Heavy Quark Dynamics in the QGP: Boltzmann vs Langevin V. Greco Santosh Kumar Das Francesco Scardina 52 nd International Winter Meeting on Nuclear Physics Bormio, January 2014

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

Two Main Observables in HIC Two Main Observables in HIC  Nuclear Modification factor AA - 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

 I ntroduction the early ideas ( sketch of the historical path… )  Failure of pure jet quenching (p T < 8-10 GeV)  problematic R AA - v 2 relation  Non perturbative effect: Resonant D-like scattering at T>T c  Quark Dynamics in the QGP:  problematic R AA - v 2 relation  Boltzmann vs Langevin: - Is the charm really heavy? - Build-up of elliptic flow Outline Heavy Quark in the Hot QGP

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 K e e D B

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, Scardina, Di Toro, Greco, PRC82(2010) No interaction means R AA =1 and v 2 =0. More interaction decrease R AA and increase v 2 A typical example

 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. Physics: 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” 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 T increase

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 More realistic also for lQCD-V(r), g decreases 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 (2010) 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…  Better recent agreement in He, Fries, Rapp, Phys. Rev C86 (2012) 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 K e e D B

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 t03x0t03x0 exact solution Solved in a grid with the same tecniques of BAMPS, Xu-Greiner PRC’04 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

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: Then Fokker-Planck is 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 For small individual momentum transfer Fluctuation –Dissipation Theorem applies: A=B/2TE

When and if Boltzmann dynamics -> Langevin? How this depends on M,T,d  /d  or k? Charm and Bottom scattering in a Gluon Bulks in thermal equilibrium at T=400 MeV

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 LangevinBoltzmann T= 400 MeV Charm S.K. Das et al.,arXiv: Larger momentum spread -> large spread in the angular distributions -> back to back Charm-antiCharm angular correlation

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

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 % Implication for observable, R AA ? Once R AA is fixed the main point is if v 2 and angular correlation are the same?  Realistic simulation of A+A S.K. Das et al.,arXiv: m D =1.6 GeV

R AA & v 2 Boltzmann vs Langevin Fixed same R AA (p T )  v 2 (p T ) about 25% higher - dependence on the specfic scattering matrix ( isotropic case -> larger effect ) This may be the reason of the large v 2 in BAMPS Angular DD correlation? Work under progress

 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,LPM 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 fully understand. Upcoming new data at both RHIC and LHC: D(v 2 ), B(R AA,v 2 ), e ±  Boltzmann vs Langevin: - For Bottom no differences, but charm… does not seems to have a Brownian motion - However same R AA (p T ) by readjusting Drag by 15-50% - Even fixed R AA -> V 2 larger (25%-…)

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)

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

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 ±

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

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

Drag

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 Same tecniques of BAMPS, Xu-Greiner PRC’04

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

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

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

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]

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)