Lecture I: introduction to QCD

Marco van LeeuwenUtrecht University

Jyväskylä Summer School 2008

2

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)

General QCD references

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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

5

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:s decreases with Q2

Pole at =

QCD ~ 200 MeV ~ 1 fm-1

Hadronic scale

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Asymptotic freedom and pQCD

At 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

8

Low Q2: confinement

Lattice QCD potential

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

9

Singularities in pQCD

Closely related to hadronisation effects

(massless case)

Soft divergence Collinear divergence

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Singularities in phase space

11

How to picture a QCD event

MC event generators use this picture

Initial hard scatteringhigh virtuality Q2

generateshigh-pT partons

Followed by angle-ordered gluon

emissions:fragmentation

At hadronic scale:hadronisation prescription

(e.g. clustering in HERWIG)

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QCD matter

Bernard et al. hep-lat/0610017

Tc ~ 170 -190 MeV

Energy density from Lattice QCD

Deconfinement transition: sharp rise of energy density at Tc

Increase in degrees of freedom: hadrons (3 pions) -> quarks+gluons (37)

c ~ 1 GeV/fm3

4gTg: deg of freedom

Nuclear matterQuark Gluon Plasma

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QCD phase diagram

Tem

per

atu

re

Confined hadronic

matter

Quark Gluon Plasma(Quasi-)free quarks and gluons

Nuclear matter

Neutron stars

Elementary collisions(accelerator physics)

High-density phases?

Ea

rly u

niv

ers

e

Critical

Point

qqB ~

Bulk QCD matter: T and B drive phases

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Heavy quarks

Definition: heavy quarks, m >> QCD

Charm: m ~ 1.5 GeVBottom: m ~ 4.5 GeVTop: m ~ 170 GeV

M. Cacciari, CTEQ-MCNet summer school 2008

Complications exist: QCD, EW corrections; quark mass defined in different ways

‘Perturbative’ hadronisation

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Regimes of QCD

Asymptotic freedomDilute, hard scattering

Bulk matter, cold

Deconfined matterBulk matter, hot

Baryon-dense matter (neutron stars)

Bound statesHadrons/hadronic matter

Heavy ion physics

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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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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

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’

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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

CDF, PRD75, 092006

DIS to measure PDFs

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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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e+e- → qq → jets

Direct measurement of fragmentation functions

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pQCD illustrated

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),(

CDF, PRD75, 092006

jet spectrum ~ parton spectrum

nTTT ppdp

dN

ˆ

1

ˆˆ

jet

hadronT

P

pz ,

fragmentation

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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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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

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Global analysis of FFproton anti-protonpions

De Florian, Sassot, Stratmann, PRD 76:074033, PRD75:114010

... or do a global fit, including p+p dataUniversality still holds

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Heavy quark fragmentation

Light quarks Heavy quarks

Heavy quark fragmentation: leading heavy meson carries large momentum fraction

Less gluon radiation than for light quarks, due to ‘dead cone’

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Dead cone effect

Radiated wave front cannot out-run source quark

Heavy quark: < 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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Factorisation in perturbative QCD

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),(

Parton density functionNon-perturbative: distribution of partons in protonExtracted from fits to DIS (ep) data

Matrix elementPerturbative component

Fragmentation functionNon-perturbativeMeasured/extracted from e+e-

Factorisation: non-perturbative parts (long-distance physics) can be factored out in universal distributions (PDF, FF)

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Reminder: parton kinematics

ep DIS:

Know: incoming electron 4-momMeasure: scattered electon 4-momReconstruct: exchanged 4-mommomentum fraction of struck quark

e+e-

Know: incoming electrons 4-momMeasure: scattered quark (jet) directionsReconstruct: exchanged 4-mom = parton momenta

p+p: direct access to underlying kinematics only via • , jet reconstruction• Exclusive measurements (e.g. di-leptons, di-hadrons)

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Differential kinematics in p+pExample: 0-pairs to probe low-x

p+p simulation

hep-ex/0502040

Forward pion

Second pion

Resulting x-range

Need at least two hadrons to fix kinematics in p+p

211

ees

px T

36

Direct photon basics

direct

fragment

Gordon and V

ogelsang, PR

D48, 3136

Small Rate: Yields

NLO: quarks radiate photons

LO: does not fragment,direct measure of partonic kinematics

‘fragmentation photons’

Direct and fragmentation contributionsame order of magnitude

37

R

Experimental challenge: 0

Below pT=5 GeV: decays dominant at RHIC

38

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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(fragment) / (inclusive)

Experimental access to fragmentation • Two Methods in p+p 200GeV

– Isolation cut ( 0.1*E > Econe(R=0.5) ): identifies non-fragmentation photons– Photons associated with high-pT hadron: fragmentation

PHENIX, PRL98, 012002 (2007)

R E Triggering leadinghadron

Look at associatedphotons

(Isolated)/(all direct)

Only ~10% of show significant associated hadronic activity

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Perturbative QCD processes

• Hadron production• Heavy flavours• Jet production

– e+e- → jets – p(bar)+p → jets

• Direct photon production

Measurem

ent difficulty

The

ory

diff

icul

ty

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Summary

• QCD is theory of strong interactions– Fundamental d.o.f quarks and gluons– Ground state: hadrons (bound states)

• Perturbative QCD, asymptotic freedom at high Q2, small distances

• Factorisation for pQCD at hadron colliders:– DIS to measure proton structure– e+ e- to measure fragmentation functions– Calculate jet, hadron spectra at hadron colliders

More on bulk QCD next lecture

42

QCD NLO resources

• PHOX family (Aurenche et al)http://wwwlapp.in2p3.fr/lapth/PHOX_FAMILY/main.html

• MC@NLO (Frixione and Webber)http://www.hep.phy.cam.ac.uk/theory/webber/MCatNLO/

You can use these codes yourself to generate the theory curves!

And more: test your ideas on how to measure isolated photons or di-jets or...

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Extra slides

44

DIS kinematics

dσ~

2

Lμν Wμν

Ee

E

Ep

q = k – k’, Q2 = -q2

Px = p + q , W2 = (p + q)2

s= (p + k)2

x = Q2 / (2p.q)

y = (p.q)/(p.k)

W2 = Q2 (1/x – 1)

Q2 = s x y

s = 4 Ee Ep

Q2 = 4 Ee E’ sin2θe/2y = (1 – E’/Ee cos2θe/2)x = Q2/sy

The kinematic variables are measurable

Leptonic tensor - calculable

Hadronic tensor- constrained by

Lorentz invariance

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DIS kinematics

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QCD and quark parton model

S. Bethke, J Phys G 26, R27

Running coupling:s grows with decreasing Q2

Asy

mpt

otic

free

dom

At low energies, quarks are confined in hadrons

Confinement, asymptotic freedom are unique to QCD

At high energies, quarks and gluons are manifest

gqqee

Theory only cleanly describes certaint limits

Study ‘emergent phenomena’ in QCD

47

Resolved kinematics inDeep Inelastic Scattering

small x

large x

x = partonic momentum fraction

DIS: Measured electron momentum fixes kinematics

),(2

),(2

14 2

22

2

2

4

2

2

2

QxFy

QxFy

yxQdxdQ

dL

eXep