May 2005 CTEQ Summer School 1

Global Analysis of QCDand Parton Distribution Functions

Dan StumpDepartment of Physics and Astronomy

Michigan State University

Ref: Pumplin, Stump, Huston, Lai, Nadolsky, Tung,New generation of parton distributions with uncertainties from global QCD analysis, JHEP07 (2002) 012.

May 2005 CTEQ Summer School 2

“QCD is our most perfect physical theory.”

-- Frank Wilczek

F. Wilczek, Nuclear Physics A663&664 (2000) 3c-20c.

May 2005 CTEQ Summer School 3

High energy particles interact through their quark and gluon constituents – the partons.

Asymptotic freedom : the parton cross sections can be approximated by perturbation theory.

Factorization theorem : Parton distribution functions of the nucleon are the link between the PQCD theory and measurements on nucleons.

May 2005 CTEQ Summer School 4

Motivations for global analysis of QCD

• the deep structure of the nucleon

• testing QCD – gluon radiation, higher order perturbation theory, the value of αS

• The PDF’s are needed to calculate cross sections for scattering processes at the LHC; the search for new physics.

May 2005 CTEQ Summer School 5

The goals of QCD global analysis are

• to construct accurate PDF’s;

• to know the uncertainties of the PDF’s;

• to enable predictions, including uncertainties.

May 2005 CTEQ Summer School 6

The parton model and global analysis of QCD ---inclusive scattering processes

May 2005 CTEQ Summer School 7

Outline1/ Introduction2/ Experiments3/ Methods of Analysis4/ Results

May 2005 CTEQ Summer School 8

PDF’s from Global Analysis

QCD TheoryLO, NLO, NNLOMS-bar factorizationDGLAP evolution

DataDIS (H1, ZEUS, BCDMS, NMC, CCFR)DY (E605, E866)High ET jets (CDF, D0)W asymmetry (CDF)

),(),( 22 QxfQxf ii δ±

αS(MZ)

PhenomenologyCTEQ, MRST, Alekhin, GGK, H1, ZEUS, …

May 2005 CTEQ Summer School 9

2/Experiments

May 2005 CTEQ Summer School 10

The HERA e±p collider

May 2005 CTEQ Summer School 11

Theory of deep-inelastic electron scattering

( )[ ]{ }),(),( 2222

24

2

2

2

112

QxFyQxFyQxdQdx

dL−−+= πασ

scorrection same ),(

scorrection ),(),(

)(

)(

+=

+=∑2

1

2222

2 QxFx

QxqxeQxF

em

iii

em

+ corrections

May 2005 CTEQ Summer School 12

H1 collaboration at HERA

Data used in the CTEQ6 analysis…DIS e± + p e± + X @ low-x 104 pointsDIS e± + p e± + X @ high-x 126 points… published 2000, 2001

May 2005 CTEQ Summer School 13

ZEUS collaboration at HERA

Data used in the CTEQ6 analysis …DIS e± + p e± + X 229 points… published 2001

May 2005 CTEQ Summer School 14

BCDMS collaboration

DIS µ+p µ+X 339 pointsDIS µ+d µ+X 251 points

Bologna - CERN - Dubna - Munich - SaclayNA4 muon scattering experiment at CERN

History: 1976 (C. Rubbia) to 1994

Homework Problem -- Why was µυον scattering used?Why is µd an interesting contrast to µp?

May 2005 CTEQ Summer School 15

NMC collaboration at CERN

DIS µ+p µ+X 201 pointsDIS µ+d µ+X 123 points… published 1997

The kinematic range 0.0001 < x < 0.7 and 0.01< Q2 < 70 GeV2 is covered .

May 2005 CTEQ Summer School 16

CCFR collaboration

• In the CTEQ6 analysis, number of data points = 156; from publications of 1997 and 2001

Chicago Columbia Fermilab Rochester

• The Lab E neutrino experiments at Fermilab (E744 in 1985; and E770 in 1987-88).

• Measurements of F2(x,Q2) and xF3(x,Q2) for ν and ν DIS

Homework Problem: What do we learn from neutrino/antineutrino scattering that we don’t know from electron scattering?

May 2005 CTEQ Summer School 17

Theory of deep-inelastic neutrino scattering

[ ]{[ ] } ),()(

),(),()(

yxxFy

yxFyyxFysG

dydxd

LF

32

22

222

11

114

−−±

−−+=π

σ

[ ][ ] scorrection ),(),(),(

scorrection ),(),(),(

+−=

++=

∑

∑

iii

iii

QxqQxqxQxFx

QxqQxqxQxF

2223

2222

2

2

May 2005 CTEQ Summer School 18

Experiment E605

For CTEQ6 : 119 data points

The Drell-Yan process

May 2005 CTEQ Summer School 19

The Drell-Yan process — lepton pair production in hadroncollisions

( )2221

22

212

1

01

FXab

FbFaba

X

Qxx

xfxfdxdx

µσ

µµσ

/,,ˆ

),(),(,

→×

=∑∫

May 2005 CTEQ Summer School 20

The Drell-Yan process

Experiment E866

Homework Question:E866 measured the asymmetry of down and up anti-quarks in the nucleon sea using Drell-Yan di-muons produced in 800 GeV proton interactions with hydrogen and deuterium targets. How does it work?

Xp

Xp

+→++→+

−+

−+

µµµµ

deuterium hydrogen

… using 800 GeV protons from the Tevatron

The NuSea Collaboration

May 2005 CTEQ Summer School 21

FNAL E866 – the NuSea Collaboration

Homework Problem: How does this experiment tell us about the light-quark flavor asymmetry in the nucleon sea?

May 2005 CTEQ Summer School 22

Inclusive jet productionat the Tevatron collider

CDF collaboration: 33 data points at central rapidity (-0.7 < η < 0.7)

D0 collaboration: 90 data points in five rapidity bins (-3 < η < 3)

TeV ~at jet 2sXpp +→+

May 2005 CTEQ Summer School 23

D0 Collaboration, Inclusive jet production in ppbar collisions, PRL 86, 1707 (2001).

May 2005 CTEQ Summer School 24

D0 Collaboration, Inclusive jet production in ppbar collisions, PRL 86, 1707 (2001).

May 2005 CTEQ Summer School 25

Lepton charge asymmetry from W+/W- production (CDF collaboration)

lyA versus)/()( −+−+ +−= σσσσHomework Problem: What can the asymmetry A tell us about the PDF’s?

May 2005 CTEQ Summer School 26

CDF Collaboration, Measurement of the lepton charge asymmetry in W boson decays produced by ppbar collisions, PRL 81, 5754 (1998).