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

Heavy Quark & QGP SPS LHC Zhu et al. (2006) RHIC Temperature Heavy because:  M >>  QCD (particle physics)  M>> T (plasma physics)

Specific of Heavy Quarks  m c,b >>  QCD  m c,b >>  QCD produced by pQCD processes (out of equil.)  0 <<  QGP   0 <<  QGP they go through all the QGP lifetime  m c,b >> T 0 no thermal production  eq >  QGP >>  q,g   eq >  QGP >>  q,g carry more information  m>>T  m>>T  q 2 <<m 2 dynamics reduced to Brownian motion  q 0 lQCD Comparing m HQ to  QCD and T

 Then: introduction the early ideas  Failure of pQCD and jet quenching (p T < 8-10 GeV)  problematic R AA - v 2 relation  Non perturbative effect: Resonant D-like scattering at T>T c  Now: Quark Dynamics in the QGP:  problematic R AA - v 2 relation  Boltzmann vs Langevin: is the charm really heavy? … Outline Heavy Quark in the Hot QGP

V. Greco, et al., PLB595(2004)202  V 2e well correlated to V 2D  V 2 of D and J/  correlated in a coalescence approach V 2 of electrons Flow mass effect Some years ago … Difference between (Therm+Flow) – Pythia Small: p T spectra does not disentagle the two cases What is the charm interaction in the QGP? Does charm flow at RHIC ? fit to  Au+Au 200 AGeV charm bottom Pythia Therm+Flow Pythia Batsouli, Nagle, Gyulassy PLB557 (03) 26 Pythia Hydro Decay -> e ±

Ideas about Heavy Quarks before RHIC 1)m Q >>m q HQ not dragged by the expanding medium: - spectra close to the pp one-> large R AA - small elliptic flow v 2 2) m Q >> m q,  QCD provide a better test of jet quenching: - Color dependence ( quark fragm. ): R AA (B,D) > R AA (h) - Mass dependence ( dead cone ): R AA (B)> R AA (D)> R AA (h) Brownian Motion? sQGP c,b quarks From scattering matrix |M| 2 from some theory… T<<m Q Fokker-Planck approach in Hydro bulk Standard Dynamics of Heavy Quarks in the QGP

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) B D g p T [GeV] u,d Parton Level R AA (p T ) We obtained that at p T ~5GeV, R AA (e-) > 0.5±0.1 at RHIC (M.D. QM05) Problems with Ideas 1 - Jet Quenching prediction pfpf pipi k × pipi pfpf k a c  v=p/m >>1/g Radiative bremsstrahlung is dominant

Problems with Ideas 2 Again at LHC energy heavy flavor suppression is similar to light flavor especially at high p T : quite small mass ordering of R AA However charm is not really heavy …

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

Moore & Teaney, PRC71 (2005) Fokker-Plank for charm interaction in a hydro bulk It’s not just a matter of pumping up pQCD elastic cross section: too low R AA or too low v 2 Multiplying by a K-factor pQCD data Diffusion coefficient Charm dynamics with upscaled pQCD cross section scattering matrix

R AA and v 2 correlation R AA can be “generated” faster than v 2 The relation between R AA and time is not trivial and depend on how one interact and loose energy with time. This is general, seen also for light quarks No interaction means R AA =1 and v 2 =0. More interaction decrease R AA and increase v 2 A typical example

AGeV 20-30%  Scardina, Di Toro, Greco, PRC82(2010) Liao, Shuryak PRL 102 (2009) GLV radiation formula Jet quenching for light q and g Tuned to get the same R AA Time dependence of E loss Elliptic Flow Simple modeling: jets going straight and radiate energy Elliptic flow only from path length

 The R AA - v 2 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 p T -spectra & v 2 with hydrodynamics.  It is true that a non full equilibrium dynamics (t HQ > t QGP ) contains more information, that we have not been able to fully disentangle. In 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≥T c

Asakawa J/  J/  ( p  0 ) disappears around 1.7 T c “Light”-Quark Resonances 1.4T c [ Asakawa+ Hatsuda ’03 ] Indications from lQCD We do not know what is behind  bound states, resonances, … cq does not undergo a free scattering, but there are remants of confinement!? There can be Qq (D-like) resonant scattering!? There can be Qq (D-like) resonant scattering!? Spectral Function c “D”“D” c _ q _ q

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

With lQCD- V(r):  one can expect more V 2 with the same R AA because there is a strong interaction just when v 2 is being formed. Case shown is the most extreme one lQCD pQCD Opposite T-dependence of  not a K-factor difference Drag coefficient Drag Coefficient from lQCD-V(r) ImT increase with temperature compensates for decreasing scatterer density Drag coefficient  = D/mT Does it solve the problem of “ too low R AA or too low v 2 ” ?

Impact of hadronization mechanism Hees-Mannarelli-Greco-Rapp, PRL100 (2008) Impact of hadronization Coalescence increase both R AA and v 2 toward agreement with data f q from , K Greco,Ko,Levai - PRL90 ? add quark momenta Uncertainties: extraction of V(r) - (U vs F) V 2 of the bulk and hypersurface B/D ratio [essential the possibility that we have to disentangle them at LHC]

 Simultaneous description of R AA and v 2 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… ) Various Models at Work for RHIC

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 v 2 ( 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

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

Relativistic Boltzmann Equation Collisions Field Interaction Free streaming f Q (x,p) is a one-body distribution function for HQ in our case f q,g is integrated out as bulk dynamics in the Coll. integral for Charm Molnar’05, Ko’06, Greiner ‘09, Bass ‘12 … Gain Loss Collision rate Rate of collisions per unit time and phase space Solved discretizing the space in  x, y   cells t03x0t03x0 exact solution

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 Simulation in a box: charm

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

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

Boltzmann approach Langevin approach Common Origin is the Matrix Element Drag Coefficient -> Diffusion coefficient -> M -> d  /d  M -> A i, B ij M scattering matrix of the collisions process Total and differential cross section

When and if Boltzmann dynamics -> Langevin? How this depends on M,T,d  /d  or k?

Momentum transferAngular dependence of  Differential Cross section and momentum transfer: Charm  more isotropic -> Larger average momentum transfer For Charm isotropic cross section can lead K> M c S.K. Das et al.,arXiv: Changing m D we simulate different angular dependencies of scatterings m D =gT =0.83 GeV for  s =0.35

Boltzmann vs Langevin (Charm)  The smaller the better Langevin approximation works  At t ≈ 4-6 fm/c difference can be quite large for m D ≥ 0.8 GeV (K≈M c and M c ≈3T) Charm S.K. Das et al.,arXiv: m D =0.4 GeV Charm m D =0.83 GeV m D =1.6 GeV Time evolution of the p-spectra

In bottom case Langevin approximation ≈ Boltzmann But Larger M b /T (≈ 10) the better Langevin approximation works Bottom R AA : Boltzmann = Langevin Bottom T= 400 MeV m D =0.83 GeV T= 400 MeV m D =0.4 GeV Bottom

Momentum evolution of a single 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 M c /T=3 -> M c / = 1 A part of dynamic evolution involving large moment transferred is discarded with Langevin approach LangevinBoltzmann T= 400 MeV Charm S.K. Das et al.,arXiv:

T= 400 MeV Momentum evolution of a single Bottom LangevinBoltzmann 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 M b /T=10

Momentum evolution for charm vs temperature BoltzmanBoltzmann T= 400 MeV Charm 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 T= 200 MeV At 200 MeV Mc/T= 6 -> start to see a peak with a width Charm

Implication for observable, R AA ? The Langevin approach indicates a smaller R AA thus a larger suppression. Charm T= 400 MeV m D =0.83 GeV

However one can mock the differences of the microscopic evolution and reproduce the same R AA of Boltzmann equation just changing the diffusion coefficient by about a 30 % Implication for observable, R AA ? Now, the main point is if the v 2 and the angular correlation generation can also be the same. Work under progress, making the comparison with a realistic simulation of HIC S.K. Das et al.,arXiv: m D =1.6 GeV

 R AA - v 2 of HQ seems to indicate: - Elastic collisional dynamics ( up to 6-8 GeV ) - Interaction not trivially decreasing with  -1 ≈ T 3 ≈  -1 ( heavy resonances above T c or … ) - Hadronization of by coalescence of heavy quarks Conclusions and perspective HQ physics in QGP contains information that we have not yet been able to understand  Boltzmann vs Langevin: - For Bottom most likely no differences, but charm… does not seems to have a Brownian motion - Possible to get same R AA (p T ) by readjusting Drag by 15-50% - Is the R AA -V 2 and the angular correlation D-Ď different?

Dream!?  A new era for the understanding of charmonia - At LHC could be possible to relate open and hidden heavy flavor, both D and J/  should come from the same underlying dNc/dp T d  -> R AA & v 2 (p T ) (at least up to 3-4 Gev) Open Flavor Hidden Greco, Ko, Rapp-PLB595(04) - softer p T spectra of J/  dN/dp T of D ( partially observed) - Large elliptic flow v 2 (J/  )  v 2 (D)

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

Main reason for a much reduced coalescence effect: - at variance with the light quark case you don ’ t add equal momenta p u ~ p c *m u /m c + 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  c/D =1 ? What mechanism is behind it? -the v 2 of  c is enhanced according to QNS scaling? (that is not 3/2 v 2D )  c /D measurement not well determined even in pp ( at FERMILAB) at least in PRL 77(1996) 2388

Differential Cross section and momentum transfer: Charm & Bottom

Drag

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 Simulation in a box: Bottom

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

Quarkonium  Heavy-Quark Elliptic Flow Some remnant of the signal, but At LHC the regeneration component should dominate …  V 2c =V 2q +100% recombination + all at freeze-out all at freeze-out Rapp, Blaschke, Crochet, Prog.Part.Nucl.Phys.65(2010)  100% primordial J/   V 2c realistic +100% recombination + all at freeze-out all at freeze-out  V 2c realistic +100% recomb + not at f.o. not at f.o. [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), [4] X. Zhao, R. Rapp, 24th WWND, [5] Y. Liu, N. Xu, P. Zhuang, NPA 834 (06), 317. [1] [2] [3] [4]

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

J/  elliptic flow v 2 STAR Preliminary Not really in disagreement with the suppression-regeneration model but against the idea of all J/  formed thermally at freeze-out (stat. model) may be… [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, [4] X. Zhao, R. Rapp, 24th WWND, [5] Y. Liu, N. Xu, P. Zhuang, NPA, 834, 317. [6] U. Heinz, C. Shen, priviate communication. MB 7.8fm MB 20-40% 20-60% 7.8fm Zebo Tang, USTC QM2011 But need more central and more precise, again high resolution! What about v n of J/  have we explored the power of the v n analysis? Disfavor coalescence from thermalized charm quarks,

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

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

Two Main Observables in HIC  Nuclear Modification factor AA R = 1 nothing new going on - Modification respect to pp - Decrease with increasing partonic interaction  Anisotropy p-space:Elliptic Flow v 2 pxpx pypy Increases with c s =dP/d  and  or 1/  ! x y z centrality xxxx v2v2v2v2