Heavy Quark Dynamics in the QGP:Heavy Quark Dynamics in the QGP:Boltzmann vs LangevinBoltzmann vs Langevin

V. GrecoV. Greco

Santosh Kumar Das

Francesco Scardina

Heavy Quark & QGPHeavy Quark & QGP

SPS

LHC

Zhu et al. (2006)

RHIC Temperature

Heavy because:

M >> QCD (particle physics)

M>> T (plasma physics)

Specific of Heavy QuarksSpecific of Heavy Quarks

mmc,bc,b >> >> QCDQCD produced by pQCD processes (out of equil.)

00 << << QGPQGP they go through all the QGP lifetime

mmc,bc,b >> T >> T00 no thermal production no thermal production

eq eq >>QGPQGP >> >> q,gq,g carry more information

-------- m>>Tm>>T q2<<m2 dynamics reduced to Brownian motion

q0<< |q| Concept of potential V(r) <-> lQCD

Comparing mComparing mHQHQ to to QCD QCD and Tand T

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?…

Ou

tlin

eHeavy Quark in the Hot QGPHeavy Quark in the Hot QGP

V. Greco, et al., PLB595(2004)202

V2e well correlated to V2D

V2 of D and J/ correlated in a coalescence approach

V2 of electrons

Flow mass effect

Some years ago …Some years ago …

Difference between (Therm+Flow) – Pythia Small: pT spectra does not disentagle thetwo cases

What is the charm interaction in the QGP? Does charm flow at RHIC ?

fit to

Au+Au 200 AGeV

charm

bottom

PythiaTherm+Flow

Therm+Flow

Pythia

Batsouli, Nagle, Gyulassy PLB557 (03) 26

Pythia

Hydro

Decay -> e±

Ideas about Heavy Quarks before RHICIdeas about Heavy Quarks before RHIC1)mQ>>mq HQ not dragged by the expanding medium:

- spectra close to the pp one-> large RAA

- small elliptic flow v2

2) mQ >> mq,QCD provide 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)

Brownian Motion?

sQGP

c,b quarks

ppkMkdp23 ),(

223 ),(2

1ppkMkdD

Fromscattering

matrix |M|2• from some theory…

T<<mQ

Fokker-Planck approachin Hydro bulk

2

,2

,, )(

p

fD

p

pf

t

f bcbcbc

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)

1000gdN

dy

B

D

g

pT [GeV]

u,d

Pa

rto

n L

ev

el

RA

A(p

T)

We obtained that at pT~5GeV, RAA(e-) > 0.5±0.1 at RHIC (M.D. QM05)

Problems with Ideas 1 - Jet Quenching prediction

pfpik

×pi pf

kac

v=p/m >>1/g

Radiative bremsstrahlung

is dominant

Problems with Ideas 2Problems with Ideas 2

Again at LHC energy heavy flavor suppression Again at LHC energy heavy flavor suppression

is similar to light flavor especially at high pis similar to light flavor especially at high pT T ::

quite small mass ordering of Rquite small mass ordering of RAA AA

However charm is not really heavy … 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 pQCD does not work may be the real cross section is a K factor larger?larger?

pQCD does not work may be the real cross section is a K factor pQCD does not work may be the real cross section is a K factor larger?larger?

Problems with ideas 1Problems with ideas 1

Radiative energy loss not sufficient

Charm seems to flow like light quarksq

q

Heavy Quark strongly dragged by interaction with light quarksHeavy 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

ItIt’’s not just a matter of pumping up pQCD elastic cross section:s not just a matter of pumping up pQCD elastic cross section:too low too low RRAAAA or too low v or too low v22

Multiplying by a K-factor pQCD

data

data

Diffusion coefficient

Charm dynamics with upscaled pQCD cross section

22

)()(3 ),( kpkMkdD cqgcqg

scattering matrix

RAA and v2 correlation

RAA can be “generated” faster than v2

The relation between RAA and time is not trivial and depend on how oneinteract and loose energy with time. This is general, seen also for light quarks

No interaction means RAA=1 and v2=0. More interaction decrease RAA and increase v2

A typical example

20

0

3 2

4

9

TsR P

log,r,CE

Au+Au@200 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 RAA

Time dependence of Eloss Elliptic Flow

Simple modeling: jets going straight and radiate energy

Elliptic flow only from path length

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

Asakawa

J/

J/ (p 0) disappearsaround 1.7 Tc

“Light”-Quark Resonances

1.4Tc

[Asakawa+ Hatsuda ’03]

Indications from lQCDIndications 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) There can be Qq (D-like) resonant scattering!?resonant scattering!?

There can be Qq (D-like) There can be Qq (D-like) resonant scattering!?resonant scattering!?

Spectral Function

c

“D”

c

_q

_q

qcqc ,

),(),(),( 111 TUTrUTrV dT

dFTFU 1

11

Scattering states included:Singlet + Octet –triplet -sextet

Kaczmarek et al., PPS 129,560(2004)

VGTVT

qg

Q TS

• Equation closed with the equivalent equation in the light sector,here simplified with a constant m and

• Solve in partial wave expansion

VVlQCDlQCD gives resonance states! gives resonance states!

QQQQQ SSSS 0

““Im TIm T”” dominated by meson and diquark channel

lQCD

Extraction of V(r) mainsource of uncertainty

With lQCD- V(r): one can expect more V2 with the same RAA because there is a strong interaction just when v2 is being formed.

Case shown is the most extreme one

lQCD

pQCD

Opposite T-dependence of Opposite T-dependence of not a K-factor differencenot a K-factor difference

Dra

g co

effic

ient

Drag Coefficient from lQCD-V(r)

ImT increase with temperature compensates

for decreasing scatterer density

ppkMkdp23 ),( Drag coefficient

= D/mT

Does it solve the problem of“too low RAA or too low v2” ?

Impact of hadronization mechanismImpact of hadronization mechanism

Hees-Mannarelli-Greco-Rapp, PRL100 (2008)

Impact of hadronizationCoalescence increase

both RAA and v2

toward agreement with data

fq from , KGreco,Ko,Levai - PRL90

?

BDbcbcMqbcBDBD DfffC

Pd

Nd,,,,,3

,3

add quark momenta

Uncertainties:Uncertainties:

extraction of V(r) - (U vs F)V2 of the bulk and hypersurface

B/D ratio

[essential the possibility that we have

to

disentangle them at LHC]

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…)

Various Models at Work for RHICVarious Models at Work for RHIC

Various Models at Work for LHCVarious 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

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? RAA 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

ppkMkdp23 ),(

223 ),(2

1ppkMkdD

Fromscattering

matrix |M|2

• Elastic pQCD

• T-matrix V(r)-lQCD

• Soft gluon radiation

• …

T<<mQ

HQ scattering in QGPHQ scattering in QGPLangevin simulation

in Hydro bulk 2

,2

,, )(

p

fD

p

pf

t

f bcbcbc

Relativistic Boltzmann Relativistic Boltzmann EquationEquation

CollisionsCollisionsField Interaction Free streaming

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

for Charm Molnar’05,Ko’06, Greiner ‘09, Bass ‘12 …

Gain

Loss

Collision rate

Rate of collisionsper unit time and

phase space

Solved discretizing the space in x, ycells

t0

3x0exact

solution

Simulations in which a particleensemble in a box evolves dynamicallyBulk composed only by gluons inthermal equilibrium at T=400 MeV

Due to collisions charm approaches the thermal equilibrium with the bulk

Simulation in a box: charmSimulation in a box: charm

Boltzmann Boltzmann -> -> Fokker-Fokker-PlanckPlanck

The relativistic collision integral can be re-written in terms of transferred momentum k=p-p’

Defining the probabilityw for HQ to be scatteredfrom p -> p+k

This re-definition of the collision integralallows to derive directly theFokker-Planck approximation

Landau and/or Svetisky approximation

Boltzmann Boltzmann -> -> Fokker-Fokker-PlanckPlanck

Expansion for smallMomentum transfer

pf)k,p(pp

kkfp

kkdCji

jii

i

2

322 2

1

Fokker – Planck equation

The Boltzmann Collision Integral, under this approximation, becomes:

B. Svetitsky PRD 37(1987)2484

Drag:<p> Diffusion:<p2>

fg defined through the rate of radiative energy loss

Then Fokker-Planck can be solved stochastically by the Langevin equations

Boltzmann approachLangevin approach

ii

cpqqpi

pppp)q(fqpqp

ME

pd

E

qd

E

qd

EA

44

2

3

3

3

3

3

3

2

1

2222222

1

jiij ppppB )(2

1

20

2222

16

1

sMsc

gcgc MdtMs

Common Origin is the Matrix Element

Drag Coefficient -> <p>

Diffusion coefficient -> <p2>

M -> d/dM -> Ai, Bij

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 Differential Cross section and momentum transfer: Charmmomentum transfer: Charm

• more isotropic -> Larger average momentum transfer

• For Charm isotropic cross section can lead K> Mc

S.K. Das et al.,arXiv:1312.6857

• Changing mD we simulate different angular dependencies of scatterings

• mD=gT =0.83 GeV for s=0.35

Boltzmann vs Langevin (Charm)Boltzmann vs Langevin (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)

Charm

S.K. Das et al.,arXiv:1312.6857

mD=0.4 GeV

Charm

mD=0.83 GeVmD=1.6 GeV

Time evolution of the p-spectraBoltzmannLangevin

pddN

pddN

33

In bottom case Langevin approximation ≈ BoltzmannBut Larger Mb/T (≈ 10) the better Langevin approximation works

Bottom RAA: Boltzmann = Langevin

Bottom

T= 400 MeV

mD=0.83 GeV

T= 400 MeV

mD=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 Mc/T=3 -> Mc/<pbulk> = 1

•A part of dynamic evolution involving large moment transferred is discarded with Langevin approach

GeVppd

dN

initial

103

Langevin Boltzmann

T= 400 MeV T= 400 MeV

Charm Charm

S.K. Das et al.,arXiv:1312.6857

T= 400 MeV T= 400 MeV

Momentum evolution of a single Bottom GeVp

pd

dN

initial

103

Langevin Boltzmann

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

Momentum evolution for charm vs temperatureBoltzman Boltzmann

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

GeVppd

dN

initial

103

T= 200 MeV

• At 200 MeV Mc/T= 6 -> start to see a peak with a width

Charm

Implication for observable, RAA?

The Langevin approach indicates a smaller RAA thus a larger suppression.

Charm

T= 400 MeV

mD=0.83 GeV

mD=0.83 GeV

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 %

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, makingthe comparison with a realisticsimulation of HIC

S.K. Das et al.,arXiv:1312.6857

mD=1.6 GeV

RAA- v2 of HQ seems to indicate:

- Elastic collisional dynamics (up to 6-8 GeV)

- Interaction not trivially decreasing with -1≈ T3 ≈ -1

(heavy resonances above Tc or …)

- Hadronization of by coalescence of heavy quarks

Conclusions and perspective 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 RAA(pT) by readjusting Drag by 15-50%

- Is the RAA-V2 and the angular correlation D-Ď different?

Dream!?Dream!?

A new era for the understanding of charmoniaA 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/dpTd -> RAA & v2 (pT) (at least up to 3-4 Gev)

Open FlavorOpen Flavor

HiddenHidden

)(v

/

2 Tc

Tc

p

dpdN

Greco, Ko, Rapp-PLB595(04)

- softer pT spectra of J/ dN/dpT of D (partially observed)

- Large elliptic flow v2(J/) v2(D)

Baryon contamination due to coalescence … !?Baryon contamination due to coalescence … !?

• Explanation for large v2e : v2c > v2D

Heavy-Flavor and jet quenching- Workshop, Padova 29-9-2005Heavy-Flavor and jet quenching- Workshop, Padova 29-9-2005

P. Soresen, nucl-ex/0701048, PRC (07)G. Martinez-Garcia et al., hep-ph/0702035 PLB(08)

Apparent reduction if c/D ~1due 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 predicta 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 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 c/D =1 ? What mechanism is behind it? -the v2 of c is enhanced according to QNS scaling? (that is not 3/2 v2D)

c/D measurement not well determined even in pp ( at FERMILAB)at least in PRL 77(1996) 2388

Differential Cross section and Differential Cross section and momentum transfer: Charm & Bottommomentum transfer: Charm & Bottom

Drag

Simulations in which a particleensemble in a box evolves dynamicallyBulk composed only by gluons inthermal equilibrium at T=400 MeV

Due to collisions Bottom Approaches the thermal equilibrium with the bulk

Simulation in a box: BottomSimulation 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, butSome remnant of the signal, butAt LHC the regeneration componentAt LHC the regeneration component

should dominate …should dominate …

VV2c2c=V=V2q 2q ++100% recombination 100% recombination ++ all at freeze-outall at freeze-out

Rapp, Blaschke, Crochet, Prog.Part.Nucl.Phys.65(2010)

100% primordial J/100% primordial J/

VV2c2c realistic realistic +100% recombination ++100% recombination + all at freeze-outall at freeze-out

VV2c2c realistic realistic +100% recomb ++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), 232301.[4] X. Zhao, R. Rapp, 24th WWND, 2008.[5] Y. Liu, N. Xu, P. Zhuang, NPA 834 (06), 317.

[1]

[2]

[3]

[4]

Zhao and Rapp, arXiv:1008.5328

Suppression-regeneration models

At 20-60% small regeneration component even decreasing with pT

Yuan, Xu, Zhuang, PRL97(2006)

Regeneration

J/J/ elliptic flow v elliptic flow v22

STAR Preliminary

Not really in disagreement with the suppression-regeneration modelbut 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, 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.

MB

7.8fm

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 vn of J/ have we explored the power of the vn analysis?

Disfavor coalescence from thermalized charm quarks,

Pure statistical model at Tc

+ corona effect

A. Andronic, P. B-M., et al., NPA 789 (2007)

Enhancement of J/ at LHC!?

Rapp R., X. Zhao, arXiV:1102.2194[hep-ph]

)(2015/

)(5.2/

)(1.0/

LHCdydN

RHICdydN

SPSdydN

cc

cc

cc

2/ ccJ NN

Including both suppression and regenerationduring all the evolution

From the point of view of the shear viscosityFrom the point of view of the shear viscosity

lQCD-quenched

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

Csernai et al., PRL96(06)

Two Main Observables in HICTwo Main Observables in HIC

ddpNdN

ddpNdpR

TNN

coll

TAA

TAA /

/)(

2

2

Nuclear Modification factorNuclear Modification factor AA R = 1 nothing new going on

- Modification respect to pp- Decrease with increasing partonic interaction

...)2cos(v21π2φ 2

TTTT dpp

dN

ddpp

dN

Anisotropy p-space:Anisotropy p-space:Elliptic Flow vElliptic Flow v22

px

py

Increases with cIncreases with css=dP/d=dP/dandandor 1/or 1/!!

xy z

centrality

xx

vv22