1

-- do hadrons, consisting of u,d,s, allow for this

we will see: no

-- what’s about heavy mesons (c,b)

tomography of a plasma possible

Collaborators:

P.-B. Gossiaux , R. Bierkandt, K. Werner

Subatech/ Nantes/ France

Nuclear Winter Workshop, Big Sky, Febr 09

How can we look into the interior of a QGP?

2

Centrality Dependence of Hadron Multiplicities

can be described by a very simple model (confirmed by EPOS)

No (if stat. Model applied) or one free parameter

Calculation of the Cu+Cu results without any further input

arXiv:0810.4465

3

strange non-strange

works for non strange and strange hadrons at 200 AGeV

Cu+Cu: completely predicted from Au+Au and pp

Theory = lines

4

at 62 AGeV

and even et SPS

5

….. and even if one looks into the details:

For all measured hadrons the core/corona ratio is strongly correlated with ratio of peripheral to central HI collisionsTheory reproduces the experimental results quantitativelyEror bars are not small enough to improve the simple model

6

This model explains STRANGENESS ENHANCEMENTespecially that the enhancement at SPS is larger than at RHIC

Strangeness enhancement in HI is in reality

Strangeness suppression in pp

string

Strangeness suppr in pp

PRD 65, 057501 (2002)

7

- Central Mi /N part same in Cu+Cu and Au+Au (pure core)- very peripheral same in Cu+Cu and Au+Au (pp) increase with N part stronger in Cu+Cu

- all particle species follow the same law

Φ is nothing special (the strangeness content is not considered in this model) Strangeness enhancement is in reality strangeness suppression in pp (core follows stat model predictions which differ not very much) - works for very peripheral reactions (Ncore =25). The formation of a possible new state is not size dependent

Particle yield is determined at freeze out by phase space (with γS = 1 (a lower γS models corona contributions)

8

Rescattering later -> neither yield nor spectra sensitive to state of matter before freeze out

Light hadrons insensitive to phase of matter prior to freeze out (v2 or other collective variables?)

Production: hard process described by perturbative QCD initial dσ/dpT is known (pp) comparison of final and initial spectrum: gives direct information on the interaction of heavy Q with the plasma if heavy quarks are not in thermal equilibrium with the plasma : tomography possible

Why are heavy quarks (mesons) better?

9

Individual heavy quarks follow Brownian motion: we can describe the time evolution of their distribution by a

Fokker – Planck equation:

fBfAtf

pp

K

Input reduced to Drift (A) and Diffusion (B) coefficient.

Much less complex than a parton cascade which has to follow the light particles and their thermalization as well.

Can be combined with adequate models for the dynamics of light quarks and gluons (here hydrodynamics of Heinz and Kolb)

Interaction of heavy quarks with the QGP

10

drift and diffusion coefficient

:take the elementary cross sections for charm scattering (Qq and Qg) and calculate the coefficients (g = thermal distribution of the collision partners)

|M|2 = lowest order QCD with (αs( 2πT) , m_D)

and then introduce an to study the physics.

Diffusion (BL , BT) coefficient Bνμ ~ << (pν - pν

f )(pμ -

pμf )> >

taken from the Einstein relation A = p/mT BL

A (drift) describes the deceleration of the c-quark B (diffusion) describes the thermalisation

Strategy:

overall K factor

11

p +p(pQCD)

c and b carry direct informationon the QGP

QGP expansion: Heinz & Kolb’s hydrodynamics

K=1 drift coeff from pQCD

This may allow for studying plasma properties usingpt distribution, v2 transfer, back to back correlations etc

Interaction of c and b with the QGP

K< 40: plasma does not thermalize the c or b:

12

RAA or energy loss is determined by the elementary elastic scattering cross sections. q channel:

Neither α(t) =g2/4 nor κmD2= are well determined

α(t) =is taken as constant [0.2 < α < 0.6] or α(2πT)

mDself2 (T) = (1+nf/6) 4πas( mDself

2) xT2 (Peshier hep-ph/0607275)

But which κ is appropriate?κ =1 and α =.3: large K-factors are necessary to describe data

Is there a way to get a handle on α and κ ?

Weak points of the existing approaches

13

Loops are formed

If t is small (<<T) : Born has to be replaced by a hard thermal loop (HTL) approach like in QED:(Braaten and Thoma PRD44 (91) 1298,2625)

For t>T Born approximation is ok

QED: the energy loss

( = E-E’)

Energy loss indep. of the artificial scale t* which separates the 2 regimes.

B) Debye mass

mD regulates the long range

behaviour of the interaction

PRC78 014904, 0901.0946

14

This concept we extend to QCD

HTL in QCD cross sections is too complicated for simulations

Idea: - Use HTL (t<t*) and Born (t>t*) amplitude to calculate dE/dx make sure that result does not depend on t*

- determine which gives the same energy loss as if one uses a cross section of the form

In reality a bit more complicated: with Born matching region of t*

outside the range of validity of HTL (<T) -> add to Born a constant ’

Constant coupling constant -> Analytical formula -> arXiv: 0802.2525Running -> numerically

15

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)

Observable = T-L effective coupling * Process dependent fct

“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

Additional inputs (from lattice) could be helpful

15

Describes e+e- data

A) Running coupling constant

16

Large enhancement of cross sections at small t

Little change at large t

Largest energy transfor from u-channel gluons

The matching gives 0.2 mD for running S for theDebye mass and 0.15 mD not running!

17

The expaning plasma

18

. c-quark transverse-space distribution according to Glauber

• c-quark transverse momentum distribution as in d-Au (STAR)… seems very similar to p-p (FONLL) Cronin effect included.

• c-quark rapidity distribution according to R.Vogt (Int.J.Mod.Phys. E12 (2003) 211-270).

• QGP evolution: 4D / Need local quantities such as T(x,t) taken from hydrodynamical evolution (Heinz & Kolb)

•D meson produced via coalescence mechanism. (at the transition temperature we pick a u/d quark with the a thermal distribution) but other scenarios possible.

Au + Au @ 200 AGeV

19

minimum bias

NewK=1,5-2

Central and minimum bias events described by the same parameters.The new approach reducesthe K- factor

K=12 -> K=1,5-2

No radiative energy loss yet(complicated: Gauge+LPM)

pT > 2 bottom dominated!!more difficult to stop,compatible with experiment

Difference between b and c becomes smallerin minimum bias events

RAA

b

20

NewK=1,5-2

v2 of heavy mesons depends on where fragmentation/ coalescence takes place

end of mixed phase beginning of mixed phase

minimum bias out of plane distribution v2

Centrality dependence of integrated yield

21

6-8 fm

4-6 fm

2-4 fm0-2 fm

The stopping dependsstrongly on the positionwhere the Q’s are created

The spectra at large pT

are insensitive to theQ’s produced in the centerof the plasma No info about plasma center

At high momenta the spectrumis dominated by c and b produced close to the surface

Conclusion:Singles tell little about the center of the reactions

centrality dependence of RAA for c quarks

22

Strong correlation betweencentrality of the production and the final momentum difference of Q and Qbar

A ) Decreasing relative energy loss with increasing pt

B) Small ΔpT same path length from center

Pairs with small ΔpT can be usedto test the theoryto explore the center of thereaction

c cbar pairs are more sensitive to the center

23

p(Q) p(Qbar)

Due to geometry:The final momentumdifference is smallerfor centrally producedpairs

pairs

Singles: RAA flat at large pt

Pairs : RAA increases with pt

Less relative energy lossTypical pQCD effectNot present in AdS/CFT

24

Conclusions

• Experimental data point towards a significant (although not complete) thermalization of c and b quarks in QGP tomography of the plasma possible

• Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop pQCD calculations come close to the experimental RAA and v2.

• Radiative energy loss has to be developed

• Ads/CFT prediction differ: Experiment will decide

• pQCD calculations make several predictions which can be checked experimentaly

• Very interesing physics program with heavy quarks after the upgrate of RHIC and with LHC

25

Horowitz et Gyulassy 0804.4330Gubser PRD76, 126003

Wicks et al. NPA783 493 nucl-th/0701088Fixed coupling coll+radiative

pQCD dσ/dt: only mass dependentin the subdominant u-channel

AdS/CFT versus pQCD

AdS/CFT: final dpT/dt = -c T2/MQ pT

AdS/CFT:Anti de Sitter/conformal field theory

RHIC centralRCB = RAA charm/RAAbottom

26

Cacciari et al. hep-ph/0502203 and priv. communication

and at LHC?

For large pT: distribution of b and c identical

27

LHC will sort out theories as soon as RCB is measured

pQCD: RCB =1 for high pt:neither initial distrnor σ depends on the mass

AdS/CFT massdependence remains

But: what is the limitof the model?? Forvery large pt pQCDshould be the righttheory

LHC central

28

Conclusions

• Experimental data point towards a significant (although not complete) thermalization of c and b quarks in QGP tomography of the plasma possible

• Using a running coupling constant, determined by experiment, and an infrared regulator which approximates hard thermal loop pQCD calculations come close to the experimental RAA and v2.

• Radiative energy loss has to be developed

• Ads/CFT prediction differ: Experiment will decide

• pQCD calculations make several predictions which can be checked experimentaly

• Very interesing physics program with heavy quarks after the upgrate of RHIC and with LHC

29

0.05 0.1 0.15 0.2 0.25 0.3

0.1

0.2

0.3

0.4

dEdxGeVfm

s2Tt mD2T

T0.25GeV

p20GeVcs0.2

mD0.45GeV

THEN: Optimal choice of in our OBE model:

(T) 0.15 mD2(T)

with mD2 = 4s(2T)(1+3/6)xT2

s(2)

Model C: optimal 2

… factor 2 increase w.r.t. mod B (not enough to

explain RAA)T(MeV) \p(GeV/c) 10 20

200 0.36 (0.18)

0.49

(0.27)

400 0.70 (0.35)

0.98

(0.54)

dx

cdEcoll

)(Convergence with “pQCD” at high T

13

30

Surprisingly we expect for LHC about the same v2 as at RHICdespite of the fact that in detail the scenario is rather different

31(provided g2T2<< |t*| << T2

)

Braaten-Thoma:

HTL: collective

modes +

Large |t|: close coll.

Bare propagator

...3/

*ln

3

2

D

2D

m

tm

dx

dEsoft ...

*ln

3

2 2

D

t

ETm

dx

dEhard

SUM:

3/ln

32

D

2D

mETm

dxdE

Low |t|: large distances

Indep. of |t*| !

(Peshier – Peigné) HTL: convergent kinetic

(matching 2 regions)

11

32

E: optimal , running s,eff

C: optimal , s(2T)

19

Transport coefficientsDrag coefficient Diff. coefficient

Long. fluctuations

Running s and Van Hees &Rapp: roughly same trend

mod C – mod E - AdS/CFT Evolution ? Not so clear

Caution: One way of implementing running s

33

HTL+semihard, neededto have the transitionin the range of validityof HTLdE/dx does not dependon t*

The resulting values areconsiderably smaller than those used up to now.

34

Goal: find observables which are sensitive to the interaction of heavy quarks with the plasma -> agreement of predictions provide circumstantial evidence that the plasma is correctly described

prob

Pt initial [GeV]

Pt final [GeV]

Q with small pt initial gain momentum (thermalization)

with large pt inital loose momentum Distribution very broad

Tomography of the plasma

35

Where are we?

36

Teaney & MooreK=12

NewK=1.5-2

b

c

central

The new approach reducesthe K- factor

K=12 -> K=1,5-2

No radiative energy loss yet(Hallman )

pT > 2 bottom dominated!!more difficult to stop,compatible with experiment

central events

37

Where can we improve?

38

Moore and Teaney:Hydro with EOS which gives the largest v2 possibledoes not agree with data. Drift Coefficient needed forRAA corresp. to K=12

Van Hees & RappCharmed resonances exists in the plasma Dynamics = expanding fireball:

K12

RAA=(dσ/dpT)AA /(( dσ/dpT )pp Nbinary)

v2 = < cos2φ> ..

RAA and v2 need different values of K:Only exotic hadronization mechanisms may explain

thelarge v2

39

Averaged of inital positions and of the expanding plasma

pT final (>5GeV) = pT ini – 0.08 pT ini – 5 GeV dominant at large pT

Functional form expected from the underlying microscopic energy loss but numerical value depends on the details of the expansion

momentum loss of c in the plasma

40

There is a double challenge: description of the expanding plasma ANDdescription of interaction of the heavy quarks with this plasma

Model of van Hees and Rapp:v2 seems to depend on howthe expanding plasma isdescribed

if we use their drift coefficientin our (Heinz-Kolb) hydro approach (which describes the v_2 of the other mesons)

we get 50% less v_2

Preliminary andpresently under investigation

But if one looks into the details ….