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

!2

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

!3

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

!4

What is QCD?

From: T. Schaefer, QM08 student talk

!5

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

!6

Seeing quarks and gluons

In high-energy collisions, observe traces of quarks, gluons (‘jets’)

!7

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

!8

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

!9

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

!10

Part I: Hard processes in fundamental collisions

!11

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

!12

Seeing quarks and gluons

In high-energy collisions, observe traces of quarks, gluons (‘jets’)

!13

Singularities in pQCD

Closely related to hadronisation effects

(massless case)

Soft divergence Collinear divergence

!14

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

!15

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

!16

XpeXepe ee +→++→+ ±±± )( :CC , :NC νν

NC:

CC:

DIS: Measured electron/jet momentum fixes kinematics: x, Q2

Example DIS events

!17

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

!18

Factorisation in DIS

Integral over x is DGLAP evolution with splitting kernel Pqq

!19

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

!20

p+p → dijet at Tevatron

Tevatron: p + p at √s = 1.9 TeV

Jets produced with several 100 GeV

!21

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),(),( →= ∑∫

!22

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)

!23

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

!24

€

Rγ

Experimental challenge: π0 → γγ

Below pT=5 GeV: decays dominant at RHIC

!25

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?

!26

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

!28

e+e- → qq → jets

Direct measurement of fragmentation functions

!29

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

!30

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

!31

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

!32

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

!33

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

!36

Heavy Quark Fragmentation II

Significant non-perturbative effects seen even

in heavy quark fragmentation

!37

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

!38

Part II: Nuclear Modification Factor RAA

!39

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