Heavy-quark energy loss
at RHIC and LHC
Andrea Dainese
Padova – University and INFN
based on work in collaboration with:
N.Armesto, M.Cacciari, C.Salgado, U.Wiedemann
PANIC 2005, Santa Fe, 24.10.2005
Andrea Dainese
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Layout
Energy loss for massive partons à la BDMPS
Model: quenching weights + geometry
Results for RHIC
the baseline for “non-photonic” electrons
RAA vs experimental data
Testing E loss with heavy-to-light ratios at LHC
Conclusions
PANIC 2005, Santa Fe, 24.10.2005
Andrea Dainese
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Parton E Loss in the BDMPS formalism
path length L

kT
qˆ 
kT2
l
transport coefficient
Radiated-gluon energy distrib.:
l
(BDMPS case)
 c /  for   c
dI

  sCR 
2
d
(

/

)
for   c
 c
CR
c  qˆL2 / 2
R  c L
Casimir coupling factor: 4/3 for q, 3 for g
sets the scale of the radiated energy
related to constraint kT < ,
controls shape at  << c
Baier, Dokshitzer, Mueller, Peigne‘, Schiff, NPB 483 (1997) 291.
Zakharov, JTEPL 63 (1996) 952.
Salgado, Wiedemann, PRD 68(2003) 014008.
PANIC 2005, Santa Fe, 24.10.2005
Andrea Dainese
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Lower E loss for heavy quarks ?
In vacuum, gluon radiation suppressed at q < mQ/EQ
Gluonsstrahlung probability
 “dead cone” effect
1

Q
[q 2  (mQ / EQ ) 2 ]2
Dead cone implies lower energy loss (Dokshitzer-Kharzeev, 2001):
energy distribution dI/d of radiated gluons suppressed by angledependent factor
Dokshitzer
suppress high- tail
2
 m  1 
d
I
d
I
calculation
Detailed massive

 1   Q  2 
 q 
 feature
confirms
d HEAVY thisdqualitative
E
LIGHT
Q 
 69(2004)

(Armesto, Salgado, Wiedemann, PRD
114003)
2
Dokshitzer, Khoze, Troyan, JPG 17 (1991) 1602.
Dokshitzer and Kharzeev, PLB 519 (2001) 199.
PANIC 2005, Santa Fe, 24.10.2005
Andrea Dainese
R = 105
4
Model vs RHIC “light” data
Model: pQCD + E loss probability (quenching weights) +
Glauber collision geometry
Density ( q̂ ) “tuned” to match RAA in central Au-Au at 200 GeV
(Quark Matter 05)
qˆ  4  14 GeV 2 /fm
Similar results by
Eskola, Honkanen,
Salgado, Wiedemann
Dainese, Loizides, Paic, EPJC 38 (2005) 461.
matches pT-indepence of suppression at high pT
PANIC 2005, Santa Fe, 24.10.2005
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Model for heavy quarks
Initially only charm
Baseline at RHIC: PYTHIA, with
EKS98 shadowing, tuned to match pTshape of D cross section measured in
d-Au by STAR (QM04)
Heavy-quark E loss using (m/E)dependent QW
q̂ extracted from p0,h RAA (central)
Thermalize charms that lose all energy
dN/dmT  mT exp(-mT/T), T = 300 MeV
Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) 054027.
EKS98: Eskola, Kolhinen, Salgado, EPJC 9 (1999) 61.
PANIC 2005, Santa Fe, 24.10.2005
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baseline dN/dpT
baseline RAA
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Charm RAA at RHIC
qˆ  4 14 GeV 2 /fm
(extracted from light-hadron data)
effect of the mass
thermalized
component
larger
other contributions
uncertainties become important
Small effect of mass for charm (~50% for D, ~30% for e) at
low pT [large uncertainties!]
Basically no effect in “safe” pT-region
Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) 054027.
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Charm + beauty + DY electrons at RHIC
(pQCD baseline revised, and its uncertainties)
PHENIX preliminary data (QM)
vs FONLL uncertainty band
FONLL (see Ramona’s talk):
electron spectrum may be
~50% c + ~50% b
for 3 < pT < 8 GeV
Large
uncertainty
b/c
We investigated
theonDY
crossing
point in pT: from
component:
scales/masses
it
< 10% up to 10variation
GeV
changes from 3 to 9 GeV
Note: still, electron cross
section in pp at 200 GeV
underestimated at high pT
FONLL calculation: Cacciari, Nason, Vogt, hep-ph/0502203
Drell-Yan from: Gavin et al., hep-ph/9502372
Comparison: Armesto, Cacciari, Dainese, Salgado, Wiedemann, in preparation
PANIC 2005, Santa Fe, 24.10.2005
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RAA of c and b electrons at RHIC
Due to larger mass of b quark electron RAA increased to ~0.4
Mass uncertainty (in E loss) and scales uncertainty (in pQCD
 b/c crossing) being studied
PHENIX (nucl-ex/0510047)
STAR (preliminary, QM)
mass uncertainty
mass and scale
uncertainty
Armesto, Cacciari, Dainese, Salgado, Wiedemann, in preparation
Armesto @ Quark Matter 05
PANIC 2005, Santa Fe, 24.10.2005
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v2 at high pT from E loss
The azimuthal asymmetry --v2 or RAA(f)-- of D and B
mesons in non-central collisions tests:
f = p/2
using FONLL
baseline
f=0
PHENIX p0 v2
at low/moderate pT: recombination scenario, v2 of c/b quarks, hence
degree of thermalization of medium
at higher pT: path-length dependence of E loss (almond-shaped
medium => v2 ~ 0.05--0.10)
what about
heavy-flavour e?
only from E loss
Cole @ Quark Matter 05
v2 from E loss: Dainese, Loizides, Paic, EPJC 38 (2005) 461
PANIC 2005, Santa Fe, 24.10.2005
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Heavy Quark Energy Loss at LHC
~100 cc pairs and ~5 bb pairs per central Pb-Pb collision
Experiments will measure with good precision RAA for D and
B, and for their decay leptons
What can we learn from
a comparative quenching study of
massive and massless probes at the LHC?
PANIC 2005, Santa Fe, 24.10.2005
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Heavy Flavour RAA at LHC
Baseline: PYTHIA, with EKS98 shadowing, tuned to
reproduce c and b pT distributions from NLO pQCD (MNR)
*
2
ˆ
ˆ
q

7

q

25

100
GeV
/fm
(m/E)-dep. E loss with LHC
RHIC
Armesto, Dainese, Salgado, Wiedemann, PRD 71 (2005) 054027.
MNR: Mangano, Nason, Ridolfi, NPB 373 (1992) 295.
PANIC 2005, Santa Fe, 24.10.2005
Andrea Dainese
* EKRT Saturation model:
Eskola, Kajantie, Ruuskanen, Tuominen,
NPB 570 (2000) 379.
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Color-charge and mass dep. of E loss
with Heavy-to-Light ratios at LHC
D( B)
h
Heavy-to-light ratios: RD( B ) / h ( pt )  RAA
( pt ) RAA ( pt )
Compare g  h , c  D and b  B
Eq  E g
mass effect
For 10 < pT < 20 GeV, charm behaves like a m=0 quark,
light-flv hadrons come mainly from gluons
RD/h enhancement probes color-charge dep. of E loss
RB/h enhancement probes mass dep. of E loss
Armesto, Dainese, Salgado, Wiedemann, PRD71 (2005) 054027
PANIC 2005, Santa Fe, 24.10.2005
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Conclusions
The (open) heavy-flavour era of heavy-ion physics has begun
Heavy flavours: testing ground for our understanding of
radiative energy loss
However, we need a solid perturbative baseline:
c/b relative contribution has large th. uncertainty (e.g. FONLL)…
which, still, doesn’t accomodate RHIC pp data
DY should be included in electron comparisons at ~10 GeV
Current e data tend to be overpredicted at high pT
Proposed observables at the LHC:
Heavy-to-light ratios as probes of E loss…
… color-charge dependence (RD/h)
… parton-mass dependence (RB/h)
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EXTRA SLIDES
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B.Muller’s QM Theory Summary
RHIC data
sQGP
Density of
scatterings
qˆ   k
QGP
Range of color force
2
T
2

l
 5  15 GeV 2 /fm
Baier’s plot
Cold nuclear matter
PANIC 2005, Santa Fe, 24.10.2005
1/Ntrig dN/dj
Pion gas
Emergence of away-side jet will
make determination of q^ easier.
Andrea Dainese
8 < pT(trig) < 15 GeV/c
pT(assoc) > 5 GeV/c
STAR Preliminary
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Medium Expansion
The density of scattering centers is time-dependent:

 
ˆq( )  qˆ0   0 
 = 1.5, 1.0, 0.5, 0
 
Dynamical scaling law:
same spectrum obtained
for equivalent static
trasport coefficient
2 0 L
qˆ  2  d (   0 )qˆ ( )
L 0
Calculations for a static
medium apply to
expanding systems
Salgado and Wiedemann, PRL 89 (2002) 092303
PANIC 2005, Santa Fe, 24.10.2005
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Application: Parton Quenching Model
QW + Glauber-based medium geometry and density profile
+ PYTHIA for parton generation and fragmentation
The procedure in short:
1) generate parton (q or g) with PYTHIA (or back-to-back pair)


2) calculate its L and average q̂ along the path [qˆ (s )  TATB (s )]
3) use quenching weights to get energy loss
4) quench parton and then hadronize it (independent fragm.)
pT
PYTHIA
 CR , pT
dN/dpT
P(E; CR , qˆ, L)
 L, qˆ
pT – E
Dainese, Loizides, Paic, EPJC 38 (2005) 461.
PANIC 2005, Santa Fe, 24.10.2005
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pT
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Extrapolation in c.m.s. energy
Intermediate RHIC energy s = 62 GeV
Extrapolation in s: assuming q̂  Ngluons/volume  (s)0.6
(EKRT saturation model)
2
ˆ
ˆ
First test: q62 GeV  q200 GeV / 2  7 GeV /fm
energy extrapolation works reasonably well
EKRT: Eskola, Kajantie, Ruuskanen, Tuominen, NPB 570 (2000) 379.
PHENIX Coll., JPG 31 (2005) S473.
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Model prediction for LHC
Extrapolation to LHC according to saturation model gives:
qˆ5.5 TeV  7  qˆ 200 GeV  100 GeV 2 /fm
?!?
5.5 TeV
RAA
h
Dainese, Loizides, Paic, EPJC 38 (2005) 461.
Vitev and Gyulassy, PRL 89 (2002) 252301.
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200 GeV
RAA

2
indep. of pT
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Why RAA is flat  Surface effect
Most partons from inner part are totally absorbed
Prod. points in (x,y) for partons giving hadrons with pT > 5 GeV:
increasing s
Energy loss is “saturated”: many partons radiate all their
energy
before
getting out
Loizides, PhD
Thesis, nucl-ex/0501017
Long path lengths exploited only by high energy partons


E

E
, with 0.5    1
 effectively,
 RAA doesn’t increase at high pT
 Exercise: L  L  RAA increases with pT
PANIC 2005, Santa Fe, 24.10.2005
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Lower E loss for heavy quarks ?
Detailed massive calculation shows that:
Medium-induced gluon radiation fills
the dead cone
kT
Still, kT-integrated radiation is
suppressed, but only for quite
large m/E (i.e. large m, low pT)*
dI / dd 2 ( / c  0.1)
m/E = 0.1
massive
R = 105
massless
dead cone
 2 ( kT2 )
*Warning: large uncertainties
Armesto, Salgado, Wiedemann, PRD 69 (2004) 114003.
PANIC 2005, Santa Fe, 24.10.2005
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D
AA
h
AA
R ( pT )
The heavy-to-light ratio: RD / h ( pT ) 
R ( pT )
What enters the game:
1) (c) quark vs gluon (Casimir factor)
2) harder charm pT distribution:
3) harder charm fragm.
4) mass effects
RHIC




RD/h > 1
RD/h up
RD/h down
RD/h up
1) dominates > 12-13 GeV
2) and 3) ~ compensate
4) dominates below 12 GeV
Warning: significant non-pert.
effects (e.g. reco) below 6-7 GeV
PANIC 2005, Santa Fe, 24.10.2005
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pp  QQ: pQCD calculations vs data
Calculation of partonic cross section
̂
standard: Fixed Order (NLO) Massive (e.g. MNR code)
state-of-the-art: Fixed Order Next-to-Leading Log (FONLL)
  pT
 more accurate at high pT
B production
at Tevatron
(1.96 TeV)
Charm
production
slightly underpredicted
is well described
by FONLL
at Tevatron
(1.96 TeV)
& at RHIC (200 GeV)
Cacciari, Frixione, Mangano, Nason
and Ridolfi, JHEP0407 (2004) 033
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CDF, PRL91 (2003) 241804
FONLL: Cacciari, Nason
Q  e+X
Cacciari, Nason, Vogt,
hep-ph/0502203
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Calculating Parton Energy Loss
E  
c
0
dI
d 
  s C R c   s C R qˆ L2
d
E  qˆ 
gluons volume-density and
interaction cross section
Probe the medium
Finite parton energy (qualitatively)

If E < c (e.g. small pT parton with large L):
E  
E
0
dI
d 
  s CR
d
Ec   s C R
E qˆ L
 dependence on parton energy
 qˆ  qˆ 1/ 2
: smaller sensitivity to density
 L2  L
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Heavy-quark production at the LHC
pp: Important test of pQCD in a new energy domain
Remember the “15-years saga of b production at Tevatron”*
Baseline predictions: NLO (MNR code) in pp + binary scaling
(shadowing included for PDFs in the Pb)
ALICE baseline for charm / beauty:
system : Pb-Pb (0-5% centr.)
sNN :
5.5 TeV
QQ
 NN
[mb]
QQ
Ntot
EKS 98
Cshadowing
4.3 / 0.2
115 / 4.6
0.65 / 0.80
p-Pb (min. bias)
8.8 TeV
pp
14 TeV
7.2 / 0.3
0.8 / 0.03
0.84 / 0.90
11.2 / 0.5
0.16 / 0.007
--
Theoretical uncertainty of a factor 2—3 (next slide)
* M.Mangano
MNR code: Mangano, Nason, Ridolfi, NPB373 (1992) 295.
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