P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS

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 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)

Based on


I. “Understanding” the RHIC HQ-data

What is the dominant E loss mechanism @ RHIC ?

What can we extract from experimental data ?

01


2 1 1 2Q2GeV20.2

0.4

0.6

0.8

1

1.2

eff

nf3

nf2

SL TL

Effective s(Q2)

(Dokshitzer 95, Brodsky 02)

“Universality constrain” (Dokshitzer 02) helps reducing

uncertainties:

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).


(hard) production of heavy quarks in initial NN collisions + kT broad. (0.2 GeV2/coll

Bulk Evolution: non-viscous hydro (Heinz & Kolb) T(M) & v(M)

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


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


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


e fft; 0 .2

P H E N I X

m o d e l E


p T G eV c2 4 6 8

0 .5

1 .0

1 .5R A A le p t


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


e fft; 0 .2

P H E N I X

m o d e l E


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


From P. Braun-Munzinger (INPC 2010)

06


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


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


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


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


ru n . ; 0 .2 P H E N IX


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


• 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


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:


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


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)


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


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

Que

nchi

ng

Less «central»

Most «central»

Experimentally: no base-line for pp ?

c-quarks

Nch/ Nchmax

1

1

0.9

First study, showing the possibility of an

effect to be measured

http://arxiv.org/abs/1012.0764


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


Basic ingredients

Drag coefficient:

18

Running s

Fixed s + resonances

Diffusion coefficient B tuned to satisfy Einstein relation: asymptotic thermal distribution


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:


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



21

Texas AM: Everything uniform but the velocity field

x

=1.33fm/cy Calibration

Kolb-Sollfrank-Heinz (2000)



22

Texas AM: Everything uniform but the velocity field

Calibration

Rather good agreement for

the velocity

Good agreement for the bulk flow



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 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 quark evolution

Nuclear Modification factor

25

All heavy quarks observables evaluated with the pre-point prescription


Crossed ingredients

: More quenching with the fireball then with the (original) KH hydro

How can we conclude ?

RAA compatible


Heavy quark evolutionDifferential Elliptic flow

26


: More coupling with the Nantes microscopic model

: Higher elliptic flow from the fireball


Heavy quark evolutionInclusive elliptic flow

27

Various gedanken decoupling energy densities for the c quarks

+73%

Large deviations at early times


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


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



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



31

several levels of subtle and somehow paradoxal conclusions:


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


Confirms the proper calibration of the fireball (5.5% v2 for pions)

Comparing with 2 different freeze out prescriptions:

?


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 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


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


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


Back Up HQ


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


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


: 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


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


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


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


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


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


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


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


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:


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


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


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


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


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


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


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


Basics of Coherent Radiation

See Peigné & Smilga (2008) for some analytical results pertaining to HQ

Subject of numerous (mosty numerical) investigations


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


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


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


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

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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

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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

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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 ?

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Competition

Data oriented better than extra formulas



ru n . ; 0 .2 P H E N IX


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



ru n . ; 0 .2 P H E N IX


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


3

39



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


4

40



ru n . ; 0 .2 P H E N IX


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


4But syst. Error due to p-p

Data compatible with E path-length L in stationnary QGP.41


Round 6

5.1/6


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


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

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Finite Size effects

Today

Semi-coherent

Iterated GB

Phase diagram


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


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


III. Future observables for HQ Energy loss


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

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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


Back Up J/Psi


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


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


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

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``````We do not need recombination !’’’’’’’… except that Q and Qbar may be close in phase space


(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

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Turning on (re)combination + hard dissoc


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


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

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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

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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


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

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Hard probe

Soft probe

Tdiss/Tc >(>)1

Tdiss/Tc 1


Best parameters from RAA

“Optimal” choices in the (Tdiss, fus.) parameter plane

Conclusion: Tdiss [0.2,0.3]… but difficult to go beyond

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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

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central

Hard probe

Soft probe

Tdiss/Tc >(>)1

Tdiss/Tc 1

Semi-Hard probe


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

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Finer analysis: role of HQ energy loss


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

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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)


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


The keystone (?): v2

In fact, due to possible elastic cross section of J/, v2 is only conclusive per se if one observes NO v2

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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

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Tdiss=0.3 GeV

RAA


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

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Prediction for LHC:

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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.

P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS

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Transcript of P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS