progress on studying uncertainties of parton

A New Generation of Parton Distributions with Uncertainties from Global QCD Analysis What’s new in this Global QCD Analysis of PDF’s? • New Data, + all available correlated systematic errors (old & new) • New methods and techniques of analysis unable quantitative error treatments and reliable uncertainty studies: (J. Pumplin, D. Stump)

New Results and physical applications • New generation of CTEQ PDF’s: eigenvector sets which characterize the behavior of overall χ2 in the neighborhood of the global minimum; • Precision W/Z physics at the Tevatron/LHC • Parton Luminosities at the Tevatron, LHC, RHIC, VLHC Þ predictions on X-sections and their uncertainties for Higgs-, top-productions, high pT jets, ... etc.

Outlook

J. Pumplin, D.R. Stump, J. Huston, H.L. Lai, P. Nadolsky, and W.K. Tung Michigan State Univ. hep-ph/0201195


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Global QCD Analysis in a Nutshell Master Equation for QCD Parton Model { the Factorization Theorem m M m ^ Q M   a FA(x; ; ) = fA(x; ) Fa (x; ; )+O(( )2) Q Q

X



a

 Q

H

H F^a

FA

a

A

fAa

A

Experimental Input

Q

Hard Cross-section perturbative calculable (may contain snLogn(M/Q))

Parton Dist. Fn. Non-Perturbative Parametrization at Q0 GLAP Evolution to Q

Sources of Uncertainties and Challenges: (and uncertainties on errors!)
Experimental errors;
Parametrization dependence;
Higher-order corrections; Large Logarithms;
Power-law (higher twist) corrections.

Experimental Input: Phyical Processes & Experiments DIS

SLAC BCDMS NMC, E665 H1, ZEUS

*, W, Z

eN N

q

N N g

DY

pN N kN pN

Dir.Ph. pN N kN pN

CDHS, CHARM CCFR CHORUS

q q

E605, E772 NA51 E866

*, W, Z

q q

q

*, W, Z

CDF, D0

(dir)

g

q

WA70, UA6 E706 CDF, D0

Jet Inc. pp

CDF, D0

Q (GeV)

100 100

101

102

101

1/X

102

103

104

DIS (fixed target) HERA (’94) DY W-asymmetry Direct-γ Jets

The kinematic range in the (x, Q) plane of data points included in a typical global QCD analysis – CTEQ5

Whats new/old since CTEQ5? z New Data ◆

◆

◆

◆

new DIS data from H1/ZEUS jet cross sections from D0 as a function of η updated E866 DrellYan deuteron/proton ratio re-analyzed CCFR F2

z Old data ◆ ◆

BCDMS DIS NMC DIS now use measurements at separate energies with full correlation info

◆ ◆ ◆ ◆ ◆

CCFR F3 E665 DIS E605 DY CDF W asym CDF inclusive jets


    !" #%$'&%(*) +-,/. &(1032/&*45) 06) 785 ? ?EGF? H FC ? < 2NMO0M = BDC ? : JK L ? < 0*$&O7P Q 9:; < >? I : I ~ /~ C < Bv H ‰WŠ/‹ g q ~ @A #%f $'&-40 06) 5€,WMP‚M+&O0V&WPc( ) . .„ƒ& … v'†6‡bB 0*H$&O7Pc&O06) u'M/.„+ˆ72/&. … ~ ‡bB u7NPDPc&'u*06) 785'(Œ[‚7P(1Q(10V&W+ZM06) u-&WPDPX7PX( U Ža/ƒ/. ) (O$&2&OT/,/&WP\) +&W50M/.N&P\Pc7NPc(' w ? ) (0*$&’ (10M/52NMPc2Z2/&O“) M06) 785”7[0*$&3P^M/5278+•a/5uO7P\P^&W. M0V&2 ‘ &P\Pc7NP U ? ‘  ~ ) (G0*$&–H’ (10M/52NMPc22/&*“/) MO06) 785”—7[? 0*$&˜0*$ B u78+-,/. &*0V&. Q u7NPDPc&. MO0V&'2™ (1Q(10V&W+ZM06) u-&WPDPX7P785 C U

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high Q

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10

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x0.008

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x0.00253

x0.00161

x0.00102

ZEUS data low x values

x0.0013

x0.0008

x0.000632

x0.0004

x0.000253

x0.000161

0

0.25

0.5

0.75

1

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10000

x0.65

x0.4

x0.25

x0.18

x0.13

x0.08

x0.05

x0.032

x0.021

x0.013



 ZEUS

Collaboration: S. Chekanov et al., Eur. Phys. J. C 21 (2001) 443 [hep-ex/0105090].

Comparison of the CTEQ6M t to the ZEUS data in separate x bins. The data points include the estimated corrections for systematic errors. The error bars are statistical errors only.

F2 x,Q2 
offset

2.5

F2 x,Q2 
offset

11

0

20

40

60

80

4

2

k

0 i

k ki

2

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i

4

0

20

40

60

80

4

2

0 Di Ti Αi

2

ZEUS

4

i

Dicorrected = Di

i

k=1

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Histogram of residuals for the ZEUS data. The curve is a Gaussian of width X 1. (a)
= (D rb T )= . (b) A similar comparison but without the corrections for systematic errors on the data points.

N

100

N

12

0 r

1

2

3

1

1


1

2

2


2

3

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4

3

4

k

k

1

2

3

4


2


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NMC shifts

0 r

1

2

3

1

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4

Systematic shifts for the ZEUS data (10 systematic errors) k 1 2 3 4 5 6 7 8 9 10 r^ 1:67 0:67 1:25 0:44 0:00 1:07 1:28 0:62 0:40 0:21 Systematic shifts for the NMC data (11 systematic errors) k 1 2 3 4 5 6 7 8 9 10 11 r^ 0:67 0:81 0:35 0:25 0:05 0:70 0:31 1:05 0:61 0:26 0:22

15

0.00001

0.001

0.1

100

200

300 pT
GeV

D0 Jet cross section

400 500

1.  10
6

0.0001

0.01

1

100

100

200 300 pT
GeV

CDF jet cross section

400

500

 D

Collaboration: B. Abbott et al.; CDF Collaboration: T. Aolder et al..



Comparison of the CTEQ6M t to the inclusive jet data. (a) D (the boundary values of the 5 rapidity bins are 0; 0:5; 1:0; 1:5; 2:0 and 3:0). (b) CDF (central rapidity, 0:1 < jj < 0:7).

dΣdpT
nbGeV

10

dΣdpT
nbGeV

data
theorytheory versus pT
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0.5

1.5 1 0.5 0
0.5

0 Η 0.5

100 1.5 1 0.5 0
0.5

200

300

400

1.5 1 0.5 0
0.5

200

300

100

500 1.5 1 0.5 0
0.5

0.5 Η 1

100

1.5 Η 2

400

500

400

500

200

300

400

500

400

500

2 Η 3

100

200

300

1 Η 1.5

100

200

300

Closer comparison between CTEQ6M and the D jet data as fractional dierences. The Tevatron inclusive jet cross section implies a hard gluon: g (x) is large at large x. Recall CTEQ4HJ and CTEQ5HJ.

16

17

-50

0

50

-50 100

0

50

-50 100

0

50

100

50

100

200

250

300

350

Jet Transverse Energy

150

MRST

CTEQ4HJ

Statistical Errors only

CTEQ4M

400

GeV

0.4 0.3 0.2 0.1 0
0.1
0.2 100

200 300 pT
GeV

CDF inclusive jet

400

corrected data
theory theory

CDF inclusive jet cross section

CDF collaboration: T. Aolder, et al.

(D-T)/T


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a= 1

c20 + Dc2

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PDF Uncertainties z Use Hessian technique (T=10)

Gluon Uncertainty z Gluon is fairly wellconstrained up to an xvalue of 0.3 z New gluon is stiffer than CTEQ5M; not quite as stiff as CTEQ5HJ

±

Fractional Uncertainty

≈

-0.1

0

20

0.1 ≈

0

0.1

-0.2

-0.1

0

0.1

0.2

0.3

0.4

50

√s^ (GeV)

102

− Q-Q --> γ* (Z)

− Q-Q --> W+ (W-)

G-G

Luminosity function at TeV RunII

200

400

≈

≈ 0.1

-0.1

0 20

≈

0.1

-0.1

0

≈

≈

-0.1

0

0.1

-0.1

0

0.1

50

√s^

(GeV)

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Q-G --> γ*

Q-G --> W+

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Luminosity function at TeV RunII








 

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400

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0.1

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0

0.1

±

Fractional Uncertainty

0.2

50 102

^ √s (GeV)

200

− Q-Q --> W-

− Q-Q --> W+

G-G

500

Luminosity function at LHC

103

≈

≈

≈

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-0.1

0

0.1

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0

0.1

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0

0.1

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102

√s^

(GeV)

200

500

Q-G --> W-

Q-G --> W+

Q-G --> Z

Q-G --> γ*

Luminosity function at LHC



Fractional Uncertainty






  

 


    
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##

103

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Outlook This is only the very beginning of studying uncertainties in global QCD analysis in a quantitative manner This work demonstrates that the new techniques for global analysis developed recently are viable and practical. The new results are very useful for the physics programs of the Tevatron, Hera, and LHC, There is a lot of room for collaboration among theorists and experimentalists Many other sources of uncertainties in the overall global analysis have not yet been incorporated: Theoretical uncertainties due to higher-order PQCD corrections and resummation; Uncertainties introduced by the choice of parametrization have been explored extensively, but not yet quantitatively formulated. Heavy quark effects and charm production data in NC and CC experiments will be systematically analyzed

Þ More quantitative information on strange, charm, bottom distributions. Continued progress in this venture is of vital importance for our understanding of the parton structure of hadrons (fundamental physics of its own right), for precision SM physics studies at future colliders, and for New Physics searches.


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E866

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