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HQ Collisional energy loss at RHIC & Predictions for the LHC
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Transcript of HQ Collisional energy loss at RHIC & Predictions for the LHC
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(
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