HQ Collisional energy loss at RHIC &
Predictions for the LHC
P.B. Gossiaux
SUBATECH, UMR 6457
Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS
Collaborators
J. Aichelin, A. Peshier, R. Bierkandt
GOAL of the STUDY
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 as (cf. previous work of Peshier), "crude" IR
regulator
2) Fokker – Planck equation…
Might not be applicable : "hard" transfers, # of collisions
not systematically large at the periphery
… or detailed balance not satisfied
(just E loss, no E gain )
1
2
From a more phenomenological point of view:
3) Need to crank up the 22 cross sections in order to
reproduce the RAA
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 22 cross sections
and look whether this helps solving points 3) and 4)
If yes: consider other observables and make predictions for
LHC
Global Model
Evolution of heavy
quarks in QGP
(thermalization)
D/B formation at the boundary of
QGP through coalescence of c/b
and light quark + fragmentation
(hard) production of heavy quarks
in initial NN collisions
Quarkonia formation in QGP
through c+cY+g fusion
process
3
Heavy quarks in QGP
In pQGP, heavy quarks are assumed to interact with partons of
type "i" (massless quarks and gluons) with local 22 rate:
Ri
Associated transport coefficient (drag, energy loss,…)
depend on the QGP macroscopic parameters (T, v, m) 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 QqQ'q' &
QgQ'g' collisions: MC approach
4
Oldies
Cross sections
We start from Combridge (79) as a basis:
However, t-channel is IR divergent => modelS
5
Naïve regulating of IR divergence:
1
1
With m(T) or m(t)
Models A/B: no as - running
m2(T) = mD2 = 4pas(1+3/6)xT2
Customary choice
as(Q2) 0.3 (mod A)
as(2pT) (mod B) ( 0.3)
dEcoll ( c )
dx
T(MeV) \p(GeV/c)
10
20
200
0.18
0.27
400
0.35
0.54
… of the order of a few % !
6
7
Other 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
1 dNe
• Q-Fragmentation and decay  e
as in Cacciari, Nason & Vogt 2005.
• No D (B) interaction in hadronic
phase
pt dpt
non phot. electrons
1
p p
all
0.01
D K 20
B K 20
0.0001
1.
10
6
10
8
D B K 20
c b crossing
1.
2
4
6
8
10
pt
8
Results for model B:
RAA
RAA lept
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Au Au central;
c
2 T
trans max
Au Au; central; n. ph. e
1.4
Boltzmann
1.2
PHENIX
1
PHENIX
STAR
trans max
2 T ; K 20
STAR
0.8
b
0.6
e B
0.4
all
0.2
e D
B
all
2
4
6
8
2
4
6
8
10
pT GeV c
Evolution  beginning
: Cranking factor
of cross-over
N.B.: Overshoot due to coalescence
One reproduces the RAA shape at the price of a huge cranking
K-factor  The end of coll Eloss in pQGP ?
m2(T)
2
= mD ? Model C: remembering of HTL
(but still no as–running vs Q2)
HTL
Low |t|
Idea:Take m2(T) in the propagator of Combridge in order
to reproduce the "standard" Braaten – Thoma Eloss
1
1
With m(T) calibrated on BT
9
Braaten-Thoma:
(Peshier – Peigné)
(provided
g2T2<<
Low |t|
|t*| <<
T2
)
Large |t|:
HTL
Bare
propagator
+
-dmn

2
t* 
2
  ...
 a mD ln 

dx
3
m
/
3
 D

dEsoft
SUM:
10
 ET 
dEhard 2
2
  ...
 a mD ln 

dx
3
t
*


dE  2 a mD2 ln  ET 
dx 3
 mD / 3 
Indep. of |t*| !
Comparing with dE/dx in our model:
In QGP: g2T2> T2 !!!
dE
BT: Not Indep. of |t*| !
GeV fm
dx
0.4
T2
0.3
station.
hard
T 0.25GeV
0.1
s
0
semi
hard
0.2
2
HTL
0
mD 0.45GeV
0.01
0.02
0.05
0.1
provided
g2T2<< |t*| << T2
We introduce a semi-hard
propagator --1/(t-n2) -- for
|t|>|t*| to attenuate the
discontinuities at t* in BT
approach.
HTL hard
HTL
p 20GeV c
0.2 mD
2(T)
B.T.
m2D
semi hard
0.2
m2(T) 
0.2
0.5
1
t
GeV2
Recipy: n2 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
11
Model C: no
Q2
– running, optimal
12
m2
Also Refered as mod C
THEN: Optimal choice of m in our OBE model:
dE
as(2pT)
GeV fm
dx
0.4
m2(T) 
s
0.15 mD
2(T)
t
0.3
2 T
mD2 T
0.2
T 0.25 GeV
p 20GeV c
with mD2 = 4pas(2pT)(1+3/6)xT2
0.1
s
0.05
dEcoll ( c )
dx
T(MeV) \p(GeV/c)
10
20
200
0.36
0.49
(0.18)
(0.27)
0.70
0.98
(0.35)
(0.54)
400
0.2
mD 0.45GeV
0.1
0.15
0.2
0.25
… factor 2 increase w.r.t. mod B
0.3
13
Results for model C:
R AA lept
1.4
R AA lept
1.4
Au Au; central
Boltzmann
1.2
2 T ;
0.8
Boltzmann
trans max
0.15, K 8
PHENIX
1
Au Au; central
STAR
1.2
2 T ;
e B
0.15, K 5
PHENIX
1
0.8
trans min
STAR
e B
0.6
0.6
0.4
0.2
0.4
all
e D
2
4
6
8
Evolution  beginning
of cross-over
: Cranking factor
0.2 P GeV c
T
all
e D
10
2
4
6
8
10
PT GeV c
Evolution  end of cross-over
Rate chosen “as at Tc”
One reproduces the RAA shape at the price of a large cranking
K-factor (8-5)
More recently (2-3 years  now)
14
Model D: running as
m2(T)  mDself2 (T2) = (1+nf/6) 4pas( mDself2) xT2
Self consistent mD
Cf Peshier hep-ph/0607275
dEcoll
dx
T(MeV) \p(GeV/c)
10
20
200
0.30
0.36
(0.18)
(0.27)
0.63
0.80
(0.35)
(0.54)
400
Indeed reduction of log increase…
…not much effect seen on the RAA
Model E : running as AND optimal
• Effective as(Q2) (Dokshitzer 95, Brodsky 02)
• Bona fide “running HTL”: as  as
eff
1.2
S L
(Q2)
15
m2
T L
1
0.8
nf 3
0.6
nf 2
0.4
same method as for model C:
0.2
semi-hard propag.
2
1
1
2
Q2 GeV2
dEcoll ( c / b)
dx
m2(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
drag "A" of heavy quarks
A GeV fm
3
E
2
c quarks
T 0.4GeV
A GeV fm
5
10
15
20

d p
f 
dt
dE
 -A
dx
C
1
Reminder:
16

-A
f
At large velocity
p GeV c
3
b quarks
2
E
T 0.4GeV
1
A GeV fm
C
5
10
15
20
p GeV c
3
E
c quarks
2
p 10GeV c
C
1
T GeV
0.1
0.2
0.3
0.4
0.5
Conclusion: including running as
and IR regulator calibrated on
HTL leads to much larger values
of coll. Eloss as in previous works
Central RAA for model E & interm. conclusion:
17
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
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)
Our
present
framework
Min. 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” ?
18
Could other observables help ?
Azimutal Correlations for Open Flavors
D/B
Transverse plane
Q
What can we learn about
"thermalization" process from the
correlations remaining at the end of
QGP ?
Initial correlation (at RHIC); supposed
back to back here
Q-bar
Dbar/Bbar
-
How does the coalescence fragmentation mechanism affects the
"signature" ?
19
20
Azimutal correlations at RHIC:
* Intermediate pT: both pT >1GeV/c and < 4GeV/c
Ce
Ce
e
1.0
0.8
0.6
Au Au central
1 pT e
4
1 pT e
4
0.2
0
0.6
0.4
E, K 1
E, K 2
B, K 12
1
2
1.0
0.8
tr min
vac.
0.4
e
0.2
3
rel
rad
4
5
6
0
Mexican hat (?) for model E
1 pT e
4
1 pT e
4
tr min
produced back
vac. (Q and Qvac.
to back in trans. Plane)
E, K 1
E, K 2
B, K 12
1
2
3
rel
 no correlation left for central collisions
Similar width for the 2 upper curves
(smaller dE/dx)
Au Au min. bias
rad
4
5
6
10-20 % correlation left for
min bias collisions
magnify
0.20
0.15
0.10
0.05
Possible discrimination ?
0.05
1
2
3
4
5
6
Probing the energy loss with RAA at large pT:
21
* large pT: mostly corona effect (?)
* Naïve view (b=0):
Opaque
Transparent
Thickness: a x l(Tc,s)
* More quantitatively: let us focus – within the model E – on c-quarks
produced at transverse position < rcrit
Path-length dependence
(of course, built in, but
survives the “rapid” cooling)
rcrit = 2fm rcrit = 4fm
rcrit = 6fm rcrit = 9fm
Fin. vs init. distribution of c
“some” Q produced at center
manage to come out
larger
thermalization for
inner quarks
22
More theoretical cuts:
Decreasing
for central
Q
Translucid
pT
pTin
Opaque
pTfin
Transparent
 cst at
periphery
pTin (GeV/c )
Creation dist to
the center (fm)
pTin (GeV/c )
* Challenge: tagging on the “central” Q, i.e. getting closer to the
ideal “penetrating probe” concept:
Q-Qbar correlations (at RHIC):
LQ
LQ
 back
to back
while
LQ
LQ
LQ  LQ 
pT ( Q )  pT (Q)
LQ  LQ  pT ( Q )  pT (Q)
* Reversing the argument: selecting pT ( Q )  pT (Q)
might bias the data in favor of “central” pairs
Possible
caveat:
LQ

LQ
 Need for a numerical
study
23
24
Q-Qbar correlations (at RHIC):
Average dist. to center
Privilege of simulation: retain Q and Qbar
from the same “mother” collision (exper.:
background substraction)
5fm
Indeed some (favorable)
bias for init pT > 5GeV/c
4fm
3fm
pTin (Q)  pTin ( Q )
Some hope to discriminate
between “running” and
“non running” models
(From the theorist point of
view at least)
RAA c quarks
1.000
0.500
no pt selection
single part
0.100
0.050
2 part
0.010
0.005
pt
0
5
0.1 x pt
10
15
20
25
30
pt or pt GeV c
Rcb ratio of c to b RAA(pT)(at RHIC):
25
rescaling: x 1.8
RHIC; Central Au Au; 200AGeV
RCB
5fm
1.0
dN
Rad. Ell.
Ell. fixed
0.8
1100
dy
AdS CFT;D 3
4fm
AdS CFT;D
0.6
0.4
AdS CFT;
3fm
Ell. running
1
5.5
Horowitz (SQM 07): large mass
dependence of AdS/CFT transp
coefficient – scaling variable: pl1/2
T2/2Mq L-- ≠ moderate dependence
in rad pQCD -- log(pT/M) --.
0.2
5
10
15
pT GeV c
RCB  1 for pQCD rad
Collisional Energy loss sets upper limit on Rcb. Clear possibility to
discriminate between various models.
Towards… LHC
26
D & B mesons at LHC
LHC; Central Pb Pb; 5.5TeV
RAA
2.0
model C: s 2 T ; 0.15
rescaling: x 5
model E: running s ; 0.2
rescaling: x 1.8
1.5
RHIC
LHC; Central
B mesons
1.0
RAA
model E: running s ;
rescaling: x 1.8
1.5
0.2
0.5
B mesons
D mesons
1.0
10
1600 
0.5
dN ch
dy
 2200
10
RHIC < LHC
15
20
y 0
25
30
30
40
50
pT GeV c
• RAA  1 at asymptotic pT
values, mostly seen in running as
models.
D mesons
5
20
pt GeV c
• medium at LHC relatively less
opaque that at RHIC
27
RCB at LHC
rescaling: x 1.8
LHC; Central Pb Pb; 5.5TeV
RCB
Rad Ell
1.0
Ell. running
0.8
Ell. fixed
dN
1750 2900
dy
Rad, q 40 100
0.6
Taken from
Horowitz SQM07
AdS CFT;D 3
AdS CFT;D 1
AdS CFT; 5.5
0.4
0.2
20
40
60
80
pT GeV c
Clear distinction between various Eloss mechanisms:
LHC will reveal it !
Azimutal B-Bbar correlations at LHC:
dN
d
1
0.1
rel
LHC
Pb Pb central
B B azim. correl
1 pT B ,pT B 4
4 pT B ,pT B 10
0.01
0.001
10 pT B ,pT B 20
10
4
10
5
10
6
Despite E loss,
Large
signal/background
for pT>10 GeV/c
20 pT B ,pT B 50
1
2
3
rel
rad
4
5
6
Prediction for the transverse broadening of the Q-jet,
related to the B transport coefficient
28
29
Electrons (D&B) @ LHC
RAA lept
Au Au Pb Pb; central
Boltzmann
trans min
Modele E: running s
1.4
1.2
1.0
0.8
K=1.8
0.6
0.4
dN ch
1600 
dy
0.2
5
RHIC < LHC
10
15
20
 2200
y 0
25
30
PT GeV c
Same trends as for open flavors
v2 for Electrons (D&B) @ LHC
v2 LHC < v2 RHIC (in agreement with “smaller” relative
opacity at LHC) and turns over for smaller pT (under study).
30
Conclusions – Prospects:
31
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
Bol.
FP
0.1
FP th
2fm c
10
1
0.01
0.001
0.0001
5
5
10
Bol.
T=400 MeV
as=0.3
Collisions with quarks & gluons
FP
0.1
FP th
10fm c
10
1
0.01
0.001
0.0001
5
5
10
Model B / 1
7
Results for model 1:
RAA
RAA
Au Au; central; n. ph. e
1.4
Boltzmann
1.2
trans max
PHENIX
1
Au Au; central; n. ph. e
1.4
2 T ; K 20
STAR
Boltzmann
1.2
0.8
2 T ; K 12
PHENIX
1
e B
0.6
STAR
coal.
fragm.
fragm.
0.8
e B
trans min
0.4
0.2
0.6
e D
all
2
4
6
8
10
p0.4
T GeV c
0.2
e D
Evolution  beginning
of cross-over
2
all
4
6
8
10
pT GeV c
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
With such cranking, the model I can be considered at most as
an effective one calibrated on RAA(why not ?).
Considering (nevertheless) v2:
v2 lept
v2 lept
0.12
Au Au; min. bias
all
D K 20
B K 20
D B K 20
Boltz.
0.12
tr max
2 T ; K 20 40
Au Au; min. bias
all
D
B
D B
Boltz.
tr min
2 T ; K 12
Phenix data
0.08
Phenix data
0.08
0.04
K 40
0.04
K 20
pT GeV c
pT GeV c
1
2
3
1
2
3
4
4
Conclusions:
1. v2 of Q still increases considerably during the cross-over
(contrarily to the one of thermalized quarks)
2. Reasonnable agreement with the data
Model C / 2
14
Minimum bias case
RAA
v2 lept
Au Au; min bias; n. ph. e
1.4
1.2
Boltzmann
trans min
2 T ;
0.15, K 5
Boltzmann
tr min
0.12
PHENIX
1
Au Au; min. bias
tr max
0.8
2 T ;
0.15
Phenix data
0.08
e B
0.6
0.4
K 5
0.04
0.2
all
2
e D
4
6
8
10
K 8
pT GeV c
pT GeV c
1
2
3
4
Similar conclusions as for model 1:
1. v2 of Q still increases considerably during the cross-over
(contrarily to the one of thermalized quarks)
2. Reasonnable agreement with the data
Model E / 4
Model 4 (and 4bis): running as AND optimal
m2
m2(T)  0.2 mD2 (T2)= (1+nf/6) 4pas(mD2) xT2
same method as
for model 2:
& as(Q2)
16
Mesoscopic aspects of the model
18
Differential cross section of c-quark in
the different variations of the model
d
cg cg
dt
With gluons
a.u.
1. 107
2 T ,
With quarks
1. 106
t ,
2
t ,
d
cq cq
dt
100000.
a.u.
2 T ,
6
1. 10
t ,
2
t ,
100000.
2
2
t
m 2D T
10000
1
0.2mD2 self T
&
t T2
Ec 10GeV
T 0.4 GeV
1000
1
2
3
4
5
0.15mD2 T
m 2D self T
0.2mD2 self T
t
&
t T2
0.11 6
T 0.4GeV
m 2D self T
0.11 6
2
m 2D T
Ec 10GeV
0.15mD2 T
t
2
10000
2
2 T ,
2
t
2
1. 107
2
2 T ,
6
t
2
3
4
5
6
t
: Large deviations at small and
intermediate moment transfer
: hard transfer due to
u-channel
19
Probability P(w) of energy loss per fm/c:
P w
100.
With gluons
With quarks
10.
T 0.4GeV
1.
p0 10GeV c
0.1
c quarks g
0.01
P w
0.001
100.
10.
T 0.4GeV
1.
p0 10GeV c
0.1
c quarks q
0.0001
0.
2.
4.
6.
8.
10.
w GeV
: Large deviations at small and
intermediate energy transfer
0.01
0.001
0.0001
0.
2.
4.
6.
8.
10.
w GeV
: hard transfer due to
u-channel
v2
RHIC
v2 lept
0.14
0.12
e
0.1
0.08
all
Boltzmann
trans min
D B
e B run. ;
0.2, rate x 1
e D
Phenix
0.06
0.04
0.02
min. bias v 2 lept
0.5
1
1.5
2
2.5
3
3.5
0.12
4
PT GeV c
Au Au; min. bias
0.1
Phenix data
0.08
0.06
0.04
0.02
0.5
1
1.5
2
2.5
3
3.5
4
pT GeV c
LHC
v2 c&D
min. bias Pb Pb ; model E
dN
LHC dy 2200
0.12
tr min
D
tr min
frag
tr max
0.08
tr min
c
tr max
0.04
K 1.8
K 2.5
0
1
2
3
4
5
pT GeV c
6
7
RCB
Looking for a Robust, Detectable Signal
– Use LHC’s large pT reach and identification of c and b to
distinguish
• RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi)
• Asymptotic pQCD momentum loss:
erad ~ as L2 log(pT/Mq)/pT
• String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
– Independent of pT and strongly dependent on Mq!
– T2 dependence in exponent makes for a very sensitive probe
– Expect: epQCD
0 vs. eAdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST