Heavy quarks production in heavy ions colli sions Heavy quarks diffusion in hydrodynamics or “How confident can we be in the Fokker-Planck coefficients we extract from / constrain with exp. data ?” P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS I. Understanding (partly) the present RHIC data on HQ E-loss; the Nantes viewpoint II. Influence of the medium on our understanding Heavy quarks production in heavy-ion collisions, W. Lafayette With J. Aichelin, M. Bluhm, Th. Gousset, H. van Hees, R. Rapp and S. Vogel,
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P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS
Heavy quarks diffusion in hydrodynamics or “How confident can we be in the Fokker-Planck coefficients we extract from / constrain with exp. data ?”. Heavy quarks production in heavy-ion collisions, W. Lafayette. P.B. Gossiaux SUBATECH, UMR 6457 - PowerPoint PPT Presentation
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Heavy quarks production in heavy ions collisions
Heavy quarks diffusion in hydrodynamicsor
“How confident can we be in the Fokker-Planck coefficients we
extract from / constrain with exp. data ?”
P.B. GossiauxSUBATECH, UMR 6457
Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS
I. Understanding (partly) the present RHIC data on HQ E-loss; the Nantes viewpoint
II. Influence of the medium on our understanding
Heavy quarks production in heavy-ion collisions, W. Lafayette
With J. Aichelin, M. Bluhm, Th. Gousset, H. van Hees, R. Rapp and S. Vogel,
Heavy quarks production in heavy ions collisions
• Heavy quarks thermalization in ultra relativistic heavy ion collisions: Elastic versus Radiative, P.B. Gossiaux}, V. Guiho & J. Aichelin, Journal of Physics G 32 (2006) S359
• Towards an understanding of the single electron data measured at the BNL Relativistic Heavy Ion Collider (RHIC), P.B. Gossiaux & J. Aichelin, Phys. Rev. C 78, 014904 (2008); [arXiv:0802.2525 ]
• Tomography of quark gluon plasma at energies available at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), P.B. Gossiaux, R. Bierkandt & J. Aichelin, Physical Review C 79 (2009) 044906; [arXiv:0901.0946]
• Tomography of the Quark Gluon Plasma by Heavy Quarks, P.-B. Gossiaux & J. Aichelin, J. Phys. G 36 (2009) 064028; [arXiv:0901.2462]
• Energy Loss of Heavy Quarks in a QGP with a Running Coupling Constant Approach, P.B. Gossiaux & J. Aichelin, Nucl. Phys. A 830 (2009), 203; [arXiv:0907.4329]
• Competition of Heavy Quark Radiative and Collisional Energy Loss in Deconfined Matter, P.B. Gossiaux, J. Aichelin, T. Gousset & V. Guiho, J. Phys. G: Nucl. Part. Phys. 37 (2010) 094019; [arXiv:1001.4166]
• Gluon Radiation at small kT and Radiative Energy Loss of Heavy Quarks; I. The Bethe-Heitler Regime, J. Aichelin, P.B. Gossiaux & Th Gousset (In preparation)
IR safe. The detailed form very close to Q2 =0 is not important does not contribute to the energy loss
Large values for intermediate momentum-transfer => larger
cross section
Collisional E loss : The Peshier – Gossiaux – Aichelin approach (2008)
Motivation: Even a fast parton with the largest momentum P will undergo collisions with moderate q exchange and large s(Q2). The running aspect of the coupling constant has been “forgotten/neglected” in most of approaches
A model; not a renormalizable theory02
eff(Q2,T=0)
Heavy quarks production in heavy ions collisions 03
Running s : some Energy-Loss values for purely collisional processes
T(MeV) \ p(GeV/c) 10 20
200 1 / 0.65 1.2 / 0.9
400 2.1 / 1.4 2.4 / 2
10 % of HQ energydx
bcdEcoll
)/(
E: optimal , running eff
C: optimal , s(2T)
Drag coefficient
(reso)
Transp. Coef …
… of expected magnitude to reproduce the data (we “explain” the transport coeff.
in a rather parameter free approach).
Heavy quarks production in heavy ions collisions
(hard) production of heavy quarks in initial NN collisions + kT broad. (0.2 GeV2/coll
Quarkonia formation in QGP through c+c+g fusion process
D/B formation at the boundary of QGP (or MP) through coalescence of c/b
and light quark (low pT) or fragmentation (high pT)
Schematic view of the global framework
04
QGP
MC@sHQ suppression
MP
Evolution of HQ in bulk : Fokker-Planck or reaction rate + Boltzmann
(no hadronic phase)
HG
Heavy quarks production in heavy ions collisions
cs t raterate tr m a x
e fft; 0 .2
P H E N I X
m o d e l E
A u A u 6 0 . . . ; tra n sm in
p T G eV c2 4 6 8
0 .5
1 .0
1 .5R A A le p t
cs t raterate tr m a x
e fft; 0 .2
P H E N I X
m o d e l E
A u A u 4 0 6 0 ; tra n sm in
p T G eV c2 4 6 8
0 .5
1 .0
1 .5R A A le p t
Observables (Au-Au) vs (rescaled) Model
One reproduces RAA on all pT range with cranking K-factor 2 which permits to accommodate the “unknowns”
Best observable so far: RAA for single non-photonic electrons
05
cs t raterate tr m a x
e fft; 0 .2
P H E N I X
m o d e l E
A u A u 2 0 4 0 ; tra n sm in
p T G eV c2 4 6 8
0 .5
1 .0
1 .5R A A le p t
cs t raterate tr m a x
e fft; 0 .2
P H E N I X S T A R
m o d e l E
A u A u cen tral; tra n sm in
p T G eV c2 4 6 8
0 .5
1 .0
1 .5R A A le p t
cs t raterate tr m a x
e fft; 0 .2
P H E N I X
m o d e l E
A u A u 1 0 2 0 ; tra n sm in
p T G eV c2 4 6 8
0 .5
1 .0
1 .5R A A le p t
K=2K=2 K=2
K=2 K=2
: P h e n ix R u n 4 : P h e n ix R u n 7
e De B
e D Ball
B oltzmannt rans m in ra te run. ; 0.2, ra te 2A u A u; 200 G eV ; m in. bias
1 2 3 4 5P T G e V c
0.05
0.00
0.05
0.10
0.15
v 2 le p t
Heavy quarks production in heavy ions collisions
From P. Braun-Munzinger (INPC 2010)
06
Heavy quarks production in heavy ions collisions
Dominates as small x as one “just” has to scatter off the virtual gluon k’
Eikonal limit (large E, moderate q)
Basic (massive) Gunion-BertschRadiation deflection of current (semi-classical picture)
k’
Gluon thermal mass ~2T (phenomenological; not in BDMPS)
with
Quark mass
Both cures the colinear divergences and influence the radiation spectra 07
Heavy quarks production in heavy ions collisions
Radiation spectra
For coulomb scattering:
… to convolute with your favorite elastic cross section
Strong dead cone effect for x>mg/MQ
(mass hierarchy)
Light quark
(I)
c-quark
b-quark
Little mass dependence (especially from qc)
(II)
If typical qT :
Strong mass effect in the average Eloss (mostly dominated by region II), similar to
AdS/CFTInteresting per se, but not much connected to the quenching or RAA.
08
Heavy quarks production in heavy ions collisions
Results with (Coherent) Radiation Included
1. Coherence: Some moderate increase of RAA for D at large pT.
2. No effect seen for B
e D
s[0.2,0.3]
e B.
s[0.2,0.3]
Conclusions can vary a bit depending on the value of the transport coefficient
Indication that RAA at RHIC is mostly the physics of rather numerous but small E losses, not very sensitive to coherence .
All non-photonic
electrons
s[0.2,0.3]
09
Heavy quarks production in heavy ions collisions
A u A u ; 2 0 4 0B o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX
co ll rad ia t L P M co llK 2
K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
A u A u ; c e n tra lB o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX S T A R
rad ia t co ll L P M co llK 2 K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
Collisional vs {Radiative + Coll}
The present data cannot decipher between the 2 local microscopic E-loss scenarios 10
A u A u ; 1 0 2 0B o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX
co ll rad ia t L P M co llK 2
K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
: P h en ix R u n 4 : P h en ix R u n 7
coll, ra te 2coll radia t
ra te 0.6B oltzmannt rans m in ra te
run. ; 0.2A u A u; 200 G eV ; min. bias
1 2 3 4 5P T G e V c
0.05
0.00
0.05
0.10
0.15
v 2 le p t
Rescaling: K=0.6
Heavy quarks production in heavy ions collisions
• D and B separately (in any case)
• tagged HQ jets and IAA (and other correlations)
The heavy-quark physics at play for RHIC measured up to now (RAA and v2) is the one of small (relative) E-loss (and thus of the Fokker-Planck equation)…
even at the largest pT
RAA and v2 physics
What we need
In our view, it is nevertheless more plausible to describe the physics in terms of a rather strong collisionnal energy loss
supplied with an even stronger radiative energy loss (at least for “>>” 1).
Interpretation
Bad control on the theory
Explains why purely collisional models “work” so well
11
Heavy quarks production in heavy ions collisions
Gossiaux & Aichelin, 2008
Minimal at Tc
QGP properties: low momentum
Moore-Teaney:
4
“robust”pQCD 3 x 4
/s DT/6
2T D
/s 0.5
at Tc
Strong coupling; AdS/CFT:/s DT/2 2T D
/s 1.5
4
4
at Tc
But diffusion constant of heavy quark is already an interesting quantity in itself and could be evaluated on the lattice !!! 12
As we reproduce experimental data with rescaled model:
Heavy quarks production in heavy ions collisions
QGP properties: stopping power
Exp. cannot resolve between those various trends
Gathering all rescaled models (coll. and radiative):
Seems “under control”
quite consistent as the drag coefficient reflects the average momentum loss (per unit time) => large weight on x 1
13
Challenge
Heavy quarks production in heavy ions collisions
D & B meson: RHIC II (radiat + collisional)
Collis., rate x 2
Collis. + Rad (LPM), rate x 0.6
s(rad)=0.3
… some small deviations for D spectra at large pT
14
pT=5GeV/c
Z. Xu (sqm08)
pT=10GeV/c
PRC 78 (fig 9)
Heavy quarks production in heavy ions collisions
D & B meson: LHC (radiat + collisional)
D spectra in Pb-Pb (5.5 TeV): Some window to decipher
between the various Energy-loss models, for pT > 20 GeV/c
B spectra in Pb-Pb (5.5 TeV): Pretty independent of E-loss model (properly calibrated
w.r.t. RHIC data) 15
Heavy quarks production in heavy ions collisions
QGV in pp at LHC ? arXiv:1012.0764
Combining MC@sHQ with EPOS
16
Centrality number of initial individual parton-parton collisions
In EPOS: Nch
Motivation: initial energy density in pp (LHC) ~ in CuCu (RHIC) possible quenching of (heavy flavours) jets
II. Influence of the medium on heavy quarks phenomenology
Motivations :
I. We want to use experimental data to constrain the transport coefficient as much as possible
II. 2 groups (Texas AM & Nantes) have proposed models compatible with the non-photonic single-electron data, although the drag coefficients differ by a significant amount… How can this be possible ?
17
Role of the other ingredients ?
Models microscopic model of HQ-QGP interactions (transport coefficients) + medium + initial distributions + hadronization + kinetic equation + …
Need for a collaboration: big thanks to Ralf and Hendrik
Methodology: exchanging some ingredients of the models into a single framework (the Nantes MC@sHQ)
Caution: The aim of this study is not to reproduce the data at all price
Heavy quarks production in heavy ions collisions
Basic ingredients
Drag coefficient:
18
Running s
Fixed s + resonances
Diffusion coefficient B tuned to satisfy Einstein relation: asymptotic thermal distribution
Heavy quarks production in heavy ions collisions
Basic ingredients
19
Transport: both solve FP equation through a Langevin Monte Carlo realization…
Back to the continuous stochastic process:
Gaussian auto-correlated
Multiplicative noise
But: a) we do not have a continuous process (smallest time scale: the collision)
b) we can evaluate the average momentum loss directly from the elastic cross section (fundamental blocks are not and g but Ap=–+g g’ and B=2g2 ): No ambigity
• Spurious drift:
• Ambiguity: for a small dt, at which value of should we consider g ? Ito vs Stratonovich
However: Several realizations are possible
Ito pre point (Nantes)
Ito post point (Texas AM)
In principle equivalent if one chooses:
Heavy quarks production in heavy ions collisions
Basic ingredientsThe medium:
20
Nantes: Kolb-Heinz 2D+1 ideal hydrodynamics with Bjorken invariance (azhydro V2.0)
Texas AM: Fireball of the Landau-Type: T(t), s(t)=S/V(t), (t)
Transverse plane:
x
y
2b
Volume:
2a
x
y
2b
2a
Heavy quarks production in heavy ions collisions
Basic ingredientsThe medium:
21
Texas AM: Everything uniform but the velocity field
x
=1.33fm/cy Calibration
Kolb-Sollfrank-Heinz (2000)
Heavy quarks production in heavy ions collisions
Basic ingredientsThe medium:
22
Texas AM: Everything uniform but the velocity field
Calibration
Rather good agreement for
the velocity
Good agreement for the bulk flow
Heavy quarks production in heavy ions collisions
Basic ingredientsThe medium:
23
Temperature evolution along time:
T=180 MeV, =2.25 GeV/fm3
Pure QGP
Conclusion: Good confidence that the
“bulk” fireball is calibrated at the best
=0.82 GeV/fm3 =0.46 GeV/fm3
T=165 MeV, =1.64 GeV/fm3
Mixed phase
EOS of the same type (QGP described within the MIT bag model, 1st order transition), with rather similar parameters.
Heavy quarks production in heavy ions collisions
Heavy quark evolution
Nuclear Modification factor
24
All heavy quarks observables evaluated with the pre-point prescription
original models (almost)
Crossed ingredients
: More coupling with the Nantes microscopic model (as seen from the drag coefficient)
How can we conclude ?
RAA compatible
Heavy quarks production in heavy ions collisions
Heavy quark evolution
Nuclear Modification factor
25
All heavy quarks observables evaluated with the pre-point prescription
original models (almost)
Crossed ingredients
: More quenching with the fireball then with the (original) KH hydro
How can we conclude ?
RAA compatible
Heavy quarks production in heavy ions collisions
Heavy quark evolutionDifferential Elliptic flow
26
original models (almost)
: More coupling with the Nantes microscopic model
: Higher elliptic flow from the fireball
Heavy quarks production in heavy ions collisions
Heavy quark evolutionInclusive elliptic flow
27
Various gedanken decoupling energy densities for the c quarks
+73%
Large deviations at early times
Heavy quarks production in heavy ions collisions
Summary of HQ
28
Is there something special with Heavy Quarks (due to their inertia) as compared to light ones ?
Degree of thermalization
Resonances Running s
KH hydro Low Intermediate
fireball Intermediate High
Heavy quarks production in heavy ions collisions
Back on the bulk v2 and on calibration
29
Probes of the bulk v2:
I. So called momentum anisotropy
with
Directly evaluated from the energy-stress momentum; known to be closely related
to the elliptic flow (Kolb, Sollfrank & Heinz 2000)
The fireball systematically overshoots the hydro, starting from early times !!!
HQ just inherits this larger anisotropy
Heavy quarks production in heavy ions collisions
Back on the bulk v2 and on calibration
30
II. Elliptic flow of light quarks and ensuing pions Particle spectra:
KH with Cooper-Frye freeze out
Fireball: freeze out at constant
lab time t
fireball with Cooper-Frye freeze out
Asymptotic distribution in the VHR post-point
Langevin
fireball with Milekhin-like freeze out
Heavy quarks production in heavy ions collisions
Back on the bulk v2 and on calibration
31
several levels of subtle and somehow paradoxal conclusions:
KH with Cooper-Frye freeze out
fireball with Cooper-Frye freeze out
fireball with Milekhin-like freeze out
Confirms the excess of intrinsic v2 in the fireball on the absolute level
KH with Cooper-Frye freeze out
Confirms the proper calibration of the fireball (5.5% v2 for pions)
Comparing with 2 different freeze out prescriptions:
?
Heavy quarks production in heavy ions collisions
Calibration at a relative level
32
Bona fide argument: ?
“One should calibrate the fireball using the asymptotic distributions (of light quarks) that results from Langevin transport one uses for the heavy quarks”
Hendrik Van Hees Remember: Several realizations are possible
Ito pre point (Nantes) Ito post point (Texas AM)
• The medium calibration is intricately linked with the transport model one uses (exchanging the ingredient “medium” alone has no meaning)
• It is not legitimate to perform the HQ simulations in the fireball with the pre-point prescription.
HQ lq
HQ
lq
Heavy quarks production in heavy ions collisions
Heavy quarks with pre-point vs post-point
33
The post-point vs pre-point prescription has little influence on the heavy quark observables (consequences of u.p/p0 are not mass independent).
In particular, the post-point prescription does not bring the “fireball results” in the range of the “pre-point KH hydro”
All heavy quarks observables evaluated with the Nantes FP coefficients
Heavy quarks production in heavy ions collisions
Summary and conclusions (1)
34
This all together explain why one is able to describe the heavy flavor data with smaller FP coefficients within the fireball than in the KH hydro, although they both reproduce the pions elliptic flow
With respect to the Kolb Heinz hydro + Cooper-Frye reference:
hydro
0 collectivity
fireball
Light quark sector heavy quark sector
Larger intrinsic v2
Compensation due to the u.p/p0
factor in equil. distribution
Similar v2()
Nearly negligible effect of u.p/p0 factor;
pre-point post-point
Overall increase of v2(HQ)
“Bona fide” is sometimes too optimistic
Heavy quarks production in heavy ions collisions
Summary and conclusions (2)
35
hydro
0 collectivity
fireball
Light quark sector heavy quark sector
Larger intrinsic v2
Similar v2()
2 rather different v2(HQ) for a
given set of FP coefficient
Large influence of the medium on the extraction of FP coefficient from the experimental data
Third global level of interpretation:
After all, the KH hydro with a kinetic freeze out a given rather all energy density is a model among others…
Good candidate for medium with a genuine Milekhin freeze out
HQ rather insensitive to the freeze out
assumptions
First study, not exhaustive and to be pursued
Heavy quarks production in heavy ions collisions
Back Up HQ
Heavy quarks production in heavy ions collisions
More on different freeze out prescriptions
Assuming locally equilibrated distributions for all flavours
(End of Mixed phase)
Toy model: Uniform thermalized fluid at finite
velocity vz=0.5c
Heavy quarks production in heavy ions collisions
Properties of QGP we would like to understand / quantify
Barometer, /s but also diffusion coefficient D and drag
RAA(,pT) v2(,pT)
RAA(HQ,pT) v2(HQ,pT)
Densitometer,
Probing the (strong) QGP by hard probe tomography… what does it means exactly ?
1. Basic hard probe – medium interaction scaled by the density
2. Strong (ordered) QGP will act coherently on large distances
3. Shocking quasi-particles with increasing masses when pT decreases ?
dynamometer
In principle: Mass hierarchy of E loss; in practice: single electron puzzle (SEP)
But we need a consistent description…
Challenge n°2
01
Heavy quarks production in heavy ions collisions
: 5-15 GeV2/fm (strong debate TECHQM)
dNg/dy: 1400 for both GLV and WHDG (compensation between the additional coll E loss and the path length fluctuations)
Optimal parameters
More pT-dependence in the models than in the data
Challenge n°1
Nevertheless, one has to get the “right” parameter (for instance the transport coefficient) from QCD before claiming one “understands”
A nice interpolation is not an explanation
03
Heavy quarks production in heavy ions collisions
Applying those approaches to HQ
N. Armesto, A. Dainese, C. A. Salgado and U. A. Wiedemann, Phys. Rev D (hep-ph/0501225) & Phys.Lett. B637 (2006) 362-366 hep-ph/0511257
K. J. Eskola, H. Honkanen, C. A. Salgado and U. A. Wiedemann, Nucl. Phys. A 747(2005) 511
Conclude to rough agreement, subjected to b/c ratio in p-p
Fixed geometry
ASW (just radiative energy loss; extended BDMPS)
V2 from spatial asymmetry of the path length
04
Heavy quarks production in heavy ions collisions
Applying those approaches to HQ
Fixed L
WHDG
• coll Eloss (BT and TG) !!!• “…E loss and their fluctuations…”• path length fluctuations in a fixed geometry• Lb > Lc = Lu > Lg (self quenching) helps in the direction of reducing single electron puzzle• no genuine QGP evolution (mocking of Bjorken scenario)• coll E loss distribution assumed gaussian • fixed s
Beauty stays the problem… but beauty is there
So-called “Failure of pQCD approach”
05
Heavy quarks production in heavy ions collisions
The weak to strong axis
ADS/CFT
Non-perturbative, lattice potential scattering models (see R. Rapp and H Van Hees 0903.1096 [hep-ph] for a review)
“Standard” pQCD (WHDG, ASW,…)
Distorsion of heavy meson fragmentation functions due to the existence of bound mesons in QGP, R. Sharma, I. Vitev & B-W Zhang 0904.0032v1 [hep-ph]
Beyond the static scatterer limit: M. Djordjevic, Preprint arXiv:0903.4591 [nucl-th] (2009) and previous work with U. Heinz
HTL for x not << 1 ?
Valuable works, but some questions remains… and how to
reconcile them all stays a challenge
Non perturbative equivalent for g+Q ? No radiative !
from Rapp & Van Hees 0903.1096
06
Heavy quarks production in heavy ions collisions
ADS/CFTVarious results from our holographic friends (trailing string):
Drag coefficient
Maximal velocity for the validity of present AdS/CFT
(Pretty strong dependence on the mass)
Applied for the first time to URHIC by Horowitz and Gyulassy (Phys. Lett. B666 320,2008.)
If such a strong mass hierarchy in AdS/CFT, how will it solve the single electron puzzle ?
pQCD: E
07
Heavy quarks production in heavy ions collisions
ADS/CFT
In fact, Fokker Planck with tunable drag coeffi :
(cf. Gossiaux & Guiho (SQM04), Van Hees & Rapp (05), Moore & Teaney (05))
Applied recently in a more realistic hydro evolution by Akamatsu et al. (0809.1499v3 [hep-ph] & 0907.2981v2 [hep-ph])
So-called Success of ADF/CFT
If such a strong mass hierarchy in AdS/CFT, how will it solve the single electron puzzle ?Challenge n°3
08
Heavy quarks production in heavy ions collisions
a possible hierarchy (very prospective)
pT
AdS/CFT for the incoming
parton
pQCD radiative for the large E parton, but AdS/CFT for
the radiated gluon pQCD for most of the partons
in the jet
Asymptotic freedom
(Akamatsu)(C. Marquet & T. Renk:
0908.0880 [hep-ph])
Novel path length dependences (E L3)
for light parton
09
Heavy quarks production in heavy ions collisions
eff(Q2,T=0)
08
-local-model: medium effects at finite T in t-channel
Low |t|
Large |t|
|t*|
OGE with effective polarisation(T)=0
.2 mDself2(T)HTL:
collective modes
BT
Bona Fide running HTL: s-> s(t) in L and T
hard
Semi-hard
Max. insensitivity
mDself2 (T) = (1+nf/6) 4eff(mDself
2) T2
Heavy quarks production in heavy ions collisions
0 .1 0 .2 0 .5 1 .0r fm 2
4
6
8
1 0
d V
d rG e V fm
0 .1 0 .2 0 .5 1 .0r fm 2
4
6
8
1 0
d V
d rG e V fm
10
-local-model: Eff. Running s vs lQCD
T=0
V=UKZ, PoS LAT2005 (2005) 192
optimal , running eff
O. Kaczmarek & F. Zantow (KZ) (nf=2 QCD), P.R.D71 (2005) 114510
Genuine non-pert (string)
Finite T
T1.1 Tc
eff
V=FKZ P.R. D71 (2005)
V:=0 sector; dE/dx: finite
T1.5 Tc
eff
Some overshooting at large distance
Merging at 2 Tc
Heavy quarks production in heavy ions collisions 11
-local-model: Eff. Running vs fixed s
BT
• Good agreement with PP for large T and large P
• Running s is more than a cranking of BT (different shapes and T-dependences)
E: optimal , running eff
Dark bands: Peshier & Peigné (2008)
Light bands: theoretical uncertainty related to the prescription for the
HTL-hard transition
Conclusions:
Heavy quarks production in heavy ions collisions
II. Despite the unknowns (b-c crossing, precise kt broaden.,…), unlikely that collisional energy loss could explain it all alone
III. It is however not excluded that the "missing part" could be reproduced by some conventional pQGP process (radiative Eloss)
I. Improved collisional Eloss plays a larger role then expected
17
Central RAA vs model & intermediate conclusion
A u A u ; c e n tra lB o ltzm a n n t ra n s m in
ru n . ; 0 .2 , K 1 P H E N IX S T A R
e B
all
e D
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
e from c
e from b
Heavy quarks production in heavy ions collisions
Monte Carlo Implementation I) For each collision with a given q, we define the
conditional probability of radiation:
In practice, min=5% E to avoid IR catastrophy
II) For each collision with a given invariant mass squared s, we define the conditional total
probability of radiation:
T=150T=200
T=300T=400
mg=2T
Probes the elastic cross section at larger values of t => less
sensitive to eff at small t-values
Threshold for radiation 24
Heavy quarks production in heavy ions collisions
Monte Carlo Implementation III) For a given HQ energy E, we sample the entrance channel according to the thermal distribution of light quarks and gluons and el(s) and accept according to the conditional probability
IV) We sample “downwards” q, and then k
Hard shocks with |t|>25% s are rejected (not treated properly in our formalism)
V) P+ (1-x) P+ and transverse kick of q-k.
Fixed s
Approximation:
In “reality”, several collisions at intermediate t-values accumulate
<q> from 0.6 GeV (col) 1.1 GeV (rad) for E=15GeV and T=400.
25
Heavy quarks production in heavy ions collisions
Results
s[0.2,0.3]1. Too large quenching; good as we
obviously overestimate the radiative Eloss
2. Radiative Eloss indeed dominates the collisional one
3. Flat experimental shape is well reproduced
All non-photonic
electrons
separated contributions e D and e B.
s[0.2,0.3]
26
Heavy quarks production in heavy ions collisions
Results 1. Collisionnal + radiative energy loss
+ dynamical medium : compatible with data
2. Shape for radiative E loss and rescaled collisional E loss are pretty similar
3. To my knowledge, one of the first model using radiative Eloss that reproduces v2
27
Heavy quarks production in heavy ions collisions
Formation time for a single coll.
k’
At 0 deflection:
[fm] For x>xcr=mg/M, gluons radiated from heavy quarks are resolved in less time then those light quarks and gluon => radiation process less affected by coherence effects in multiple scattering
For x<xcr=mg/M, basically no mass effect in gluon radiation
Dominant region for quenching Dominant region for average E loss
16
Heavy quarks production in heavy ions collisions
A simplifying hypothesis [fm]
Comparing the formation time (on a single scatterer) with the
mean free path:
Coherence effect for HQ gluon radiation :
RHIC LHC
Mostly coherent
Mostly uncoherent
(of course depends on the physics behind Q)
Maybe not completely foolish to neglect
coherence effect in a first round for HQ.
(will provide at least a maximal value for the
quenching)
17
Heavy quarks production in heavy ions collisions
Basics of Coherent Radiation
See Peigné & Smilga (2008) for some analytical results pertaining to HQ
Subject of numerous (mosty numerical) investigations
Heavy quarks production in heavy ions collisions
Formation time in a random walk
One obtains an effective formation time by imposing the cumulative phase shift to be dec of
the order of unity
Phase shift at each collision
For light quark (infinite matter):
=> 3 scales: lf,mult, lf,sing &
Uncoherent radiation
Coherent radiation (BDMPS)
Suppression:
Especially important for av. energy loss
28
Heavy quarks production in heavy ions collisions
Formation time and decoherence for HQ
“Competition” between
• decoherence” due to the masses:
• decoherence due to the transverse kicks
One has a possibly large coherence number Ncoh := lf,mult/but the radiation spectrum per unit length stays mostly unaffected:
Special case: < <
=
Radiation on an effective center of length lf,mult = Ncoh
Radiation at small angle i.e. Ncoh
Compensation at leading order !
LESSON: HQ radiate less, on shorter times scales but are less affected by coherence effects than light ones !!! (dominance of 1rst order in opacity expansion)
29
Heavy quarks production in heavy ions collisions
Formation time and decoherence for HQ
Equivalent to:
Criteria: HQ radiative E loss strongly affected by coherence provided:
x
Low Energ
High Energ
Int Energ
3 regimes (2 for light quarks)
High energy: HQ behaves like a light one; coherence affects radiation from LPM on.
Int Energ
Low energy: radiation from HQ unaffected by coherence
Intermediate energy: coherence affects radiation on an increasing part of the spectrum (up to LPM*)
30
Heavy quarks production in heavy ions collisions
Regimes and radiation spectra
&
Hierarchy of scales:
High Energ: total suppr. High Energ: total suppr.
Low Energ: GB Low Energ: GB
Int Energ: partial supprInt Energ: partial suppr
c-quark b-quark
pQCD
Running s
larger coupling Larger coherence effects
xcr=mg/M
x-2 decrease (DC)
x
d2Idxdz
x
x-1/2 decrease
Effective higher for av. E loss
Spectrax-1/2 decrease
1 1 1
GB GB
DC Coh BDMPS
Light q limit x
31
Heavy quarks production in heavy ions collisions
Semi-quantitative model:
For lf,mult>gluon is radiated coherently on a distance lf,mult
Model: all scatterers acts as a single effective one with probability pNcoh(Q) obtained by convoluting individual probability of kicks
After averaging:
• Compares well to the BDMPS result (Ncoh>>1) for light quark (up to some color factor => rescaling), including the coulombian logs.
• Naturally interpolates to the massive-GB regime for Ncoh1.
• Incorporates all regimes discussed above.
with
Prevents radiation of gluon of formation time > lf,mult
32
Heavy quarks production in heavy ions collisions
Reduced spectra from coherence
: Suppression due to coherence increases with increasing energy
T 2 5 0 M e V , E 1 0 G e V
c q u a rk
G B
L P M
1 .0 00 .5 0 5 .0 00 .1 0 1 0 .0 00 .0 5 G e V 0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
d I
d z d
T 2 5 0 M e V , E 2 0 G e V
c q u a rk
G B
L P M
1 .0 00 .5 0 5 .0 00 .1 0 1 0 .0 00 .0 5 G e V 0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
d I
d z d
T 2 5 0 M e V , E 2 0 G e V
b q u a rk
G B
L P M
1 .0 00 .5 0 5 .0 00 .1 0 1 0 .0 00 .0 5 G e V 0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
d I
d z d
: Suppression due to coherence decreases with increasing mass
In (first) Monte Carlo implementation: we quench the probability of gluon radiation by the ratio of coherent spectrum / GB spectrum
More DC effect
Dominant modification at
mid-x
33
Heavy quarks production in heavy ions collisions
What is (really) missing ?• Kinematical constrains at small – large angles (Salgado, Wiedemann
030218).
• 0-opacity correction and transition radiation that partly compensates and lead to an effective retardation of the energy loss.
• Better Monte Carlo implementation for radiation caused by multiple collisions.
• Finite path Length effects : In practice, formation length are of the order of a couple of fm => HQ emanating from the corona have a path length L< lf,mult
But will it change much to the story ?
35
Heavy quarks production in heavy ions collisions
Competition
Data oriented better than extra formulas
Heavy quarks production in heavy ions collisions
A u A u ; 1 0 2 0B o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX
co ll rad ia t L P M co llK 2
K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
Round 2
2
Cranked up Collisional(Decreased) Coll+Rad
2
38
Heavy quarks production in heavy ions collisions
A u A u ; 2 0 4 0B o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX
co ll rad ia t L P M co llK 2
K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
Round 3
3
Cranked up Collisional(Decreased) Coll+Rad
3
39
Heavy quarks production in heavy ions collisions
A u A u ; 4 0 6 0B o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX
co ll rad ia t L P M co llK 2 K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
Round 4
4
Cranked up Collisional(Decreased) Coll+Rad
4
40
Heavy quarks production in heavy ions collisions
A u A u ; 6 0 9 2B o ltzm a n n t ra n s m in
ru n . ; 0 .2 P H E N IX
co ll rad ia t L P M co llK 2
K 0 .6
P T G e V c2 4 6 8 10
0.5
1.0
1.5R AA le p t
Round 5
4.1
Cranked up Collisional(Decreased) Coll+Rad
4But syst. Error due to p-p
Data compatible with E path-length L in stationnary QGP.41
Heavy quarks production in heavy ions collisions
Round 6
5.1/6
Cranked up Collisional(Decreased) Coll+Rad
5/6
Elliptical Flow
: P h en ix R u n 4 : P h en ix R u n 7
coll, ra te 2coll radia t
ra te 0.6B oltzmannt rans m in ra te
run. ; 0.2A u A u; 200 G eV ; min. bias
1 2 3 4 5P T G e V c
0.05
0.00
0.05
0.10
0.15
v 2 le p t
42
Heavy quarks production in heavy ions collisions
pQCD vs AdS/CFT
pQCD: mass hierarchy is mostly in
the tails
ucb
AdS/CFT: mass hierarchy stays in the centroid of the distribution
RAA will tell
44
Heavy quarks production in heavy ions collisions
Finite Size effects
Today
Semi-coherent
Iterated GB
Phase diagram
Heavy quarks production in heavy ions collisions
Path lengthOne way to decifer.
Standard collisionnal as well as incoherent radiation (GB) as well as LPM radiation scale like L (uniform medium)
Assumed to be L^2 if finite path length… but beware of the logs tha makes it quasi linear
Higher order in ADS/CFT
Heavy quarks production in heavy ions collisions
Collis vs radiat
Small history: col Eloss neglected, then revived in 2005 (Mustafa, Dutt Mazumber) => similar E loss for pT < 10 GeV /c
Include the qhat dep of coll E loss vs radiat
Anyhow, not the coll E loss that counts but the P(w) for small w.
Interest of “collisionnal”: flavor exchange
Discuss the mass dependence with analytical formula
Heavy quarks production in heavy ions collisions
III. Future observables for HQ Energy loss
Heavy quarks production in heavy ions collisions
pT=5GeV/c
D & B meson: RHIC II vs LHC (pure collisional)
Z. Xu (sqm08)
Rescaled collisional E loss
• RAA 1 at asymptotic pT values, mostly seen in running s models.
• medium at LHC relatively less opaque that at RHIC
31
R H IC m o d E L H C m o d E L H C m o d C
m o d e l E : r u n n in g s ; 0 .2r e sc a lin g : K 1 .8
m o d e l C : s2T ; 0 .1 5r e sc a lin g : x 5
p T G eV cd N
d y 2 2 0 0
d N
d y 1 6 0 0
2 5 10 20 50
0.5
1.0
1.5
R A AD LHC: Central Pb-Pb; 5.5 TeV
R H IC m o d E L H C m o d E L H C m o d C
m o d e l E : r u n n in g s ; 0 .2r e sc a lin g : K 1 .8
m o d e l C : s2T ; 0 .1 5r e sc a lin g : x 5
p T G eV cd N
d y 1 6 0 0
d N
d y 2 2 0 0
2 5 10 20 50
0.5
1.0
1.5
R A AB pT=10GeV/c
Heavy quarks production in heavy ions collisions
Back Up J/Psi
Heavy quarks production in heavy ions collisions
II. Quarkonia in QGP
Work in
progress
Quenching (leading hadron)
densitometer
Hidden c & b
thermometer
physics of HQ at low momentum w.r.t. fluid cell seems “under control”
Thermalisation & collectivity
barometer
Heavy quarks production in heavy ions collisions
Integrated J/ numbers @ RHIC
First, we need a baseline taking into account the cold nuclear matter effects (Shadowing, Cronin,..); we take the picture of R. Granier de Cassagnac (2007)
22
Progress to be made here
Heavy quarks production in heavy ions collisions
Integrated J/ numbers @ RHICNext, the (instantaneous) vetoing of quarkonia formation due to melting:
Good agreement obtained with a rather large value of Tdiss 2 Tc.
Some claims of “sequencial suppression” with a very bound J/ were indeed made by several physicists
23
``````We do not need recombination !’’’’’’’… except that Q and Qbar may be close in phase space
Heavy quarks production in heavy ions collisions
(Re)combination (could become dominant at LHC):
J/
Binding
Even if binding process is fast and medium-independent (quarkonia are small bound states), the distributions of Q and
Qbar in the entrance channel depend on the past history
Entrance channel
(transport theory)
NoYes
If formation time taken as the Heisenberg time, Yes
24
Turning on (re)combination + hard dissoc
Heavy quarks production in heavy ions collisions
Basic Ingredientshard dissociation taken according to Bhanot and Peskin + recoil correction (Arleo et al 2001)
Max 2 fm2 at 500 MeV 25
Cross section obtained from diss via detailed balance
Dissociation Recombination
Heavy quarks production in heavy ions collisions
Recombination: hierarchy of approaches…Statistical weights (at transition). no detailed dynamics. assumes all time scales are small vs. transition time. simple to deal with. PBM, Stachel & Andronic; Gorenstein, Kostyuk;…
… does not mean a hierarchy of answers (hopefully)!
Rapp 05
Rate equations:
Might contain the essential physics at a global level. Model of fc(x,p) needed. no possibility of studying diff. spectra. Grandchamp, rapp and Brown; (early) Thews
Transport theory. solves the caviats of other approaches. may obscure the physics. Zhang (AMPT); Bratkovskaya & Cassing (HSD); Gossiaux;…
Transport theory assuming spatial homogeneous fi(p) . diff spectra. misses surface effects, x-p correl, Q are not uniformly distributed. Thews and Mangano
Com
plex
ity
26
Heavy quarks production in heavy ions collisions
Turning on (re)combination + hard dissoc
Problem: One has to reduce the fusion probability by a factor 10 to reproduce the data (if recomb. cross section taken at face value, one arrives at RAA (most central > 2 !).
Absolute numbers are better reproduced (if one believes in mostly canonical – cranck=0.5-1 – recombination), although the RAA dependence on Npart is not as satisfying
dNc/dy3
27
Phenix
Typical value for strongly bound
Typical value for weakly bound
Problem never comes alone: Strongly bound quarkonia are the ones for which the Bhanot-Peskin approach should be legitimate. states exist early => lot of HQ pairs present in pahse space
Heavy quarks production in heavy ions collisions
Turning on (re)combination at y=2
No room left for coalescence at y=2. What are the physical mechanisms for taming the fusion ?
Good agreement with the same fus band (Cranck. [0.5,1] )
dNc/dy2
Moreover: The pQCD Bhanot and Peskin result is usually considered to be small w.r.t. other effective approaches at small s-M2
2
28
Hard probe
Soft probe
Tdiss/Tc >(>)1
Tdiss/Tc 1
Heavy quarks production in heavy ions collisions
Best parameters from RAA
“Optimal” choices in the (Tdiss, fus.) parameter plane
Conclusion: Tdiss [0.2,0.3]… but difficult to go beyond
29
Heavy quarks production in heavy ions collisions
Finer analysis: Thermometer of what ?Other parameters… Eloss, detailed Medium evolution…
Dominant production at various time depending on Tdiss… saturates before the end of the QGP
QGP
Dynamical evolution does not confirm the idea of statistical recombination in
the mixed phase
If quarkonia are a thermometer, it should be first agreed upon the phase it probes
MP
30
central
Hard probe
Soft probe
Tdiss/Tc >(>)1
Tdiss/Tc 1
Semi-Hard probe
Heavy quarks production in heavy ions collisions
No Eloss
Eloss Energy loss favors the coalescence of J/ (brings
the c quarks together in phase space )
However: Once the Energy loss has been “properly” calibrated on
non-photonic single-e RAA, then the production rates do not depend too much on the detailed phenomena
31
Finer analysis: role of HQ energy loss
Heavy quarks production in heavy ions collisions
The PT world
Softer pT spectrum as for direct production. Possible "pt shrinking" in A-A. But first, understand the kt broadening in d+Au (none seen around y=0 !?)
Tdissoc=180 MeV
(Heinz & Kolb)
Direct J/ (NN scaling)
Direct J/scaling)
Increased c-thermalization
32
Differential production might reveal more physics
Prediction for b=0 and just recombination
b=0
QGP “cools” the charms, even with the radial flow
(2004)
Heavy quarks production in heavy ions collisions
Cronin effect at initial stage (and no further effect)
… and now compared with the data:
Results for Tdiss= 0.3, 0.25, 0.2 and 0.18 (with initial Cronin effect).
Tdiss= 0.2 and NO Cronin effect.
The PT world
For this observable Tdiss= 0.3 should be favored
Unknown: influence of the
elastic cross section
Voloshin (2005)33
Heavy quarks production in heavy ions collisions
The keystone (?): v2
In fact, due to possible elastic cross section of J/, v2 is only conclusive per se if one observes NO v2
34
Heavy quarks production in heavy ions collisions
Penalized by higher power of the coupling constant w.r.t. inelastic scattering… but no threshold
Dominant process:
Investigating the role of elastic processesWork of H. Berrehrah (see QGP France 2009 & Hot
quarks 2010)
Assumption: Coulombic states
Total cross section
P(GeV/c)
Drag force
Elliptic flow
Inclusion in MC@sHQ
35
Tdiss=0.3 GeV
RAA
Heavy quarks production in heavy ions collisions
Preliminary conclusion1. Are the data compatible with the picture of a strongly bound J/ (sequential suppression) ?
2. Can we challenge the picture of statistical recombination (A. Andronic, PBM, J. Stachel) ?
3. Can we try to extract the dissociation temperature from the data ?
A rather large effective dissociation temperature (Tdiss0.25-0.3 GeV) seems to be favored by the data, provided one has a good quantitative argument to explain why the recombination of HQ should be reduced by a factor 10 w.r.t. the naive Bhanot - Peskin cross section (gluon mass ?)
Otherwise, low dissociation (Tdiss0.2 GeV) are unavoidable
Statistical recombination picture could not be recovered from the transport theory
36
Heavy quarks production in heavy ions collisions
Prediction for LHC:
37
Work to be continued during the LHC ERA:
d/dy=2b in pp
HQ Parameters:
dc/dy30 in PbPby=0
dch/d2300 in
PbPb, b=0
Hydro Parameters:
s0= 268 fm-3
(b=0)
LHC
RHIC
Fusion of c-quarks at LHC: 15-25 x more probable that at RHIC, but strong increase of the prompt J/ as well….
Administrateur
les données préliminaires du LHC, rescalées à 2.7 GeV, (interpolation) donnent dsigma/dy approx 4.3 microbarns => les RAA devraient etre réduits d'un facteur 2.