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