Hard probes of the Quark Gluon
Plasma
Part 1: Introduction, RAA
Marco van Leeuwen,
Nikhef & Utrecht University
Lectures at:
Quark Gluon Plasma and Heavy Ion Collisions
Siena, 8-13 July 2013
General QCD references
Particle Data Group topical reviews
http://pdg.lbl.gov/2004/reviews/contents_sports.html
QCD and jets: CTEQ web page and summer school lectures
http://www.phys.psu.edu/~cteq/
Handbook of Perturbative QCD, Rev. Mod. Phys. 67, 157–248 (1995)
http://www.phys.psu.edu/~cteq/handbook/v1.1/handbook.ps.gz
QCD and Collider Physics, R. K. Ellis, W. J. Sterling, D.R. Webber, Cambridge University
Press (1996)
An Introduction to Quantum Field Theory, M. Peskin and D. Schroeder, Addison Wesley
(1995)
Introduction to High Energy Physics, D. E. Perkins, Cambridge University Press, Fourth
Edition (2000)
2
Heavy Ion references
RHIC overviews:
P. Jacobs and X. N. Wang, Prog. Part. Nucl. Phys. 54, 443 (2005)
B. Mueller and J. Nagle, Ann. Rev. Nucl. Part. Sci. 56, 93 (2006)
Jet quenching reviews:
M. Spousta, arXiv:1305.6400
J. Caselderrey-Solana and C. Salgado, arXiv:0712.3443
U. Wiedemann, arXiv:0908.2306
A. Majumder and M. v. L. arXiv:1002.2206
Accardi, Arleo et al, arXiv:0907.3534
RHIC experimental white papers
BRAHMS: nucl-ex/0410020
PHENIX: nucl-ex/0410003
PHOBOS: nucl-ex/0410022
STAR: nucl-ex/0501009
LHC Yellow Reports
3
Soft QCD matter and hard probes
Heavy-ion collisions produce
QCD matter
Dominated by soft partons
p ~ T ~ 100-300 MeV
Hard-scatterings produce ‘quasi-free’ partons
 Initial-state production known from pQCD
 Probe medium through energy loss
‘Hard Probes’: sensitive to medium density, transport properties
4
Part I: Hard processes in
fundamental collisions
5
Accelerators and colliders
• p+p colliders (fixed target+ISR, SPPS, TevaTron, LHC)
– Low-density QCD
– Broad set of production mechanisms
• Electron-positron colliders (SLC, LEP)
– Electroweak physics
– Clean, exclusive processes
– Measure fragmentation functions
• ep, mp accelerators (SLC, SPS, HERA)
Many decisive QCD
measurements done
– Deeply Inelastic Scattering, proton structure
– Parton density functions
• Heavy ion accelerators/colliders (AGS, SPS, RHIC, LHC)
– Bulk QCD and Quark Gluon Plasma
6
Seeing quarks and gluons
In high-energy collisions, observe traces of quarks, gluons (‘jets’)
7
Singularities in pQCD
(massless case)
Soft divergence
Collinear divergence
Closely related to hadronisation effects
8
Hard processes in QCD
• Hard process: scale Q >> LQCD
• Hard scattering High-pT parton(photon) Q ~ pT
• Heavy flavour production m >> LQCD
Factorization
Cross section calculation can be split into
• Hard part: perturbative matrix element
• Soft part: parton density (PDF), fragmentation (FF)
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

dyd 2 pT
dtˆ
z c
abcd
parton density
matrix element FF
QM interference between hard and soft suppressed (by Q2/L2 ‘Higher Twist’)
Soft parts, PDF, FF are universal: independent of hard process
9
The HERA Collider
Located in Hamburg
The first and only ep collider in the world
e±
p
27.5 GeV
H1
Zeus
920 GeV
√s = 318 GeV
Equivalent to fixed target experiment with 50 TeV e±
10
Example DIS events
NC :
e  p  e  X ,
CC : e   p   e ( e )  X
NC:
CC:
DIS: Measured electron/jet momentum fixes kinematics: x, Q2
11
Proton structure F2
Q2: virtuality of the g
x = Q2 / 2 p q
‘momentum fraction
of the struck quark’
F2: essentially a cross section/scattering probability
12
Factorisation in DIS
Integral over x is DGLAP evolution with splitting kernel Pqq
13
Parton density distribution
Low Q2: valence structure
Soft gluons
Valence quarks (p = uud)
x ~ 1/3
Q2 evolution (gluons)
Gluon content of proton rises
quickly with Q2
14
p+p  dijet at Tevatron
Tevatron: p + p at √s = 1.9 TeV
Jets produced with several 100 GeV
15
Testing QCD at high energy
x = partonic
momentum
fraction
CDF, PRD75, 092006
Dominant ‘theory’
uncertainty: PDFs
DIS to measure PDFs
Theory matches data over many orders of magnitude
Universality: PDFs from DIS used to calculate jet-production
Note: can ignore fragmentation effects in jet production
16
pQCD illustrated
fragmentation
jet spectrum ~
parton spectrum
dN
1
 n
pˆ T dpˆ T
pˆ T
CDF, PRD75, 092006
z
pT ,hadron
Pjet
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

dyd 2 pT
dtˆ
z c
abcd
17
Fragmentation and parton showers
MC event generators
implement ‘parton showers’
Longitudinal and transverse dynamics
Hadrons
High-energy
parton
(from hard scattering)
large Q2
mF
Q ~ mH ~ LQCD
Analytical calculations: Fragmentation Function D(z, m) z=ph/Ejet
Only longitudinal dynamics
18
Part II: Nuclear Modification Factor
RAA
19
RHIC and LHC
RHIC, Brookhaven
Au+Au sNN= 200 GeV
LHC, Geneva
Pb+Pb sNN= 2760 GeV
STAR
First run: 2000
First run: 2009/2010
20
Nuclear geometry: Npart, Ncoll
b
Two limiting possibilities:
- Each nucleon only interacts once, ‘wounded nucleons’
Npart = nA + nB (ex: 4 + 5 = 9 + …)
Relevant for soft production; long timescales:   Npart
- Nucleons interact with all nucleons they encounter
Ncoll = nA x nB (ex: 4 x 5 = 20 + …)
Relevant for hard processes; short timescales:   Nbin
Transverse view
Density profile r: rpart or rcoll
Eccentricity
 

 
2
y
2
y
2
x
2
x
y
L
x
21
Centrality dependence of hard processes
Total multiplicity: soft processes
Binary collisions weight
towards small impact parameter
d/dNch
200 GeV Au+Au
Rule of thumb for A+A collisions (A>40)
40% of the hard cross section
is contained in the 10% most central collisions
22
Testing volume (Ncoll) scaling in Au+Au
Direct g spectra
PHENIX, PRL 94, 232301
PHENIX
Centrality
RAA 
dN / dpT
Au  Au
N coll dN / dpT
p p
Scaled by Ncoll
Direct g in A+A scales with Ncoll
A+A initial state is incoherent superposition of p+p for hard probes
23
0 RAA – high-pT suppression
g: RAA = 1
0: RAA ≈ 0.2
g: no interactions
RAA = 1
Hadrons: energy loss
RAA < 1
Hard partons lose energy in the hot matter
24
Nuclear modification factor
R AA 
dN / dpT
Pb Pb
N coll dN / dpT
p p
Suppression factor 2-6
Significant pT-dependence
Similar at RHIC and LHC?
So what does it mean?
25
Nuclear modification factor RAA
‘Energy loss’
1/Nbin d2N/d2pT
R AA 
dN / dpT
Pb Pb
N coll dN / dpT
p p
‘Absorption’
p+p
Downward shift
Shifts spectrum to left
Au+Au
pT
Measured RAA is a ratio of yields at a given pT
The physical mechanism is energy loss; shift of yield to lower pT
26
Getting a sense for the numbers – RHIC
0 spectra
Nuclear modification factor
PHENIX, PRD 76, 051106, arXiv:0801.4020
Oversimplified calculation:
- Fit pp with power law
- Apply energy shift or relative E loss
Not even a model !
Ball-park numbers: DE/E ≈ 0.2, or DE ≈ 3 GeV
for central collisions at RHIC
27
From RHIC to LHC
RHIC: 200 GeV
per nucleon pair
LHC: 2.76 TeV
Energy ~24 x higher
LHC: spectrum less steep,
larger pT reach
1
dN
 pT n
2 pT dpT
RHIC: n ~ 8.2
LHC: n ~ 6.4
Fractional energy loss: R AA
 DE 
 1 

E


n2
RAA depends on n, steeper spectra, smaller RAA
28
From RHIC to LHC
RHIC
LHC
RHIC: n ~ 8.2
1  0.23
6. 2
 0.20
LHC: n ~ 6.4
1  0.234.4  0.32
Remember: still ‘getting a sense for the numbers’; this is not a model!
29
Towards a more complete picture
• Energy loss not single-valued, but a
distribution
• Geometry: density profile; path length
distribution
• Energy loss is partonic, not hadronic
– Full modeling: medium modified shower
– Simple ansatz for leading hadrons: energy loss
followed by fragmentation
– Quark/gluon differences
30
Medium-induced radiation
Landau-Pomeranchuk-Migdal effect
Formation time important
radiated
gluon
propagating
parton
Radiation sees
length ~tf at once
tf 
2
kT2
Energy loss depends on density:  
and nature of scattering centers
(scattering cross section)
Transport coefficient qˆ 
q2
Energy loss
DEmed ~  S C R qˆ Ln F (m, E )
CR: color factor (q, g)
q̂ : medium density
L: path length
m: parton mass (dead cone eff)
E: parton energy
1
r
Path-length dependence Ln
n=1: elastic
n=2: radiative (LPM regime)
n=3: AdS/CFT (strongly coupled)

31
Four formalisms
Multiple gluon emission
•
Hard Thermal Loops (AMY)
– Dynamical (HTL) medium
– Single gluon spectrum: BDMPS-Z like path integral
– No vacuum radiation
•
Multiple soft scattering (BDMPS-Z, ASW-MS)
– Static scattering centers
– Gaussian approximation for momentum kicks
– Full LPM interference and vacuum radiation
•
Opacity expansion ((D)GLV, ASW-SH)
– Static scattering centers, Yukawa potential
– Expansion in opacity L/
(N=1, interference between two centers default)
– Interference with vacuum radiation
•
Fokker-Planck
rate equations
Poisson ansatz
(independent emission)
Higher Twist (Guo, Wang, Majumder)
– Medium characterised by higher twist matrix elements
– Radiation kernel similar to GLV
– Vacuum radiation in DGLAP evolution
DGLAP
evolution
See also: arXiv:1106.1106
32
Large angle radiation
Emitted gluon distribution
Gluon perp momentum k (GeV)
Opacity expansion
kT < k
Gluon momentum k (GeV)
Calculated gluon spectrum extends to large k at small k
Outside kinematic limits
GLV, ASW, HT cut this off ‘by hand’
33
Effect of large angle radiation
Single-gluon spectrum
Expand in powers of
Blue: kTmax = xE
Red: kTmax = 2x(1-x)E
L

Different definitions of x:
ASW: x E 

E
GLV: x 


Horowitz and Cole, PRC81, 024909
Opacity expansion formalisms
E
Different large angle cut-offs:
kT <  = xE E
kT <  = 2 x+ E
Factor ~2 uncertainty
from large-angle cut-off
34
Energy loss distributions
Radiated gluon distribution
Main theory uncertainty:
Large angle radiation
Multiple gluon emission:
Energy loss probability distribution
Poisson Ansatz
Broad distribution
Significant contributions at DE=0, DE=E
35
Energy loss formalisms
• Large differences between formalisms understood
– Large angle cut-off
– Length dependence (interference effects)
• Mostly ‘technical’ issues; can be overcome
– Use path-integral formalism
– Monte Carlo: exact E, p conservation
• Full 2→3 NLO matrix elements
• Include interference
• Next step: interference in multiple gluon emission
Plenty of room for interesting and relevant theory work!
36
Geometry
Density profile
Profile at t ~ tform known
Density along parton path
Longitudinal expansion
dilutes medium
 Important effect
Space-time evolution is taken into account in modeling
37
A simplified approach
Parton spectrum Energy loss distribution Fragmentation (function)
dN
dpT

hadr
dN
dE
 P(DE )  D( pT ,hadr / E jet )
jets
known
pQCDxPDF
extract
`known’ from e+e-
This is where the information about the medium is
P(DE) combines geometry
with the intrinsic process
– Unavoidable for many observables
Notes:
• This is the simplest ansatz – most calculation to date use it (except
some MCs)
• Jet, g-jet measurements ‘fix’ E, removing one of the convolutions –
more in Lecture 2 and 3
38
RAA at RHIC: ‘calibrating’ the models
ASW:
HT:
AMY:
qˆ  10  20 GeV 2 /fm
qˆ  2.3  4.5 GeV 2 /fm
qˆ  4 GeV 2 /fm
Large density:
AMY: T ~ 400 MeV
Transverse kick: qL ~ 10-20 GeV
Bass et al, PRC79, 024901 PHENIX, arXiv:1208.2254
All calculations describe the data
Not very sensitive to
energy loss distribution
Large uncertainty in
absolute medium density
39
RAA at LHC & models
ALICE: arXiv:1208.2711
CMS: arXiv:1202.2554
Broad agreement
between models and
LHC RAA
Extrapolation from
RHIC
tends to give too much
suppression at LHC
Many model curves: need more constraints and/or selection of models
40
RAA at LHC and JEWEL
JEWEL: Monte Carlo event generator with radiative+collisional energy loss
- Modified showers with MC-LPM implementation
- Geometry: expanding Woods-Saxon density
Suppression factor 2-6
Significant pT-dependence
JEWEL energy loss model agrees with measurements
(tuned at RHIC, LHC ‘parameter-free’)
41
Identified hadron RAA
M. Ivanov, A. Ortiz@QM2012
Low-intermediate pT (1-6 GeV):
Large baryon/meson ratio
Probably due to:
1) radial flow
2) parton recombination
M. Ivanov, A. Ortiz@QM2012
Baryon, meson RAA similar at pT > 8 GeV
As expected from parton energy loss
42
Identified hadron RAA (strangeness)
L: RAA~1 at pT~3 GeV/c
Smaller suppression,
L/K enhanced at low pT
Kaon, pion RAA
similar
pT  ~8 GeV/c:
All hadrons similar
partonic energy loss + pp-like fragmentation?
43
Summary
• QCD calculations: factorisation of perturbative
and universal non-perturbative components
(PDFs, FFs)
– Except e+e-: no PDF needed
• Heavy ion collisions: jet quenching
– First observable: RAA
– Qualitatively: large effect, several GeV lost or
DE/E ~ 0.2
– Detailed modeling:
• Some ‘intrinsic’ uncertainties
• In progress – more in next lectures
44
Effects in RAA
•
Parton pT spectra
–
–
•
Quark vs gluon jets
–
–
•
–
Larger density at LHC  more suppression
(profile similar?)
Path length dependence of energy loss
Parton energy dependence
–
–
•
More gluon jets at LHC  more suppression
More quark jets at high pT: RAA rises
‘Known’,
external
input
Medium density (profile)
–
•
Less steep at LHC  less suppression
Steepness decreases with pT: RAA rises
Expect slow (log) increase of DE with E  RAA rises with pT
Running of S (A Buzzatti@QM2012) ?
Energy loss distribution
–
Expect broad distribution P(DE); kinematic bounds important
Energy loss
theory
Determine/
constrain from
measurements
Use different observables to disentangle effects contributions
45
Extra slides
46
Intermezzo: Centrality
Nuclei are large compared to the range of strong force
Peripheral collision
Central collision
top view:
b
b finite
b~0 fm
front view:
Size of reaction zone, density depends on centrality:
No QGP effects in peripheral collisions
47
Centrality continued
central
peripheral
Multiplicity distribution
Experimental measure of centrality: multiplicity
48
Note: difference p+p, e++e-
p+p: steeply falling jet spectrum
Hadron spectrum convolution
of jet spectrum with fragmentation
e+ + e- QCD events: jets
have p=1/2 √s
Directly measure frag function
49
Multiple soft scattering: BDMPS, AMY
L=2 fm Single gluon spectra
L=5 fm Single gluon spectra
AMY: no large angle cut-off
+ sizeable difference at large  at L=2 fm
Using
qˆ (T ) based on AMY-HTL scattering potential
50
L-dependence; regions of validity?
Emission rate vs t (=L)
Caron-Huot, Gale, arXiv:1006.2379
E = 16 GeV
k = 3 GeV
T = 200 MeV
GLV N=1
Too much radiation
at large L
(no interference
between scatt centers)
Full =
numerical solution of
Zakharov path integral
= ‘best we know’
AMY, small L,
no L2, boundary effect
H.O = ASW/BDMPS like (harmonic oscillator)
Too little radiation at small L
(ignores ‘hard tail’ of scatt potential)
51
So what are we trying to do...
• First: understand (parton) energy process
– Magnitude, dominant mechanism(s)
– Probability distribution
• Lost energy
• Radiated gluons/fragments
– Path length dependence
– Flavour/mass dependence
– Large angle radiation?
• Future: use this to learn about the medium
52
Jet Quenching
1) How is does the medium modify parton fragmentation?
(from hard scattering)
Hadrons
• Energy-loss: reduced energy of leading hadron – enhancement of yield
at low pT?
• Broadening of shower?
• Path-length dependence
• Quark-gluon differences
High-energy
• Final stage of fragmentation
outside medium?
parton
2) What does this tell us about the medium ?
• Density
• Nature of scattering centers? (elastic vs radiative; mass of scatt. centers)
• Time-evolution?
53
Larger suppression
+ spectrum less steep:
larger density
PHENIX: arXiv:1208.2254
LHC RAA < RHIC
RAA
RAA at RHIC and LHC
Increase of RAA with pT similar at RHIC and LHC
Increase of RAA with pT:
Decrease of relative energy loss ΔE/E with pT
and/or decrease of power law index with pT (e.g. change from gluon to quark)
54
Jets in pp at √s=2.76 TeV
EMCAL installed in Dec 2010: |h|<0.8, j ~/3
R. Ma@HP
Charged tracks+EMCAL, R=0.4
R=0.2/R=0.4
Reasonable agreement with NLO calculations
Need to include hadronisation for jet shapes
55
Singularities in phase space
56
Mechanisms for modified jet chemistry
In-medium color flow/reconnection
‘Shower-thermal’
recombination
Baryon
pT=3pT,parton
Meson
pT=2pT,parton
Hot matter
Hard parton
(Hwa, Yang)
Expect large baryon/meson ratio
associated with high-pT trigger
Sapeta, Wiedemann, arXiv:0707.3494
Milhano et al
57