Matt Durham - Hard Probes 2013 1 Heavy Quarks at Low-x J. Matthew Durham [email protected].
Hard Probes of the Quark Gluon Plasma Lecture I ...leeuw179/talks/2014/L1... · Soft QCD matter and...
Transcript of Hard Probes of the Quark Gluon Plasma Lecture I ...leeuw179/talks/2014/L1... · Soft QCD matter and...
Hard Probes of the Quark Gluon Plasma!Lecture I: Introduction and pQCD
Marco van Leeuwen,!Nikhef and Utrecht University
Helmholtz School Manigod!17-21 February 2014
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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!
Gauge Theories in Particle Physics (Vol II: QCD), I.J.R. Aitchison, A.J.G. Hey !
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 referencesGeneral QCD referencesGeneral QCD referencesGeneral QCD referencesGeneral 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:0712.3443 U. Wiedemann, arXiv:0908.2306
A. Majumder and M. v. L. arXiv:1002.2206 Accardi, Arleo et al, arXiv:0907.3534!
RHIC experimental white papersBRAHMS: nucl-ex/0410020 PHENIX: nucl-ex/0410003 PHOBOS: nucl-ex/0410022
STAR: nucl-ex/0501009
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What is QCD?
From: T. Schaefer, QM08 student talk
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QCD and hadronsQuarks and gluons are the fundamental particles of QCD
(feature in the Lagrangian)
However, in nature, we observe hadrons: Color-neutral combinations of quarks, anti-quarks
Baryon multiplet Meson multiplet
Baryons: 3 quarks
I3 (u,d content)
S
stra
ngen
ess
I3 (u,d content)
Mesons: quark-anti-quark
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Seeing quarks and gluons
In high-energy collisions, observe traces of quarks, gluons (‘jets’)
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How does it fit together?S. Bethke, J Phys G 26, R27
Running coupling: αs decreases with Q2
Pole at µ = Λ
ΛQCD ~ 200 MeV ~ 1 fm-1
Hadronic scale
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Asymptotic freedom and pQCDAt large Q2, hard processes:
calculate ‘free parton scattering’
At high energies, quarks and gluons are manifest
gqqee →−+
But need to add hadronisation (+initial state PDFs)
+ more subprocesses
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Low Q2: confinement
Lattice QCD potential
α large, perturbative techniques not suitable
Lattice QCD: solve equations of motion (of the fields) on a space-
time lattice by MC
String breaks, generate qq pair to reduce field energy
Bali, hep-lat/9311009
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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, µp 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 >> ΛQCD
• Hard scattering High-pT parton(photon) Q ~ pT
• Heavy flavour production m >> ΛQCD
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/Λ2 ‘Higher Twist’)
Factorization
c
chbbaa
abcdba
T
hpp
zD
cdabtddQxfQxfdxdxK
pdydd
πσσ 0
/222 )(ˆ),(),( →= ∑∫
parton density matrix element FF
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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±
Hera at DESY near Hamburg
H1
Zeus
The HERA Collider
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XpeXepe ee +→++→+ ±±± )( :CC , :NC νν
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 γ 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
Theory matches data over many orders of magnitudeUniversality: PDFs from DIS used to calculate jet-production in pp
CDF, PRD75, 092006
DIS to measure PDFs
parton density matrix element
Dominant ‘theory’ uncertainty: PDFs
c
chbbaa
abcdba
T
hpp
zD
cdabtddQxfQxfdxdxK
pdydd
πσσ 0
/222 )(ˆ),(),( →= ∑∫
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Testing QCD at RHIC with jets
Jets also measured at RHIC
However: signficant uncertainties in energy scale, both ‘theory’ and
experiment
STAR, hep-ex/0608030
NLO pQCD also works at RHIC
RHIC: p+p at √s = 200 GeV (recent run 500 GeV)
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Direct photon basics
direct
fragment
Gordon and Vogelsang, P
RD
48, 3136
Small Rate: Yield ∝ ααs
NLO: quarks radiate photons
LO: γ does not fragment,direct measure of partonic kinematics
‘fragmentation photons’
Direct and fragmentation contributionsame order of magnitude
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€
Rγ
Experimental challenge: π0 → γγ
Below pT=5 GeV: decays dominant at RHIC
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Direct photons: comparison to theoryP. Aurenche et al, PRD73:094007
Good agreement theory-experiment From low energy (√s=20 GeV at CERN) to highest energies (1.96 TeV TevaTron)
Exception: E706, fixed target FNAL deviates from trend: exp problem?
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Direct photons LHC(Isolated prompt photons)
Good agreement data-theory also in p+p at LHC
[GeV]TE30 40 50 210 210×2
[nb/
GeV
]ηd T
/dE
σ2 d
-510
-210
10
410
710810 + X γ →p + p
JETPHOX)6| < 2.5 ( X 10η2.1 < |
)4| < 2.1 ( X 10η1.57 < |)2| < 1.44 ( X 10η0.9 < |
| < 0.9η|
NLO pQCD JETPHOX
T=ERµ=
fµ=
FµCT10 / BFG II,
MPI and hadronization corrected
< 5 GeVisoT
, E-1 = 36 pbintL = 7 TeVsCMS
[GeV]TE30 40 210 210×2
Dat
a/Th
eory
0.0
0.5
1.0
1.5
2.0
Data / JETPHOX CT10Stat. + syst. uncertaintyScale uncertainty
uncertaintysα ⊕CT10 PDF
-1 = 36 pbint = 7 TeV, LsCMS (a)
< 5 GeVisoT
| < 0.9, Eη|
[GeV]TE30 40 210 210×2
Dat
a/Th
eory
0.0
0.5
1.0
1.5
2.0
Data / JETPHOX CT10Stat. + syst. uncertaintyScale uncertainty
uncertaintysα ⊕CT10 PDF
-1 = 36 pbint = 7 TeV, LsCMS (b)
< 5 GeVisoT
| < 1.44, Eη0.9 < |
CM
S, arXiv:1108.2044
Towards hadron production: Fragmentation Functions
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e+e- → qq → jets
Direct measurement of fragmentation functions
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pQCD illustrated
c
chbbaa
abcdba
T
hpp
zD
cdabtddQxfQxfdxdxK
pdydd
πσσ 0
/222 )(ˆ),(),( →= ∑∫
CDF, PRD75, 092006
jet spectrum ~ parton spectrum
nTTT ppdp
dNˆ1
ˆˆ∝
jet
hadronT
Pp
z ,=
fragmentation
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Note: difference p+p, e++e-
p+p: steeply falling jet spectrum Hadron spectrum convolution
of jet spectrum with fragmentation
e+ + e- QCD events: jetshave p=1/2 √s
Directly measure frag function
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Global analysis of FFproton anti-protonpions
De Florian, Sassot, Stratmann, PRD 76:074033, PRD75:114010
Some FF fits include RHIC data to constrain gluon fragmentation
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Fragmentation function fits
10-3
10-2
10-1
1
10
10-3
10-2
10-1
1
10
10-3
10-2
10-1
1
10
KRE
KKP
DSS
BFGW
HKNS
AKK05
AKK08
10-1
1
10
102
FF
i/K
retz
er
10-1
1
10
102
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
zDh++h�
g(z,Q
=20
GeV
)
z
Gluon fragmentation
10-3
10-2
10-1
1
10
10-3
10-2
10-1
1
10
10-3
10-2
10-1
1
10
KRE
KKP
DSS
BFGW
HKNS
AKK05
AKK08
10-1
1
10
102
FF
i/K
retz
er
10-1
1
10
102
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
zDh++h�
u(z,Q
=20
GeV
)
z
quark (u) fragmentation
Fragmentation function fits based on e+e- have large uncertainty in gluon fragmentation
Some groups use hadron production to further constrain FFs
d’Enterria et al, arXiv:1311.1415
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Adding the LHC data in the game
d’Enterria et al, arX
iv:1311.1415
Kretzer fragmentation
10-13
10-11
10-9
10-7
10-5
10-3
10-1
10
0.5 1.0 2.0 5.0 10.0 20.0 50.0 100.0 200.0
CMS
CMS
CMS
Kretzer,
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Data/NLO
0.5 1.0 2.0 5.0 10.0 20.0 50.0 100.0 200.0
[GeV/c]
Ed3�ch/d
3p[m
bGeV
�2c3]
ps = 7000GeVps = 2760GeVps = 900GeVµ = pT
|⌘| < 1.0
pT
0.0
0.4
0.8
1.2
1.6
2.0
2.4
0.0
0.4
0.8
1.2
1.6
2.0
2.4
Dat
a/K
retz
er
2 5 10 20 50 100 200
[GeV/c]
2 5 10 20 50 100 200
CMS
ALICEKRE
KKP
DSS
scale uncert.
ct10 uncert.
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2 5 10 20 50
[GeV/c]
2 5 10 20 50
CDFBFGW
HKNS
AKK05
AKK08
0.0
0.4
0.8
1.2
1.6
2.0
2.4
0.0
0.4
0.8
1.2
1.6
2.0
2.4
Dat
a/K
retz
er
2 5 10 20 50 100
[GeV/c]
2 5 10 20 50 100
CMS
ALICE0.0
0.4
0.8
1.2
1.6
2.0
2.4
2 5 10 20
[GeV/c]
2 5 10 20
CMS
ALICE
UA1
pT
|⌘| < 1.0|⌘| < 0.8
ps = 7.0TeV
pT
|⌘| < 1.0
ps = 1960.0GeV
pT
|⌘| < 1.0|⌘| < 0.8
ps = 2760GeV
pT
|⌘| < 1.0|⌘| < 0.8
|⌘| < 2.5
ps = 900GeV
Ratios data/theory with uncertainties
Factor ~2 spread of results due to FF parameterisationsMostly due to uncertainty in gluons: next step: use data to constrain gluon FF
Also note: large scale uncertainties at pT < 5 GeV
!34
Heavy quark fragmentationLight quarks Heavy quarks
Heavy quark fragmentation: leading heavy meson carries large momentum fraction
Less gluon radiation than for light quarks, due to ‘dead cone’
!35
Dead cone effectRadiated wave front cannot out-run source quark
Heavy quark: β < 1
Result: minimum angle for radiation ⇒ Mass regulates collinear divergence
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Heavy Quark Fragmentation II
Significant non-perturbative effects seen even
in heavy quark fragmentation
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Fragmentation and parton showers
large Q2 Q ~ mH ~ ΛQCDµF
Analytical calculations: Fragmentation Function D(z, µ) z=ph/Ejet Only longitudinal dynamics
High-energy !
parton (from hard scattering)
Hadrons
MC event generators implement ‘parton showers’
Longitudinal and transverse dynamics
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Part II: Nuclear Modification Factor RAA
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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
!40
RHIC and LHC
STARSTAR
RHIC, Brookhaven LHC, GenevaAu+Au √sNN= 200 GeV Pb+Pb √sNN= 2760 GeV
First run: 2000 First run: 2009/2010
STAR, PHENIX,!PHOBOS, BRAHMS
ALICE, ATLAS, CMS, (LHCb)
Currently under maintenance!Restart 2015 with higher energy:
pp √s = 13 TeV, PbPb √sNN = 5.12 TeV
!41
Intermezzo: Centrality
Central collisionPeripheral collision
top/side view:
front view:
b~0 fm
b
Nuclei are large compared to the range of strong force
Size of reaction zone, density depends on centrality: Expect smaller/no QGP effects in peripheral collisions
b finite
!42
Centrality continuedcentralperipheral
Multiplicity distribution
Experimental measure of centrality: multiplicity
!43
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: σ ∝ Npart
- Nucleons interact with all nucleons they encounterNcoll = nA x nB (ex: 4 x 5 = 20 + …) Relevant for hard processes; short timescales: σ ∝ Nbin
!44
Centrality dependence of hard processes
dσ/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
!45
Testing volume (Ncoll) scaling in Au+Au
PHENIX
Direct γ spectra
Scaled by Ncoll
PHENIX, PRL 94, 232301
ppTcoll
AuAuTAA dpdNN
dpdNR
+
+=/
/
Direct γ in A+A scales with Ncoll
Centrality
A+A initial state is incoherent superposition of p+p for hard probes
!46
π0 RAA – high-pT suppression
Hard partons lose energy in the hot matter
γ: no interactions
Hadrons: energy loss
RAA = 1
RAA < 1
π0: RAA ≈ 0.2
γ: RAA = 1
!47
Nuclear modification factor
ppTcoll
PbPbTAA dpdNN
dpdNR
+
+=/
/
Suppression factor 2-6 Significant pT-dependence Similar at RHIC and LHC?
So what does it mean?
!48
Nuclear modification factor RAA
p+p
A+A
pT
1/N
bin d
2 N/d
2 pT
‘Energy loss’
Shift 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
+
+=/
/
!49
Getting a sense for the numbers – RHIC
Oversimplified calculation: -Fit pp with power law -Apply energy shift or relative E loss
Not even a model !
Ball-park numbers: ΔE/E ≈ 0.2, or ΔE ≈ 3 GeV for central collisions at RHIC
π0 spectra Nuclear modification factor
PH
EN
IX, P
RD
76, 051106, arXiv:0801.4020
!50
From RHIC to LHCRHIC: 200 GeV LHC: 2.76 TeV per nucleon pair
Energy ~24 x higher
LHC: spectrum less steep, larger pT reach
nT
TT
pdpdN
p−∝
π21
RHIC: n ~ 8.2 LHC: n ~ 6.4
Fractional energy loss: 2
1−
"#
$%&
' Δ−≈
n
AA EER
RAA depends on n, steeper spectra, smaller RAA
!51
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!
!52
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
To be continued… in the next lecture
Summary
• QCD is a theory of quarks and gluons, but we observe hadrons!
• Hard scattering, large Q2: factorisation!• Short distance and long distance physics can be separated (to
some extent)!• Short distance: perturbative QCD!• Long distance: non-perturbative: PDFs, FFs!
• Experimentally accessible ‘partonic’ observables:!• Jets!• Photons!
• First high-Q2 measurements in heavy ion collisions:!• Hadron (charged particle) production: no Ncoll scaling; energy
loss!• Photon production: Ncoll scaling
!53
Extra slides
!55
Jets and parton energy loss
Motivation: understand parton energy loss by tracking the gluon radiation
Qualitatively two scenarios: 1) In-cone radiation: RAA = 1, change of fragmentation 2) Out-of-cone radiation: RAA < 1
!56
Jets at LHCALICE
η
ϕ
Transverse energy map of 1 event
Clear peaks: jets of fragments from high-energy quarks and gluonsAnd a lot of uncorrelated ‘soft’ background
!57
Jet energy asymmetryCentrality
12
12
EEEEAJ +
−=
ATLAS
, arXiv:1011.6182 (P
RL)
Jet-energy asymmetry Large asymmetry seen for central events
However: • Only measures reconstructed di-jets (don’t see lost jets) • Not corrected for fluctuations from detector+background • Both jets are intereracting – No simple observable
Suggests large energy loss: many GeV ~ compatible with expectations from RHIC+theory
!58
Fragmentation function uncertaintiesHirai, Kumano, Nagai, Sudo, PRD75:094009
z=pT,h / 2√s z=pT,h / Ejet
Full uncertainty analysis being pursuedUncertainties increase at small and large z