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pQCD
A.) pQCD components in
elementary collisions
B.) modification in AA
collisions
High pT Particle Production
(the factorization theorem)
Jet: A localized collection of hadrons
which come from a fragmenting parton
hadrons
c
a
Parton Distribution Functions
Hard-scattering cross-section
b
d
hadrons
Fragmentation Function
leading
particle
High pT (>
~ 2.0 GeV/c) hadron production in pp collisions
for √s > 60 Gev:
h
d pp
0
D
d

2
2
h/c

K
dx
dx
f
(
x
,
Q
)
f
(
x
,
Q
)
(
ab

cd
)

a
b a
a
b
b
2

dyd pT
dtˆ
z c
abcd
“Collinear factorization”
Hard scattering
longitudinal
plane
Hard scattering in transverse
plane
Generally, partons
momentum
fraction
x1x2.
Point-like
 elastic
scattering
Partons have intrinsic transverse momentum kT
(Not
pT , jetin1 PHENIX
 pT , jet –0.35<<0.35)
2 0
pT , jet1  pT , jet 2  kT ,1  kT ,2
Jet Fragmentation (width of the jet cone)
Partons have to materialize
(fragment) in colorless world
jT 
jet fragmentation
transverse momentum
jet
jT and kT are 2D vectors. We measure the mean value of its
projection into the transverse plane |jTy| and |kTy| .
| k Ty | 
2

|jTy| is an important jet parameter. It’s constant value independent on
fragment’s pT is characteristic of jet fragmentation (jT-scaling).
|kTy| (intrinsic + NLO radiative corrections) carries the information on the
parton interaction with QCD medium.
 k  AA   k  vac   k  IS nucl   k  FS nucl
2
2
p+p
2
p+A
2
A+A
 k 2T 
Fragmentation Function
(distribution of parton momentum among fragments)
pi
In Principle
p parton   pi
i
| pi | cos(i )
zi 
| p parton |
In Practice
xE  
xE ztrigg
i
jet
| p parton |  | pi | cos(i )
i
 zi  1
Fragmentation function
D( z )  e  z /  z 
i
parton momenta are not known
pT  pTtrigg
| pTtrigg |2
pT cos( )

=z
p parton
 Simple relation
 z    xE  ztrigg 
0 in pp: well described by NLO
p+p->0 + X
Thermallyshaped Soft
Production
“Well Calibrated”
Hard
Scattering

Ingredients (via KKP or Kretzer)
 pQCD
 Parton distribution functions
 Fragmentation functions
hep-ex/0305013 S.S. Adler et al.
Fate of jets in heavy ion collisions?
idea: p+p collisions @ same
sNN = 200 GeV as reference
p
p
?: what happens in Au+Au to jets
which pass through medium?
Prediction: scattered quarks
radiate energy (~ GeV/fm) in the
colored medium:
 decreases their momentum
(fewer high pT particles)
 “kills” jet partner on other side
?
Au+Au
High pT Particle Production in A+A
h
dN AB
2
2

ABK
dx
dx
d
k
d
kb

a
b
a
2

dyd pT
abcd
 f a / A ( xa , Q 2 ) f b / B ( xb , Q 2 )
 g (k a ) g (k b )
0
h/c
*
c
2
c
Parton Distribution Functions
Intrinsic kT , Cronin Effect
 S A ( xa , Qa2 ) S B ( xb , Qb2 )
d

( ab  cd )
dtˆ
1
zc*
  dP( )
0
zc
(pQCD context…)
Shadowing, EMC Effect
Hard-scattering cross-section
c
Partonic Energy Loss
D (z ,Q )

Fragmentation Function
z c
a
b
d
hadrons
leading particle
suppressed
Jet fragment shape parameters jT, kT
rton distribution functions (hep-ex/0305109)
RHIC
o we understand hadron production
elementary collisions ? (Ingredient I: PDF)
RHIC
Ingredient II: Fragmentation functions
KKP (universality), Bourrely & Soffer (hep-ph/0305070)
Non-valence quark
contribution to parton
fragmentation into
octet baryons at low
fractional momentum
in pp !!
Quark separation in
fragmentation models
is important. FFs are
not universal.
z
z
Depend on Q, Einc,
and flavor
How to measure PID ?
Initial PID: charged hadrons vs. neutral pions
 Detailed PID:
 dE/dx (0.2-0.8 GeV/c)
 TOF / RICH / TRD (1.5-5 GeV/c)
 rdE/dx (5-20 GeV/c)
 V0 topology (only statistics limited)

0 in pp: well described by NLO (& LO)
p+p->0 + X
Thermallyshaped Soft
Production
“Well Calibrated”
Hard
Scattering


Ingredients (via KKP or Kretzer)
 pQCD
 Parton distribution functions
 Fragmentation functions
..or simply PYTHIA…
hep-ex/0305013 S.S. Adler et al.
pp at RHIC: Strangeness formation in QCD
nucl-ex/0607033
Strangeness production not described by leading order calculation
(contrary to pion production).
It needs multiple parton scattering (e.g. EPOS) or NLO corrections to
describe strangeness production.
Part of it is a mass effect (plus a baryon-meson effect) but in addition
there is a strangeness ‘penalty’ factor (e.g. the proton fragmentation
function does not describe L production). s is not just another light quark
How strong are the NLO corrections
in LO calculations (PYTHIA) ?
K.Eskola et al.
(NPA 713 (2003)):
Large NLO
corrections not
unreasonable at
RHIC energies.

Should be negligible
at LHC (5.5 or 14 TeV).
STAR
LHC
New NLO calculation based on STAR data
(AKK, hep-ph/0502188, Nucl.Phys.B734 (2006))
K0s
apparent Einc dependence of separated
quark contributions.
Non-strange baryon spectra in p+p
Pions agree with LO (PYTHIA)
Protons require NLO with
AKK-FF parametrization
(quark separated FF contributions)
PLB 637 (2006) 161
mt scaling in pp
Breakdown of mT scaling in pp ?
mT slopes from PYTHIA 6.3
Gluon dominance at RHIC
PYTHIA: Di-quark structures in baryon production cause mt-shift
Recombination: 2 vs 3 quark structure causes mt shift
Baryon/meson ratios – p+p collisions
PLB 637 (2006) 161
Bell shape from fragmentation is visible
Collision Energy dependence of
baryon/meson ratio
Ratio vs pT seems very energy dependent
(RHIC < < SPS or FNAL), LHC ?
Not described by fragmentation !
(PYTHIA ratios at RHIC and FNAL are equal)
Additional increase with system size in AA
Both effects (energy and system size
dependence) well described by recombination
Recombination vs. Fragmentation
(a different hadronization mechanism in medium than in vacuum ?)
Recombination at moderate PT
Parton pt shifts to higher
hadron pt.
Recomb.
Fragmentation at high PT:
Parton pt shifts to lower
hadron pT
fragmenting parton:
ph = z p, z<1
recombining partons:
p1+p2=ph
Frag.
Baryon production mechanism
through strange particle correlations
 …

0
e e  Z  qq  jets
Test phenomenological fragmentation
models
OPAL ALEPH and DELPHI measurements:
Yields and cosQ distribution between
correlated pairs distinguishes between
isotropic cluster (HERWIG) and
non-isotropic string decay (JETSET)
for production mechanism.
Clustering favors baryon production
JETSET is clearly favored by the data.
Correlated LLbar pairs are produced
predominantly in the same jet, i.e. short
range compensation of quantum numbers.
Flavor dependence of yield scaling
up, down
strange
charm
PHENIX D-mesons
• participant scaling for light quark hadrons (soft production)
• binary scaling for heavy flavor quark hadrons (hard production)
• strangeness is not well understood (canonical suppression in pp)
Charm cross-section measurements in
pp collisions in STAR
Charm quarks are believed to be produced at
early stage by initial gluon fusions
 Charm cross-section should follow number of
binary collisions (Nbin) scaling

Measurements
direct D0
(event mixing)
c→+X
(dE/dx, ToF)
c→e+X
(ToF)
c→e+X
(EMC)
pT (GeV/c)
0.13.0
0.170.25
0.94.0
 1.5
constraint
, d/dpT

, d/dpT
d/dpT
LO / NLO / FONLL?
A LO
calculation gives you a rough estimate of the cross section
A NLO calculation gives you a better estimate of the cross section and a rough
estimate of the uncertainty
Fixed-Order plus Next-to-Leading-Log (FONLL)



LO:
Designed to cure large logs in NLO for pT >> mc where mass is not
relevant
Calculations depend on quark mass mc, factorization scale F (typically
F = mc or 2 mc), renormalization scale R (typically R = F), parton
density functions (PDF)
Hard to obtain large  with R = F (which is used in PDF fits)
FONLL RHIC (from hep-ph/0502203 ):
400
NLO
381
 cFONLL

256

b
;


244
c
146
cc
134 b
99
 bbFONLL 1.8700..67
b
NLO:
CDF Run II c to D data (PRL 91,241804 (2003):
 The non-perturbative charm fragmentation
needed to be tweaked in FONLL to describe
charm. FFFONLL is much harder than used
before in ‘plain’ NLO  FFFONLL ≠ FFNLO
RHIC: FONLL versus Data
 cc (STAR from D 0  eTOF   )
 cc ( FONLL)
Matteo Cacciari
(FONLL):
 factor 2 is not a
problem
hep-ex/0609010
 factor 5 is !!!

nucl-ex/0607012


Spectra in pp seem to require a bottom contribution
High precision heavy quark measurements are tough at RHIC
energies. Need direct reconstruction instead of semi-leptonic
decays. Easy at LHC.
Conclusions for RHIC pp data


We are mapping out fragmentation and hadronization in vacuum as a
function of flavor.
What we have learned:





Strong NLO contribution to fragmentation even for light quarks at RHIC
energies
Quark separation in fragmentation function very important. Significant nonvalence quarks contribution in particular to baryon production.
Gluon dominance at RHIC energies measured through breakdown of mt-scaling
and baryon/meson ratio. Unexpected small effect on baryon/antibaryon ratio
Is there a way to distinguish between fragmentation and recombination ? Does it
matter ?
What will happen at the LHC ? What has happened in AA collisions
(hadronization in matter) ?
0 in pp: well described by NLO
p+p->0 + X
Thermallyshaped Soft
Production
“Well Calibrated”
Hard
Scattering

Ingredients (via KKP or Kretzer)
 pQCD
 Parton distribution functions
 Fragmentation functions
hep-ex/0305013 S.S. Adler et al.
Hadronization in QCD
(the factorization theorem)
Jet: A localized collection of hadrons
which come from a fragmenting parton
hadrons
c
a
Parton Distribution Functions
Hard-scattering cross-section
b
d
hadrons
Fragmentation Function
leading
particle
High pT (>~ 2.0 GeV/c) hadron production in pp collisions:
h
d pp
0
D
d

2
2
h/c

K
dx
dx
f
(
x
,
Q
)
f
(
x
,
Q
)
(
ab

cd
)

a
b a
a
b
b
2

dyd pT
dtˆ
zc
abcd
“Collinear factorization”
Modification of fragmentation functions
(hep-ph/0005044)
RAA and high-pT suppression
STAR, nucl-ex/0305015
pQCD + Shadowing + Cronin
energy
loss
pQCD + Shadowing + Cronin + Energy Loss
Deduced initial gluon density at t0 = 0.2 fm/c dNglue/dy ≈ 800-1200
 ≈ 15 GeV/fm3, eloss = 15*cold nuclear matter (compared to HERMES eA)
(e.g. X.N. Wang nucl-th/0307036)
Is the fragmentation function
modification universal ?
Modification according to
Gyulassy et al. (nucl-th/0302077)


Octet baryon fragmentation function from
statistical approach based on measured inclusive
cross sections of baryons in e+e- annihilation:
Induced Gluon Radiation
~collinear gluons in cone
“Softened” fragmentation
nchin jet : increases
zin jet : decreases
Quite generic (universal) but
attributable to radiative rather
than collisional energy loss
z
z
Jet quenching I: hadrons are
suppressed, photons are not
Energy dependence of RAA
0
nucl-ex/0504001
RAA at 4 GeV: smooth evolution with √sNN
Agrees with energy loss models
37
Radiative energy loss in QCD
Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000)
BDMPS approximation: multiple soft collisions in a medium of static color charges
Transport coefficient:
qˆ   medium  d q q
2
Medium-induced gluon radiation
spectrum:
Total medium-induced energy loss:
L
C
Emed   dz  d 
2
d
2

2
d q

dI LPM    dI BetheHeitler
qˆ  S NC







ddz  lcoherent 
ddz
 
dI LPM
~  S qˆC L ~  S qˆL2
ddz
t formation  L    c
E independent of parton energy (finite kinematics E~log(E))
E  L2 due to interference effects (expanding medium E~L)
“Jet quenching” = parton energy loss
High-energy parton loses energy by
rescattering in dense, hot medium.
q
q
Described in QCD as medium effect on parton fragmentation:
Medium modifies perturbative fragmentation before final hadronization
in vacuo. Roughly equivalent to an effective shift in z:
D p h ( z, Q )  D
2
(med)
p h
z


( z , Q )  D p h 
, Q2 
 1  E / E

2
Important for controlled theoretical treatment in pQCD:
Medium effect on fragmentation process must be in perturbative q2 domain.
Mechanisms
High energy limit: energy loss by gluon
radiation. Two limits:
(a) Thin medium: virtuality q2 controlled
by initial hard scattering (LQS, GLV)
L
q
q
g
q2
(b) Thick medium: virtuality controlled
by rescattering in medium (BDMPS)
Trigger on leading hadron (e.g. in RAA) favors case (a).
Low to medium jet energies: Collisional
energy loss is competitive!
Especially when the parent parton is a
heavy quark (c or b).
L
q
q
Extracting qhat from hadron suppression data
RAA: qhat~5-15 GeV2/fm
What does qhat q̂measure?
4 2 S N C
qˆ 
 mediumxGx, qˆL 
2
NC  1
~RHIC data
QGP
Equilibrated gluon gas:
number density ~T3
energy density ~T4
 qˆ  c
Hadronic
matter
3
4
R. Baier, Nucl Phys A715, 209c
qhat+modelling  energy
density
• pQCD result: c~2 (S? quark dof? …)
• sQGP (multiplicities+hydro): c~10
Model
uncertainties
q-hat at RHIC
RHIC data
?
sQGP?
QGP
Pion gas
Cold nuclear matter
BDMPS(ASW) vs. GLV
Baier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev
Salgado and Wiedemann PRD68 (2003) 014008
E ASWBDMPS 
Medium-induced radiation spectrum
C  qˆL2
2
qˆ  2
L
GLV

9 s3CR
4

Rough correspondence:
(Wiedemann, HP2006)
2qˆ 0 0
 d  qˆ( )  L
0
L
EGLV 
BDMPS
2
GeV
fm
GeV 2
qˆ  5
fm
qˆ  10
 sCR 2
qˆ L
4


30-50 x cold matter density
 1 dN g 
 2
 Llog E /  
 R dy 
dN g
 1800
dy
dN g
 900
dy
What do we learn from RAA?
GLV formalism
BDMPS formalism
~15 GeV
Wicks et al,
nucl-th/0512076v2
Renk, Eskola, hep-ph/0610059
E=15 GeV
Energy loss distributions very different for BDMPS and GLV formalisms
But RAA similar!
Need more differential probes
RAA for 0: medium density I
I. Vitev
C. Loizides
hep-ph/0608133v2
Use RAA to extract medium density:
W. Horowitz
I. Vitev:
1000 < dNg/dy < 2000
W. Horowitz: 600 < dNg/dy < 1600
C. Loizides: 6
< q̂ < 24 GeV2/fm
Statistical analysis to make optimal use of data
Caveat: RAA folds geometry, energy loss and fragmentation
Different partons lose different
amounts of energy
1.) heavy quark dead cone effect :
2.) gluon vs. quark energy loss:
Heavy quarks in the vacuum and in Gluons should lose more energy
the medium (Dokshitzer and
and have higher particle
Kharzeev (PLB 519 (2001) 199)) the multiplicities due to the color factor
radiation at small angles is
effect.
suppressed
Yu.Dokshitzer
…but everything looks the same at
high pt….
up,down
strange
charm ?
Particle dependencies: RAA of strangeness
A remarkable difference
between RAA and RCP
that seems unique to
strange baryons.
Ordering with strangeness
content.
‘Canonical suppression’
is unique to strange hadrons
This effect must occur ‘between’ pp and peripheral AA collisions
Strange enhancement vs. charm suppression ?
Do strange particles hadronize
different than charm particles ?
But is it a flavor effect ?
Kaon behaves like D-meson,
we need to measure Lc
An important detail: the medium is not totally opaque
There are specific differences to the flavor of the probe
plus: heavy quarks also show effects of collisional e-loss
Experiment: there are
baryon/meson differences
Theory: there are two types of e-loss:
radiative and collisional, plus
dead-cone effect for heavy quarks
Flavor dependencies map out the process of in-medium modification
BUT: heavy quarks show same e-loss than light quarks

RAA of electrons from heavy flavor decay




Describing the suppression is difficult for
models
radiative energy loss with typical gluon
densities is not enough
(Djordjevic et al., PLB 632(2006)81)
models involving a very opaque medium
agree better (qhat very high !!)
(Armesto et al., PLB 637(2006)362)
collisional energy loss / resonant elastic
scattering
(Wicks et al., nucl-th/0512076,
van Hees & Rapp, PRC 73(2006)034913)
heavy quark fragmentation and dissociation
in the medium
→ strong suppression
for charm and bottom
(Adil & Vitev, hep-ph/0611109)




Constraining
medium
viscosity
/s
Simultaneous description of
STAR R(AA) and PHENIX v2
for charm.
(Rapp & Van Hees, PRC 71, 2005)
Ads/CFT == /s ~ 1/4 ~ 0.08
Perturbative calculation of D (2t) ~6
(Teaney & Moore, PRC 71, 2005)
== /s~1
transport models require
 small heavy quark
relaxation time
 small diffusion coefficient
DHQ x (2T) ~ 4-6
 this value constrains the
ratio viscosity/entropy
 /s ~ (1.3 – 2) / 4
 within a factor 2 of
conjectured lower
quantum bound
 consistent with light hadron
v2 analysis
 electron RAA ~ 0 RAA at high pT - is bottom suppressed as well?
Energy density of matter
high energy density:
 > 1011 J/m3
P > 1 Mbar
I > 3 X 1015W/cm2
Fields > 500 Tesla
QGP energy density
 > 1 GeV/fm3
i.e. > 1030 J/cm3