heavy-Quark Transport in QGP 3. ) D-Meson Transport in Hadronic Matter 4. ) Hadronization 5. ) Heavy-Ion Phenomenology 6. ) Conclusions

2. ) Heavy-Quark Transport Coefficient • p 2 ~ m. Q T >> k 2 ~ T 2 Brownian Motion: Q Fokker Planck Eq. thermalization rate diffusion coefficient • thermal relaxation time t. Q = 1/g • Einstein relation: → check FP approximation • spatial diffusion constant: Ds = T / g m. Q • relation to bulk medium: Ds (2 p. T) ~ h / s

2. 1 Leading-Order Perturbative QCD • gluon exchange regularized by Debye mass: 2 [Svetitsky ’ 88, Mustafa et al ’ 98, Molnar et al ’ 04, Zhang et al ’ 04, Hees+RR ’ 04, Teaney+Moore‘ 04] • dominated by forward scattering off gluons • thermalization time g -1 = tc ≥ 20 fm/c long (T≤ 300 Me. V, as=0. 4)

2. 2 Perturbative QCD with Running Coupling • run as to m. D ~ g. T, rather than 2 p. T • reduced Debye mass [Peshier ‘ 07] [Gossiaux+ Aichelin ‘ 08] • factor ~10 faster thermalization: tc ≈ 2 -3 fm/c • perturbative regime? Need to resum large diagrams…

2. 3 T-Matrix Approach • In-medium scattering amplitude • thermal 2 -particle propagator: • Field-theoretic potential approach: - effective propagator: Coulomb + string [Megias et al ‘ 07] - fit to lattice-QCD free energy

2. 3. 2 T-Matrix + Lattice-Potential Approach • heavy-light T-matrix → HQ transport Thermalization Rate • vacuum spectroscopy + p. QCD limit • “Feshbach” resonances in medium gc [1/fm] In-Medium Amplitude c-q- [Riek+RR ’ 10] • factor 3 -4 faster than p. QCD: tc ≈ 4 -6 fm/c • 3 -momentum dependence: transition strong → weak

3. ) D-Meson Transport in Hadronic Matter g. D [fm-1] • effective D-h scattering amplitudes • D-meson in pion gas: - consistent with unitarized HQET [Cabrera et al ‘ 11] - factor ~10 larger in heavy-meson c. PT [Laine ‘ 11] • hadron gas at ~Tc: t. D ≈ 10 fm/c g. D [fm-1] [He, Fries+RR ’ 11, Tolos+Torres-Ricon ‘ 13]

Summary of Charm Diffusion in Matter Hadronic Matter vs. QGP vs. Lattice QCD [He et al ’ 11, Riek+RR ’ 10, Ding et al ‘ 11, Gavai et al ‘ 11] Ad. S/QCD • Shallow minimun around Tc ? • Quark-Hadron Continuity? [Gubser ‘ 07]

4. ) Heavy-Flavor Hadronization • Hadronization is an interaction! • High p. T: p. QCD with fragmentation qq- c • Low + Intermediate p. T - heavy flavor conserved through transition - hadron formation with thermal quarks: resonant Qq recombination - same interaction as in non-pert. diffusion - contributes to equilibration! D q. T D c [Ravagli+RR ‘ 07]

5. ) Charm Transport at RHIC + LHC 5. 1 QGP – Hadronization – Hadronic Matter • increased QGP-v 2 from recombination + hadronic diffusion • increased Ds-RAA from strangeness enhancement [He et al ’ 12]

5. 2 Modeling of D-mesons at LHC • No single consistent description yet • Perturbative approaches too weakly coupled

5. 3 Heavy-Flavor Electrons at √s=62 Ge. V 10% [He et al in prep] • Importance of flow and Cronin at lower energies

6. ) Conclusions • Non-perturbative interactions govern heavy flavor at CBM: - Dt ~ 5 fm/c around Tc and in hadronic phase • Large mq / T ≥ 1 → importance of Qq interactions → Effective “potential” theory, controlled by - spectroscopy + p. QCD (vacuum) - lattice QCD (finite T) • In-medium hadronization: resonance correlations manifest • Quantitative effective hadronic theory • Implications for charmonia

2. 3 Ad. S/CFT-QCD Correspondence 3 -momentum independent [Herzog et al, Gubser ‘ 06] • match energy density (d. o. f = 120 vs. ~40) and coupling constant (heavy-quark potential) to QCD Lat-QCD TQCD ~ 250 Me. V ≈ (4 -2 fm/c)-1 at T=180 -250 Me. V [Gubser ‘ 07]

3. 3 Quarkonium Spectral Functions + Correlators [Aarts et al ‘ 07] • limiting cases: assume V=U or F [Satz et al ’ 01+’ 08, Mocsy+Petreczky ’ 05+’ 08, Wong ’ 06, Cabrera, Riek+RR ’ 06+’ 10, Beraudo et al ’ 06, Lee et al ’ 09, …]

3. 4 Quarkonium Transport • Rate Equation for J/y + q, g → c +X ← D D J/y reaction rate (y -width) equilibrium limit c- c J/y • in-med properties: spectral function, encodes screening/dissociation • formation sensitive to HQ distributions [cf. also Andronic et al, Zhuang et al, Ferreiro et al, …]

4. 1 Quantitative Bulk-Medium Evolution • initial conditions (compact, initial flow? ) • Eo. S: lattice (QGP, Tc~170 Me. V) + chemically frozen hadronic phase • spectra + elliptic flow: multistrange at Tch ~ 160 Me. V p, K, p, L, … at Tfo ~ 110 Me. V [He et al ’ 11] • v 2 saturates at Tch, good light-/strange-hadron phenomenology