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Heavy Quark Dynamics in the QGP: Boltzmann vs Langevin

Heavy Quark Dynamics in the QGP: Boltzmann vs Langevin. V. Greco. Santosh Kumar Das Francesco Scardina. LHC. RHIC. Temperature. SPS. Zhu et al. (2006). Heavy Quark & QGP. Heavy because: M >> L QCD (particle physics) M>> T (plasma physics). Specific of Heavy Quarks.

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Heavy Quark Dynamics in the QGP: Boltzmann vs Langevin

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  1. Heavy Quark Dynamics in the QGP: Boltzmann vs Langevin V. Greco Santosh Kumar Das Francesco Scardina

  2. LHC RHIC Temperature SPS Zhu et al. (2006) Heavy Quark & QGP • Heavy because: • M >> LQCD (particle physics) • M>> T (plasma physics)

  3. Specific of Heavy Quarks Comparing mHQ to LQCD and T • mc,b >> LQCDproduced by pQCD processes (out of equil.) • t0 << tQGPthey go through all the QGP lifetime • mc,b >> T0no thermal production • teq>tQGP >> tq,gcarry more information • -------- • m>>T-> q2<<m2 dynamics reduced to Brownian motion • q0<< |q| Concept of potential V(r) <-> lQCD

  4. Heavy Quark in the Hot QGP • Then: introduction the early ideas • Failure of pQCD and jet quenching (pT< 8-10 GeV) • problematic RAA- v2 relation • Non perturbative effect: Resonant D-like scattering at T>Tc • Now: Quark Dynamics in the QGP: • problematic RAA- v2 relation • Boltzmann vs Langevin: is the charm really heavy? • … Outline

  5. Some years ago … charm Flow mass effect Pythia Pythia Therm+Flow Pythia Therm+Flow Hydro bottom Batsouli, Nagle, Gyulassy PLB557 (03) 26 What is the charm interaction in the QGP? Does charm flow at RHIC ? V. Greco, et al., PLB595(2004)202 Au+Au 200 AGeV fit to p Decay -> e± V2 of electrons Difference between (Therm+Flow) – Pythia Small: pT spectra does not disentagle the two cases • V2e well correlated to V2D • V2 of D and J/Y correlated in a coalescence approach

  6. Ideas about Heavy Quarks before RHIC mQ>>mq HQ notdragged by the expanding medium: - spectraclose to the ppone-> large RAA - small elliptic flow v2 2) mQ >> mq,LQCDprovide a better test of jet quenching: - Color dependence (quark fragm.): RAA(B,D) > RAA(h) - Mass dependence (dead cone): RAA(B)> RAA(D)> RAA(h) Standard Dynamics of Heavy Quarks in the QGP Fokker-Planckapproach in Hydro bulk c,b quarks T<<mQ sQGP From scattering matrix |M|2 • from some theory… Brownian Motion?

  7. × k pi pf pi pf Parton Level RAA(pT) B u,d c D k a g pT [GeV] Problems with Ideas 1 - Jet Quenching prediction gv=p/m >>1/g Radiative bremsstrahlung is dominant According to our results, charm quark suppression should be small ~ 0.7 Therefore, this suppression should be definitely much smaller than the already observed pion suppression (0.2). (M.Djordjevic QM04) We obtained that at pT~5GeV, RAA(e-)> 0.5±0.1at RHIC (M.D. QM05)

  8. Problems with Ideas 2 Again at LHC energy heavy flavor suppression is similar to light flavor especially at high pT : quite small mass ordering of RAA However charm is not really heavy …

  9. Problems with ideas 1 q q Large elliptic Flow Strong suppression S. Wicks et al. (QM06) N. Armesto et al., PLB637(2006)362 • Radiative energy loss not sufficient • Charm seems to flow like light quarks Heavy Quark strongly dragged by interaction with light quarks pQCD does not work may be the real cross section is a K factor larger?

  10. Charm dynamics with upscaled pQCD cross section Diffusion coefficient Fokker-Plank for charm interaction in a hydro bulk scattering matrix Multiplying by a K-factor pQCD data data Moore & Teaney, PRC71 (2005) It’s not just a matter of pumping up pQCD elastic cross section: too low RAA or too low v2

  11. RAA and v2 correlation No interaction means RAA=1 and v2=0. More interaction decrease RAA and increase v2 RAA can be “generated” faster than v2 A typical example The relation between RAA and time isnottrivial and depend on howone interact and looseenergy with time. Thisis general, seenalso for light quarks

  12. Jet quenching for light q and g GLV radiation formula Simple modeling: jets going straight and radiate energy Elliptic flow only from path length Scardina, Di Toro, Greco, PRC82(2010) Liao, Shuryak PRL 102 (2009) Time dependence of Eloss Elliptic Flow Tuned to get the same RAA Au+Au@200 AGeV 20-30% p0

  13. The RAA - v2 correlation is not easy to get : very good!!! • Notice that for the bulk matter (light quark and gluons) • It has been more easy to reproduce pT-spectra & v2 • with hydrodynamics. • It is true that a non full equilibrium dynamics (tHQ > t QGP) • contains more information, • that we have not been able to fully disentangle. In 2006-08 we had the idea that there can be large non-perturbative elastic scattering due to the presence of hadronic-like resonances reminiscent of confinement dynamics at T≥Tc

  14. _ _ “D” q q “Light”-Quark Resonances c c 1.4Tc [Asakawa+ Hatsuda ’03] Indications from lQCD Spectral Function J/y (p = 0) disappears around 1.7 Tc J/Y We do not know what is behindr(w): bound states, resonances, … cqdoesnotundergo a free scattering, butthere are remants of confinement!? Asakawa There can be Qq (D-like) resonant scattering!?

  15. VlQCD gives resonance states! Extraction of V(r) main source of uncertainty Scattering states included: Singlet + Octet –triplet -sextet lQCD “Im T” dominated by meson and diquark channel Kaczmarek et al., PPS 129,560(2004) • Solve in partial wave expansion • Equation closed with the equivalent equation in the light sector,here simplified with a constant m and G

  16. Drag Coefficient from lQCD-V(r) Opposite T-dependence of g not a K-factor difference Drag coefficient g= D/mT With lQCD- V(r): ->one can expect more V2 with the same RAAbecausethereis a strong interaction just when v2is beingformed. Case shownis the mostextremeone lQCD Drag coefficient pQCD ImT increase with temperature compensates for decreasing scatterer density Does it solve the problem of “too low RAA or too low v2” ?

  17. ? Impact of hadronization mechanism • Uncertainties: • extraction of V(r) - (U vs F) • V2 of the bulk and hypersurface • B/D ratio • [essential the possibilitythatwehave to • disentanglethemat LHC] Impact of hadronization Coalescenceincrease both RAA and v2 towardagreement with data Hees-Mannarelli-Greco-Rapp, PRL100 (2008) fq from p, K Greco,Ko,Levai - PRL90 add quark momenta

  18. Various Models at Work for RHIC • Simultaneous description of RAA and v2 is a tough challenge for all models our Van Hees et al., better but… • The dynamics in the hadronic part not negligible (Jan-e Alam, S.K.Das…)

  19. Various Models at Work for LHC • Models fails to get both, some hope for TAMU elastic (if radiative added) • Pure radiative jet quenching gets the lower v2 (LPM helps…) • Apart from BAMPS the Fokker-Planck is used to follow HQ dynamics. • Those getting close have heavy-quark coalescence V. Greco et al., PLB595(04)202

  20. Standard Description of HQ propagation in the QGP HQ scattering in QGP Langevinsimulation in Hydro bulk c,b quarks T<<mQ • Elastic pQCD • T-matrix V(r)-lQCD • Soft gluon radiation • … sQGP From scattering matrix |M|2 Brownian Motion? • Now what we are doing : • study the validity of the Brownian motion assumption, is it really small momentum transfer dynamics? • RAA is as smaller as for light mesons • If resonant scattering is important can it be that the momentum transfer per collisions is small?

  21. Relativistic Boltzmann Equation for Charm Molnar’05, Ko’06, Greiner ‘09, Bass ‘12 … Collisions Free streaming Field Interaction fQ(x,p) is a one-body distribution function for HQ in our case fq,g is integrated out as bulk dynamics in the Coll. integral Gain Loss Rate of collisions per unit time and phasespace Solveddiscretizing the space in (h, x, y)a cells Collision rate exact solution t0 3x0

  22. Simulation in a box: charm Simulations in which a particle ensemble in a box evolves dynamically Bulk composed only by gluons in thermal equilibrium at T=400 MeV Due to collisions charm approaches the thermal equilibrium with the bulk

  23. Boltzmann -> Fokker-Planck The relativistic collision integral can be re-written in terms of transferred momentum k=p-p’ Defining the probability w for HQ to be scattered from p -> p+k This re-definition of the collision integral allows to derive directly the Fokker-Planck approximation

  24. Boltzmann -> Fokker-Planck Landau and/or Svetisky approximation Expansion for small Momentum transfer The Boltzmann Collision Integral, under this approximation, becomes: B. Svetitsky PRD 37(1987)2484 Fokker – Planck equation Drag:<p> Diffusion:<Dp2> Then Fokker-Planck can be solved stochastically by the Langevin equations fg defined through the rate ofradiativeenergy loss

  25. Common Origin is the Matrix Element M scattering matrix of the collisions process Langevin approach Boltzmann approach M -> Ai, Bij M -> d/dW Drag Coefficient -> <p> Total and differential cross section Diffusion coefficient -> <Dp2>

  26. When and if Boltzmann dynamics -> Langevin? How this depends on M,T,ds/dQ or k?

  27. Differential Cross section and momentum transfer: Charm • ChangingmDwe simulate differentangulardependencies of scatterings • mD=gT =0.83 GeV for as=0.35 Angular dependence of  Momentum transfer S.K. Das et al.,arXiv:1312.6857 •  more isotropic -> Larger average momentum transfer • For Charm isotropic cross section can lead K> Mc

  28. Boltzmann vsLangevin (Charm) Time evolution of the p-spectra mD=0.4 GeV mD=0.83 GeV Charm Charm • The smaller <k> the better Langevin approximation works • At t ≈ 4-6 fm/c difference can be quite large for mD ≥ 0.8 GeV (K≈Mc and Mc≈3T) mD=1.6 GeV S.K. Das et al.,arXiv:1312.6857

  29. Bottom RAA: Boltzmann = Langevin T= 400 MeV mD=0.83 GeV T= 400 MeV mD=0.4 GeV Bottom Bottom In bottom case Langevin approximation ≈ Boltzmann But Larger Mb/T (≈ 10) the better Langevin approximation works

  30. Momentum evolution of a single charm Langevin Boltzmann T= 400 MeV T= 400 MeV Charm Charm • • Kinematics of collisions (Boltzmann) can throw particles at very low p soon • The motion of single HQ does not appear to be of Brownian type, on the other hand Mc/T=3 -> Mc/<pbulk> = 1 • A part of dynamic evolution involving large moment transferred • is discarded with Langevin approach S.K. Das et al.,arXiv:1312.6857

  31. Momentum evolution of a single Bottom Langevin Boltzmann T= 400 MeV T= 400 MeV Bottom Bottom • For Bottom one start to see a peak moving with a width more reminiscent of Poisson distribution More close to Brownian motion, on the other hand Mb/T=10

  32. Momentum evolution for charm vs temperature Boltzman Boltzmann T= 400 MeV T= 200 MeV Charm Charm • At 200 MeV Mc/T= 6 -> start to see a peak with a width Such large spread of momentum implicates a large spread in the angular distributions that could be experimentally observed studying the back to back Charm-antiCharm angular correlation

  33. Implication for observable, RAA? T= 400 MeV mD=0.83 GeV Charm The Langevin approach indicates a smaller RAA thus a larger suppression.

  34. Implication for observable, RAA? Now, the main point is if the v2 and the angular correlation generation can also be the same. Work under progress, making the comparison with a realistic simulation of HIC mD=0.83 GeV mD=1.6 GeV S.K. Das et al.,arXiv:1312.6857 However one can mock the differences of the microscopic evolution and reproduce the same RAA of Boltzmann equation just changing the diffusion coefficient by about a 30 %

  35. Conclusions and perspective HQ physics in QGP contains information that we have not yet been able to understand • RAA- v2 of HQ seems to indicate: • - Elastic collisional dynamics (up to 6-8 GeV) • - Interaction not trivially decreasing with r-1≈ T3 ≈ t-1 • (heavy resonances above Tc or …) • - Hadronization of by coalescence of heavy quarks • Boltzmann vs Langevin: • - For Bottom most likely no differences, but charm… • does not seems to have a Brownian motion • - Possible to get same RAA(pT) by readjusting Drag by 15-50% • - Is the RAA-V2 and the angular correlation D-Ď different?

  36. Dream!? Open Flavor • A new era for the understanding of charmonia - At LHC could be possible to relate open and hidden heavy flavor, both D and J/Y should come from the same underlying dNc/dpTdf -> RAA & v2 (pT) (at least up to 3-4 Gev) - softer pT spectra of J/Y <-> dN/dpT of D (partially observed) - Large elliptic flow v2(J/Y)<-> v2(D) Hidden Greco, Ko, Rapp-PLB595(04)

  37. coal. coal.+ fragm. G = 0.75 GeV Baryon contamination due to coalescence … !? P. Soresen, nucl-ex/0701048, PRC (07) G. Martinez-Garcia et al., hep-ph/0702035 PLB(08) Apparent reduction if Lc/D ~1 due to different branching ratio - Effect at pt~2-4 GeV region were it is more apparent the coalescence effect) • Explanation for large v2e : v2Lc > v2D Some coalescence model predict a much larger enhancement… possibility to reveal diquark correlations? Heavy-Flavor and jet quenching- Workshop, Padova 29-9-2005

  38. Main reason for a much reduced coalescence effect: • at variance with the light quark case you don’t add equal momenta • pu~ pc*mu/mc + different slope of the spectra • So there is not an enhancement equivalent to the light quark one : • do you believe to my coalescence model? • if we will observe Lc/D =1 ? What mechanism is behind it? • the v2 of Lc is enhanced according to QNS scaling? (that is not 3/2 v2D) Lc/D measurementnotwelldeterminedeven in pp ( at FERMILAB) atleast in PRL 77(1996) 2388

  39. Differential Cross section and momentum transfer: Charm & Bottom

  40. Drag

  41. Simulation in a box: Bottom Simulations in which a particle ensemble in a box evolves dynamically Bulk composed only by gluons in thermal equilibrium at T=400 MeV Due to collisions Bottom Approaches the thermal equilibrium with the bulk

  42. We consider as initial distribution in p-space a (p-1.1GeV) for both C and B with px=(1/3)p

  43. Quarkonium <-> Heavy-Quark Elliptic Flow • V2c=V2q +100% recombination + • all at freeze-out [1] • V2c realistic+100% recombination + • all at freeze-out [2] [3] • V2c realistic+100% recomb + • not at f.o. [4] • 100% primordial J/Y Rapp, Blaschke, Crochet, Prog.Part.Nucl.Phys.65(2010) [1] V. Greco, C.M. Ko, R. Rapp, PLB 595(04), 202. [2] L. Ravagli, R. Rapp, PLB 655(07), 126. [3] L. Yan, P. Zhuang, N. Xu, PRL 97(07), 232301. [4] X. Zhao, R. Rapp, 24th WWND, 2008. [5] Y. Liu, N. Xu, P. Zhuang, NPA 834 (06), 317. Some remnant of the signal, but At LHC the regeneration component should dominate …

  44. Suppression-regeneration models Regeneration Zhao and Rapp, arXiv:1008.5328 Yuan, Xu, Zhuang, PRL97(2006) At 20-60% small regeneration component even decreasing with pT

  45. 7.8fm 20-60% MB MB 7.8fm 20-40% 7.8fm J/y elliptic flow v2 Zebo Tang, USTC STAR Preliminary QM2011 Disfavor coalescence from thermalized charm quarks, [1] V. Greco, C.M. Ko, R. Rapp, PLB 595, 202. [2] L. Ravagli, R. Rapp, PLB 655, 126. [3] L. Yan, P. Zhuang, N. Xu, PRL 97, 232301. [4] X. Zhao, R. Rapp, 24th WWND, 2008. [5] Y. Liu, N. Xu, P. Zhuang, NPA, 834, 317. [6] U. Heinz, C. Shen, priviate communication. Not really in disagreement with the suppression-regeneration model but against the idea of all J/Y formed thermally at freeze-out (stat. model) may be… But need more central and more precise, again high resolution! What about vn of J/Y have we explored the power of the vn analysis?

  46. Enhancement of J/Y at LHC!? Pure statistical model at Tc + corona effect Including both suppression and regeneration during all the evolution Rapp R., X. Zhao, arXiV:1102.2194[hep-ph] A. Andronic, P. B-M., et al., NPA 789 (2007)

  47. From the point of view of the shear viscosity lQCD-quenched Csernai et al., PRL96(06) HQ are more sensitive to the details of dynamics (teq ~tQGP) It is necessary an interaction that increases as T -> Tc, i.e. when we approach the phase transition

  48. z y x py px Two Main Observables in HIC R = 1 nothing new going on • Nuclear Modification factor AA • - Modification respect to pp • Decrease with increasing • partonic interaction • Anisotropy p-space:Elliptic Flow v2 centrality Increases with cs=dP/de and s (or 1/h)! ex v2

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