HQ Collisional energy loss at RHIC & Predictions for the LHC

P.B. GossiauxSUBATECH, UMR 6457

Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS

J. Aichelin, A. Peshier, R. Bierkandt

Collaborators

GOAL of the STUDY1

Recent revival of the collisional energy loss in order to explain the large "thermalization" of heavy quarks in Au+Au collisions at RHIC at low and intermediate pT

Most often, however:1) No "real" pQCD implemented

No running s (cf. previous work of Peshier), "crude" IR regulator

Might not be applicable : "hard" transfers, # of collisions not systematically large at the periphery

2) Fokker – Planck equation…

… or detailed balance not satisfied(just E loss, no E gain )

2

3) Need to crank up the 22 cross sections in order to reproduce the RAA

From a more phenomenological point of view:

4) Difficulty (« challenge to the models ») to reproduce both the RAA and the v2 without "exotic" processes, like in-

QGP resonances. Our approach: consider heavy-Q evolution in QGP according to Boltzmann equation with improved 22 cross sections and

look whether this helps solving points 3) and 4)

If yes: consider other observables and make predictions for LHC

(hard) production of heavy quarks in initial NN collisions

Evolution of heavy quarks in QGP (thermalization)

Quarkonia formation in QGP through c+c+g fusion process

D/B formation at the boundary of QGP through coalescence of c/b and light quark + fragmentation

3Global Model

Heavy quarks in QGPIn pQGP, heavy quarks are assumed to interact with partons of

type "i" (massless quarks and gluons) with local 22 rate:

4

Ri

Associated transport coefficient (drag, energy loss,…) depend on the QGP macroscopic parameters (T, v, ) at a

given 4-position (t,x). These parameters are extracted from a "standard" hydro-model (Heinz & Kolb: boost invariant)

We follow the hydro evolution of partons and sample the rates Ri "on the way", performing the QqQ'q' &

QgQ'g' collisions: MC approach

Oldies

Cross sections We start from Combridge (79) as a basis:

5

However, t-channel is IR divergent => modelS

6Naïve regulating of IR divergence:

1 1 With (T) or (t)

Models A/B: no s - running

Customary choice(T) = mD

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

s(Q2) 0.3 (mod A)

s(2) (mod B) ( 0.3)

dx

cdEcoll

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

200 0.18 0.27

400 0.35 0.54

… of the order of a few % !

7Other hypothesis / ingredients of the model

• Au–Au collisions at 200 AGeV: 17 c-cbar pairs in central collisions

• Q distributions: adjusted to NLO & FONLL

• Cronin effect (0.2 GeV2/coll.).

• No force on HQ before thermalization of QGP (0.6 fm/c)

• Evolution according to Bjorken time until the beginning or the end of the cross-over

• Q-Fragmentation and decay e as in Cacciari, Nason & Vogt 2005.

• No D (B) interaction in hadronic phase

2 4 6 8 10pt1.108

1.106

0.0001

0.01

1

1pt

dNedpt

nonphot. electrons

all

DK20BK20

DBK20pp

cb crossing

8Results for model B:

Evolution beginning of cross-over

2 4 6 8 10pTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4

RAA

eD

all

eB

AuAu; central; n.ph. e

Boltzmanntrans max2T; K20

PHENIX STAR

: Cranking factor

One reproduces the RAA shape at the price of a huge cranking K-factor The end of coll Eloss in pQGP ?

A u A u c e n tr a l; t r a n sm a x

2T P H E N I X S T A R

B0 2 4 6 8

0 .20 .40 .60 .8

11 .21 .41 .6

R A A l e p t

allb

c

N.B.: Overshoot due to coalescence

9

Low |t|

1 1With (T) calibrated on BT

(but still no s–running vs Q2)

Idea:Take (T) in the propagator of Combridge in order to reproduce the "standard" Braaten – Thoma Eloss

(T) = mD2 ? Model C: remembering of HTL

HTL

10(provided g2T2<< |t*| << T2 )Braaten-Thoma:

HTL+

Large |t|:

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|

Indep. of |t*| !

(Peshier – Peigné)

0.01 0.02 0.05 0.1 0.2 0.5 1tGeV2

0.1

0.2

0.3

0.4

dEdxGeVfm

T0.25GeV

p20GeVcs0.2

mD0.45GeV

B.T.HTLhardstation.

HTL

semihard

hard0semi

hard20 HTL

T2 mD2

11

provided g2T2<< |t*| << T2

Comparing with dE/dx in our model:

We introduce a semi-hard propagator --1/(t-2) -- for |

t|>|t*| to attenuate the discontinuities at t* in BT

approach.

(T) 0.2 mD2(T)

In QGP: g2T2> T2 !!!

BT: Not Indep. of |t*| !

Recipy in the semi-hard prop. is chosen such that the resulting E loss is maximally |t*|-independent.

This allows a matching at a sound value of |t*| T

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

12

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: no Q2 – running, optimal 2

Also Refered as mod C

… factor 2 increase w.r.t. mod B

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

)(

2 4 6 8 10PTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4RAA lept

eB

alleD

AuAu; central

Boltzmanntrans max

2T; 0.15, K8

PHENIX STAR

13Results for model C:

Evolution beginning of cross-over Evolution end of cross-over

Rate chosen “as at Tc”: Cranking factor

One reproduces the RAA shape at the price of a large cranking K-factor (8-5)

2 4 6 8 10PTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4RAA lept

eB

alleD

AuAu; central

Boltzmanntrans min

2T; 0.15, K5

PHENIX STAR

More recently (2-3 years now)

14

Self consistent mD

Model D: running s

(T) mDself2 (T2) = (1+nf/6) 4s( mDself

2) xT2

Cf Peshier hep-ph/0607275

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

200 0.30 (0.18)

0.36 (0.27)

400 0.63 (0.35)

0.80 (0.54)

dx

dEcoll

Indeed reduction of log increase…

…not much effect seen on the RAA

2 1 1 2Q2GeV20.2

0.4

0.6

0.8

1

1.2

eff

nf3

nf2

SL TL

15

• Effective s(Q2) (Dokshitzer 95, Brodsky 02)

• Bona fide “running HTL”: s s(Q2)

Model E : running s AND optimal 2

same method as for model C:semi-hard propag.

(T) 0.2 mDself2(T)

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

200 1 / 0.65 1.2 / 0.9

400 2.1 / 1.4 2.4 / 2

dx

bcdEcoll

)/(

0.1 0.2 0.3 0.4 0.5TGeV

1

2

3AGeVfm

cquarks

p10GeVc

Reminder:

At large velocity

Ap ffdtd

A-

dx

Ed

5 10 15 20pGeVc

1

2

3AGeVfm

bquarks

T0.4GeV

16

Conclusion: including running s and IR regulator calibrated on

HTL leads to much larger values of coll. Eloss as in previous works

5 10 15 20pGeVc

1

2

3AGeVfm

cquarks

T0.4GeV

drag "A" of heavy quarksE

E

E

C

C

C

17Central RAA for model E & interm. conclusion:

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. One reproduces RAA for K=1.5-2 (<<20 with naïve model 1) on all pT range provided one performs the evolution end of mixed phase

Our present

framework

18Min. bias Results for model C &E :

mixed phase responsible for 40% of the v2 irrespectively

of the model ?! “Characterization of the Quark Gluon “Plasma with

Heavy Quarks” ?

Could other observables help ?

Azimutal Correlations for Open Flavors

What can we learn about "thermalization" process from the

correlations remaining at the end of QGP ?Q

D/B

Q-bar

Dbar/Bbar

Transverse plane

Initial correlation (at RHIC); supposed back to back here

How does the coalescence - fragmentation mechanism affects the

"signature" ?

19

vac .E , K 1E , K 2

B , K 1 2

A u A u m in . b ias

trm in1 p T e 4

1 p T e 4

re lrad 1 2 3 4 5 6

0 .2

0 .4

0 .6

0 .8

1 .0

C e e

0

Azimutal correlations at RHIC:

no correlation left for central collisions

* Intermediate pT: both pT >1GeV/c and < 4GeV/c

vac .E , K 1E , K 2

B , K 1 2

A u A u cen tral

trm in1 p T e 4

1 p T e 4

re lrad 1 2 3 4 5 6

0 .2

0 .4

0 .6

0 .8

1 .0

C e e

0

10-20 % correlation left for min bias collisions

vac .

1 2 3 4 5 6 0 .0 5

0 .0 5

0 .1 00 .1 50 .2 0Similar width for the 2 upper curves

(smaller dE/dx)

Mexican hat (?) for model E

Possible discrimination ?

(Q and produced back to back in trans. Plane)

Q

magnify

20

Probing the energy loss with RAA at large pT:

* large pT: mostly corona effect (?)

Thickness: x cs

* Naïve view (b=0):

Opaque

Transparent

* More quantitatively: let us focus – within the model E – on c-quarks produced at transverse position < rcrit Fin. vs init. distribution of c

rcrit = 2fm rcrit = 4fm

rcrit = 6fm rcrit = 9fm

Path-length dependence (of course, built in, but

survives the “rapid” cooling)

“some” Q produced at center manage to come out

larger thermalization for

inner quarks

21

More theoretical cuts:

* Challenge: tagging on the “central” Q, i.e. getting closer to the ideal “penetrating probe” concept:

in

T

T

p

p

Creation dist to the center (fm)

fin

Tp

)GeV/c(in

Tp

)GeV/c(in

Tp

Decreasing for central

Q

cst at periphery

Opaque

Translucid

Transparent

22

Q-Qbar correlations (at RHIC):

)Q()Q(QQ TT

ppLL

QL

QL

QL

QL

)Q()Q(

QQ

TTpp

LL

* Reversing the argument: selecting )Q()Q(TT

pp might bias the data in favor of “central” pairs

while

Possible caveat:

QL

QL

back to back

Need for a numerical study

23

Q-Qbar correlations (at RHIC):

Indeed some (favorable) bias for init pT > 5GeV/c

Privilege of simulation: retain Q and Qbar from the same “mother” collision (exper.:

background substraction)

Average dist. to center

)Q()Q( in

T

in

Tpp

3fm

4fm

5fm

single part

no p t se lec tion

p t 0.1 x p t

0 5 10 15 20 25 30p t or p t G eVc

1.0000.500

0.1000.050

0.0100.005

R A Ac quarks2 part

24

Some hope to discriminate between “running” and “non running” models (From the theorist point of view at least)

Rcb ratio of c to b RAA(pT)(at RHIC):

3fm

4fm

5fm

25

Collisional Energy loss sets upper limit on Rcb. Clear possibility to discriminate between various models.

A d S C F T ; 5 .5

A d S C F T ;D 1

A d S C F T ;D 3

R a d . E ll.dN

dy 11 0 0

E ll. ru n n in g

E ll. f ixe d

r e sc a lin g : x 1 .8

5 10 15p T G eV c0.2

0.4

0.6

0.8

1.0

R C B

R H IC ; C e n tr a l A u A u ; 2 0 0 A G eV

Horowitz (SQM 07): large mass dependence of AdS/CFT transp

coefficient – scaling variable: T2/2Mq L-- ≠ moderate

dependence in rad pQCD -- log(pT/M) --.

RCB 1 for pQCD rad

Towards… LHC

D m e so n s

B m e so n s

m o d e l E : r u n n in g s ; 0 .2

r e sc a lin g : x 1 .8

5 10 15 20 25 30p tG e V c

0.5

1.0

1.5

R A A

R H IC L H C ; C e n tr a l

D & B mesons at LHC

RHIC < LHC

Rescaled

collisional E

loss

220016000

y

ch

dy

dN

26

D m e so n s

B m e so n s

m o de l E : r un n ing s ; 0 .2r e sc a ling : x 1 .8

D m e so n s

B m e so n s

m o de l C : s2T ; 0 .1 5r e sc a ling : x 5

10 20 30 40 50p T G e V c

0.5

1.0

1.5

2.0R A A

L H C ; C e n tr a l P b P b ; 5 .5 T e V

• RAA 1 at asymptotic pT values, mostly seen in running s

models.

• medium at LHC relatively less opaque that at RHIC

RCB at LHC 27

Taken from Horowitz SQM07

Clear distinction between various Eloss mechanisms: LHC will reveal it !

A d SC F T; 5 .5A d SC F T;D 1A d SC F T;D 3

E ll . fix e dE ll . r u n n in g

R a d , q 4 0 1 0 0

R a d E ll

d N

d y 1 7 5 0 2 9 0 0

r e sc a lin g : x 1 .8

20 40 60 80p T G eV c0.2

0.4

0.6

0.8

1.0

R C B

L H C ; C e n tr a l P b P b ; 5 .5 T eV

Azimutal B-Bbar correlations at LHC: 28

Despite E loss, Large

signal/background for pT>10 GeV/c

Prediction for the transverse broadening of the Q-jet, related to the B transport coefficient

1 p T B , p T B 4

4 p T B , p T B 1 0

1 0 p T B , p T B 2 0

2 0 p T B , p T B 5 0

re lrad

L H CP b P b cen tral

B B

azim . co rre l

1 2 3 4 5 61 0 6

1 0 5

1 0 4

0 .0 0 1

0 .0 1

0 .1

1

d N

d re l

A u A u P b P b ; c en tr a lB o ltzm a n n tra nsm in

M o d e le E : r u n n in g s

5 1 0 1 5 2 0 2 5 3 0P T G e V c0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

1 .4

R AA le p t

RHIC < LHC

220016000

y

ch

dy

dN

K=1.8

Electrons (D&B) @ LHC 29

Same trends as for open flavors

Rescaled collisional E

loss

v2 for Electrons (D&B) @ LHC 30

v2 LHC < v2 RHIC (in agreement with “smaller” relative opacity at LHC) and turns over for smaller pT (under study).

31Conclusions – Prospects:

I. One reproduces all known HQ observables at RHIC with Collisional energy loss rescaling factor of K=1.5-2 (<<20 with naïve model 1) on all pT

range provided one performs the evolution end of mixed phase

II. Conservative predictions for LHC, found to be relatively less opaque than at RHIC, due to harder HQ initial distributions

III. LHC will permit to distinguish between various E loss mechanisms (pure collisional, mixed rad + collisional, sQGP AdS/CFT)

IV. Q-Jet broadening in azimutal correlation will permit to test B transport coefficient and better constrains the medium. Need MC@NLO for better

description of initial Q-production and e+ - e- correlations.

Back up

Boltzmann vs Fokker-Planck

10 5 5 100.0001

0.001

0.01

0.1

1Bol.

FP

FP th

2fmc

10 5 5 100.0001

0.001

0.01

0.1

1Bol.

FP

FP th

10fmcT=400 MeV

s=0.3

Collisions with quarks & gluons

Model B / 1

7Results for model 1:

Evolution beginning of cross-over

2 4 6 8 10pTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4

RAA

eD

all

eB

AuAu; central; n.ph. e

Boltzmanntrans max2T; K20

PHENIX STAR

2 4 6 8 10pTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4

RAA

coal. fragm.fragm.

eB

eD all

AuAu; central; n.ph. e

Boltzmanntrans min2T; K12

PHENIX STAR

Evolution end of cross-over

: Cranking factor

One reproduces the RAA shape at the price of a huge cranking K-factor The end of coll Eloss in pQGP ?

8

1. v2 of Q still increases considerably during the cross-over (contrarily to the one of thermalized quarks)

2. Reasonnable agreement with the data

1 2 3 4pTGeVc

0.04

0.08

0.12

v2 lept

allDK20BK20

DBK20K40

K20

Phenix data

AuAu; min. bias

Boltz.tr max2T; K2040

With such cranking, the model I can be considered at most as an effective one calibrated on RAA(why not ?).

Considering (nevertheless) v2:

1 2 3 4pTGeVc

0.04

0.08

0.12

v2 lept

allDB

DB

Phenix data

AuAu; min. bias

Boltz.tr min2T; K12

Conclusions:

Model C / 2

2 4 6 8 10pTGeVc0.2

0.4

0.6

0.8

1

1.2

1.4

RAA

eB

alleD

AuAu; min bias; n.ph. e

Boltzmanntrans min2T; 0.15, K5

PHENIX

14

1. v2 of Q still increases considerably during the cross-over (contrarily to the one of thermalized quarks)

2. Reasonnable agreement with the data

Minimum bias case

Similar conclusions as for model 1:

1 2 3 4pTGeVc

0.04

0.08

0.12

v2 lept

tr maxtr min

Phenix data

AuAu; min. bias

Boltzmann

2T;0.15

K8

K5

Model E / 4

16Model 4 (and 4bis): running s AND optimal 2

(T) 0.2 mD2 (T2)= (1+nf/6) 4s(mD

2) xT2

s(Q2)same method as for model 2:

Mesoscopic aspects of the model

Differential cross section of c-quark in the different variations of the model

With quarks

18

1 2 3 4 5 6t1000

10000

100000.

1. 106

1. 107

dcqcq

dta.u.

2T,2mD2T2T,20.15mD2Tt,2mD self2 T

t,20.2mD self2 Tt&

2t0.116tT2Ec10GeV

T0.4GeV

1 2 3 4 5 6t10000

100000.

1. 106

1. 107

dcgcg

dta.u.

2T,2mD2T2T,20.15mD2Tt,2mD self2 T

t,20.2mD self2 Tt&

2t0.116tT2Ec10GeV

T0.4GeV

With gluons

: Large deviations at small and intermediate moment transfer

: hard transfer due to u-channel

0. 2. 4. 6. 8. 10.wGeV0.0001

0.001

0.01

0.1

1.

10.

100.Pw

T0.4GeV

p010GeVccquarksq

0. 2. 4. 6. 8. 10.wGeV0.0001

0.001

0.01

0.1

1.

10.

100.Pw

T0.4GeV

p010GeVccquarksg

Probability P(w) of energy loss per fm/c:

With quarks

19

With gluons

: Large deviations at small and intermediate energy transfer

: hard transfer due to u-channel

v2

0.5 1 1.5 2 2.5 3 3.5 4pTGeVc0.02

0.04

0.06

0.08

0.1

0.12

v2 lept

Phenix data

AuAu; min. bias0.5 1 1.5 2 2.5 3 3.5 4

PTGeVc0.02

0.04

0.06

0.08

0.1

0.12

0.14

v2 lept

eDeB

eDBall

Phenix

Boltzmanntrans min

run. ;0.2, rate x 1

min. bias

RHIC

LHC

trm a x

trm in

trm infragD trm a x

trm inc L H C d N

d y 2 2 0 0m in . b ias P b P b ; m o d e l E

K 2 .5

K 1 .8

p T G eV c1 2 3 4 5 6 7

0 .0 4

0 .0 8

0 .1 2

v 2 c& D

0

RCB

– Use LHC’s large pT reach and identification of c and b to distinguish

• RAA ~ (1-(pT))n(pT), where pf = (1-)pi (i.e. = 1-pf/pi)• Asymptotic pQCD momentum loss:

• String theory drag momentum loss:

– Independent of pT and strongly dependent on Mq!– T2 dependence in exponent makes for a very sensitive probe

– Expect: pQCD 0 vs. AdS indep of pT!!• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST

rad s L2 log(pT/Mq)/pT

Looking for a Robust, Detectable Signal

ST 1 - Exp(- L), = T2/2Mq

S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006