hard probes of the quark gluon plasma part 1: introduction, r aa marco van leeuwen, nikhef &...
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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
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Particle Data Group topical reviewshttp://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)
General QCD references
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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:0712.3443U. Wiedemann, arXiv:0908.2306A. Majumder and M. v. L. arXiv:1002.2206Accardi, Arleo et al, arXiv:0907.3534
RHIC experimental white papersBRAHMS: nucl-ex/0410020PHENIX: nucl-ex/0410003PHOBOS: nucl-ex/0410022STAR: nucl-ex/0501009
LHC Yellow Reports
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Soft QCD matter and hard probes
Hard-scatterings produce ‘quasi-free’ partons Initial-state production known from pQCD Probe medium through energy loss
Heavy-ion collisions produceQCD matter
Dominated by soft partons p ~ T ~ 100-300 MeV
‘Hard Probes’: sensitive to medium density, transport properties
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Part I: Hard processes in fundamental collisions
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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, p accelerators (SLC, SPS, HERA)– Deeply Inelastic Scattering, proton structure
– Parton density functions
• Heavy ion accelerators/colliders (AGS, SPS, RHIC, LHC)– Bulk QCD and Quark Gluon Plasma
Many decisive QCD measurements done
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Seeing quarks and gluons
In high-energy collisions, observe traces of quarks, gluons (‘jets’)
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Singularities in pQCD
Closely related to hadronisation effects
(massless case)
Soft divergence Collinear divergence
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Hard processes in QCD
• Hard process: scale Q >> QCD
• Hard scattering High-pT parton(photon) Q ~ pT
• Heavy flavour production m >> QCD
Cross section calculation can be split into • Hard part: perturbative matrix element• Soft part: parton density (PDF), fragmentation (FF)
Soft parts, PDF, FF are universal: independent of hard process
QM interference between hard and soft suppressed (by Q2/2 ‘Higher Twist’)
Factorization
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The first and only ep collider in the world
e± p
27.5 GeV 920 GeV
√s = 318 GeV
Equivalent to fixed target experiment with 50 TeV e±
Loca
ted
in
Ham
bu
rg
H1
Zeus
The HERA Collider
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XpeXepe ee )( :CC , :NC
NC:
CC:
DIS: Measured electron/jet momentum fixes kinematics: x, Q2
Example DIS events
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Proton structure F2
Q2: virtuality of the x = Q2 / 2 p q‘momentum fraction of the struck quark’
F2: essentially a cross section/scattering probability
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Factorisation in DIS
Integral over x is DGLAP evolution with splitting kernel Pqq
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Parton density distributionLow Q2: valence structure
Valence quarks (p = uud)x ~ 1/3
Soft gluons
Q2 evolution (gluons)
Gluon content of proton risesquickly with Q2
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p+p dijet at Tevatron
Tevatron: p + p at √s = 1.9 TeV
Jets produced with several 100 GeV
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Testing QCD at high energy
small x
large x
x = partonic momentum fraction
Dominant ‘theory’ uncertainty: 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
CDF, PRD75, 092006
DIS to measure PDFs
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pQCD illustrated
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CDF, PRD75, 092006
jet spectrum ~ parton spectrum
nTTT ppdp
dN
ˆ
1
ˆˆ
jet
hadronT
P
pz ,
fragmentation
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Fragmentation and parton showers
large Q2 Q ~ mH ~ QCDF
Analytical calculations: Fragmentation Function D(z, ) z=ph/Ejet
Only longitudinal dynamics
High-energy
parton(from hard scattering)
Ha
dro
ns
MC event generatorsimplement ‘parton showers’
Longitudinal and transverse dynamics
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Part II: Nuclear Modification Factor RAA
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RHIC and LHC
STARSTAR
RHIC, Brookhaven
LHC, GenevaAu+Au sNN= 200 GeV Pb+Pb sNN= 2760 GeV
First run: 2000 First run: 2009/2010
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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 encounterNcoll = nA x nB (ex: 4 x 5 = 20 + …)
Relevant for hard processes; short timescales: Nbin
Transverse view
Eccentricity
Density profile : part or coll
22
22
xy
xy
x
y
L
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Centrality dependence of hard processes
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
Binary collisions weight towards small impact parameter
Total multiplicity: soft processes
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Testing volume (Ncoll) scaling in Au+Au
PHENIX
Direct spectra
Scaled by Ncoll
PHENIX, PRL 94, 232301
ppTcoll
AuAuTAA dpdNN
dpdNR
/
/
Direct in A+A scales with Ncoll
Centrality
A+A initial state is incoherent superposition of p+p for hard probes
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0 RAA – high-pT suppression
Hard partons lose energy in the hot matter
: no interactions
Hadrons: energy loss
RAA = 1
RAA < 1
0: RAA ≈ 0.2
: RAA = 1
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Nuclear modification factor
ppTcoll
PbPbTAA dpdNN
dpdNR
/
/
Suppression factor 2-6Significant pT-dependenceSimilar at RHIC and LHC?
So what does it mean?
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Nuclear modification factor RAA
p+p
Au+Au
pT
1/N
bin
d2 N/d
2 pT
‘Energy loss’
Shifts spectrum to left
‘Absorption’
Downward shift
Measured RAA is a ratio of yields at a given pT
The physical mechanism is energy loss; shift of yield to lower pT
ppTcoll
PbPbTAA dpdNN
dpdNR
/
/
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Getting a sense for the numbers – RHIC
Oversimplified calculation:- Fit pp with power law- Apply energy shift or relative E lossNot even a model !
Ball-park numbers: E/E ≈ 0.2, or E ≈ 3 GeV for central collisions at RHIC
0 spectra Nuclear modification factor
PH
EN
IX, P
RD
76, 051106, arXiv:0801.4020
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From RHIC to LHCRHIC: 200 GeVLHC: 2.76 TeV
per nucleon pair
Energy ~24 x higher
LHC: spectrum less steep, larger pT reach
nT
TT
pdpdN
p
21
RHIC: n ~ 8.2LHC: n ~ 6.4
Fractional energy loss:2
1
n
AA EE
R
RAA depends on n, steeper spectra, smaller RAA
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From RHIC to LHC
RHIC LHC
RHIC: n ~ 8.2 LHC: n ~ 6.4
20.023.01 2.6 32.023.01 4.4
Remember: still ‘getting a sense for the numbers’; this is not a model!
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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
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Medium-induced radiation
),(ˆ~ EmFLqCE nRSmed
propagating
parton
radiatedgluon
Landau-Pomeranchuk-Migdal effectFormation time important
Radiation sees length ~f at once
Energy loss depends on density: 1
2
ˆ
and nature of scattering centers(scattering cross section)
Transport coefficient
CR: color factor (q, g) : medium densityL: path lengthm: parton mass (dead cone eff)E: parton energy
q̂
2
2
Tf k
Path-length dependence Ln
n=1: elasticn=2: radiative (LPM regime)n=3: AdS/CFT (strongly coupled)
Energy loss
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Four formalisms
• 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
• Higher Twist (Guo, Wang, Majumder)– Medium characterised by higher twist matrix elements– Radiation kernel similar to GLV– Vacuum radiation in DGLAP evolution
Multiple gluon emission
Fokker-Planckrate equations
Poisson ansatz(independent emission)
DGLAPevolution
See also: arXiv:1106.1106
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Large angle radiationEmitted gluon distribution
Opacity expansion
kT < k
Calculated gluon spectrum extends to large k at small kOutside kinematic limits
GLV, ASW, HT cut this off ‘by hand’
Gluon momentum k (GeV)G
luo
n p
erp
mo
men
tum
k (
GeV
)
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Effect of large angle radiation
Ex
E
xE
Different large angle cut-offs:kT < = xE EkT < = 2 x+ E
Blue: kTmax = xERed: kTmax = 2x(1-x)E
Single-gluon spectrum
Different definitions of x:
ASW: GLV:
Factor ~2 uncertainty from large-angle cut-off
Ho
row
itz an
d C
ole
, PR
C8
1, 0
24
90
9
Opacity expansion formalisms
Expand in powers ofL
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Energy loss distributions
Radiated gluon distribution
Main theory uncertainty:Large angle radiation
Multiple gluon emission:Poisson Ansatz
Energy loss probability distribution
Broad distributionSignificant contributions at E=0, E=E
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Energy loss formalisms
Plenty of room for interesting and relevant theory work!
• 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
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Geometry
Density profile
Profile at ~ form known
Density along parton path
Longitudinal expansion dilutes medium Important effect
Space-time evolution is taken into account in modeling
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)/()( , jethadrTjetshadrT
EpDEPdEdN
dpdN
`known’ from e+e-knownpQCDxPDF
extract
Parton spectrum Fragmentation (function)Energy loss distribution
This is where the information about the medium isP(E) 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, -jet measurements ‘fix’ E, removing one of the convolutions –
more in Lecture 2 and 3
A simplified approach
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RAA at RHIC: ‘calibrating’ the modelsB
ass e
t al, P
RC
79
, 02
49
01ASW:
HT:
AMY:
/fmGeV2010ˆ 2q
/fmGeV5.43.2ˆ 2q
/fmGeV4ˆ 2q
Large density:AMY: T ~ 400 MeVTransverse kick: qL ~ 10-20 GeV
Large uncertainty in absolute medium density
PH
EN
IX, a
rXiv:1
20
8.2
25
4
All calculations describe the dataNot very sensitive to
energy loss distribution
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RAA at LHC & models
ALICE: arXiv:1208.2711CMS: 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
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RAA at LHC and JEWEL
Suppression factor 2-6Significant pT-dependence
JEWEL energy loss model agrees with measurements(tuned at RHIC, LHC ‘parameter-free’)
JEWEL: Monte Carlo event generator with radiative+collisional energy loss- Modified showers with MC-LPM implementation- Geometry: expanding Woods-Saxon density
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Identified hadron RAA
M. Ivanov, A. Ortiz@QM2012
Low-intermediate pT (1-6 GeV):Large baryon/meson ratio
Probably due to:1) radial flow2) parton recombination
M. Ivanov, A. Ortiz@QM2012
Baryon, meson RAA similar at pT > 8 GeV
As expected from parton energy loss
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Identified hadron RAA (strangeness)
Kaon, pion RAA
similar
: RAA~1 at pT~3 GeV/cSmaller suppression,/K enhanced at low pT
pT ~8 GeV/c:All hadrons similar
partonic energy loss + pp-like fragmentation?
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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 E/E ~ 0.2
– Detailed modeling: • Some ‘intrinsic’ uncertainties• In progress – more in next lectures
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Effects in RAA
• Parton pT spectra– Less steep at LHC less suppression
– Steepness decreases with pT: RAA rises
• Quark vs gluon jets– More gluon jets at LHC more suppression
– More quark jets at high pT: RAA rises
• Medium density (profile)– Larger density at LHC more suppression
(profile similar?)
– Path length dependence of energy loss
• Parton energy dependence– Expect slow (log) increase of E with E RAA rises with pT
– Running of S (A Buzzatti@QM2012) ?
• Energy loss distribution– Expect broad distribution P(E); kinematic bounds important
‘Known’, external
input
Energy loss theory
Determine/constrain from measurements
Use different observables to disentangle effects contributions
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Extra slides
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Intermezzo: Centrality
Central collisionPeripheral collision
top view:
front view:
b~0 fm
b
b finite
Nuclei are large compared to the range of strong force
Size of reaction zone, density depends on centrality:No QGP effects in peripheral collisions
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Centrality continuedcentralperipheral
Multiplicity distribution
Experimental measure of centrality: multiplicity
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Note: difference p+p, e++e-
p+p: steeply falling jet spectrumHadron spectrum convolution of jet spectrum with fragmentation
e+ + e- QCD events: jetshave p=1/2 √sDirectly measure frag function
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Multiple soft scattering: BDMPS, AMY
Using based on AMY-HTL scattering potential
L=2 fm Single gluon spectra L=5 fm Single gluon spectra
AMY: no large angle cut-off
)(ˆ Tq
+ sizeable difference at large at L=2 fm
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L-dependence; regions of validity?Emission rate vs (=L)
Caron-Huot, Gale, arXiv:1006.2379
AMY, small L,no L2, boundary effect
Full = numerical solution of
Zakharov path integral = ‘best we know’
GLV N=1Too much radiation at large L(no interference between scatt centers)
H.O = ASW/BDMPS like (harmonic oscillator)Too little radiation at small L
(ignores ‘hard tail’ of scatt potential)
E = 16 GeVk = 3 GeVT = 200 MeV
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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
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Jet Quenching
1) How is does the medium modify parton fragmentation?• Energy-loss: reduced energy of leading hadron – enhancement of yield
at low pT?
• Broadening of shower?• Path-length dependence• Quark-gluon differences• Final stage of fragmentation
outside medium?
2) What does this tell us about the medium ?• Density• Nature of scattering centers? (elastic vs radiative; mass of scatt. centers)• Time-evolution?
High-energy
parton(from hard scattering)
Hadrons
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RAA at RHIC and LHCP
HE
NIX
: arXiv:1208.2254
RA
A
LHC RAA < RHIC
Larger suppression+ spectrum less steep:larger density
Increase of RAA with pT similar at RHIC and LHCIncrease 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)
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Jets in pp at √s=2.76 TeV
R. Ma@HPCharged tracks+EMCAL, R=0.4
EMCAL installed in Dec 2010: ||<0.8, ~/3
R=0.2/R=0.4
Reasonable agreement with NLO calculationsNeed to include hadronisation for jet shapes
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Singularities in phase space
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Mechanisms for modified jet chemistry
Expect large baryon/meson ratio associated with high-pT trigger
(Hwa, Yang)
Baryon pT=3pT,parton
MesonpT=2pT,parton
Hard parton
Hot matter
‘Shower-thermal’ recombination
Sapeta, Wiedemann, arXiv:0707.3494Milhano et al
In-medium color flow/reconnection