May 2005CTEQ Summer School25 4/ Examples of PDF Uncertainty.

May 2005 CTEQ Summer School 1

4/Examples of PDF Uncertainty


Estimate the uncertainty on the predicted cross section for ppbar W+X at the Tevatron collider.

global 2

local 2’s


Each experiment defines a “prediction” and a “range”.This figure shows the 2 = 1 ranges.


This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled 2).


The final result is an uncertainty range for the prediction of W.

Survey of wBlpredictions (by R. Thorne) …

PDF set energy swBln [nb] PDF uncert

Alekhin Tevatron 2.73 0.05

MRST2002 Tevatron 2.59 0.03

CTEQ6 Tevatron 2.54 0.10

Alekhin LHC 21.5 0.6

MRST2002 LHC 20.4 0.4

CTEQ6 LHC 20.5 0.8


Inclusive W production at the Tevatron, Run 2(K factor for NNLO/NLO = 1.037 has been applied)

Red: 1 + 40 e.v. basis sets Blue: full uncertainty range 2.63 0.09 nbOrange: MRST prediction 2.690.11 nbGreen: Latest CDF value 2.7800.0140.0600.167 nbPurple: Latest D0 value 2.8650.0080.0750.186 nb


Red: 1 + 40 e.v. basis setsPurple: Full uncertainty range (error ellipse)Blue: Uncorrelated ranges, roughly 3% each

The error ellipse for W and Z production at the Tevatron, Run 2


Error ellipse for W and Z production at the LHC

Red: 1 + 40 e.v. basis setsBlue: uncorrelated rangesPurple: Full uncertainty range(error ellipse)


W production at the LHC is sensitive to the gluon distribution function.

Tevatron: W production can occur by a LO process with valence quarks.

LHC: The LO contribution must involve a sea quark; and there is an NLO contribution from a gluon.


How well can we determine the value of S( MZ ) from Global Analysis?

For each value of S, find the best global fit. Then look at the 2 value for each experiment as a function of S.


Each experiment defines a “prediction” and a “range”.This figure shows the 2 = 1 ranges.

Particle data group (shaded strip) is 0.1170.002.

The fluctuations are larger than expected for normal statistics. The vertical lines have 2

global=100,s(MZ)=0.11650.0065



Uncertainties of LHC parton-parton luminosities

212121 dxdxsxxsxfxfCsLum jiji

ij )ˆ()()()ˆ(,

Provides simple estimates of PDF uncertainties at the LHC.


PDF uncertainty for inclusive jet production at CDF and D0

Run 1 dataCTEQ6.1 – the 40 eigenvector basis sets


(D-T)/T for Run 1 dataCTEQ6.1: the 40 eigenvector basis sets


The 40 eigenvector basis sets – used to calculate PDF uncertainty in the Hessian method


Predictions for Run 2 at CDF and D0

The boundaries are the full uncertainty range from the “Master Formula”.


CTEQ6.1The u-quark PDf and its full uncertainty band.(This representation is potentially misleading because low-x and high-x are correlated!)


Comparison of MRST and CTEQ6… u-quark


Comparison of MRST and CTEQ6… u-quark


CTEQ6.1The gluon PDf and its full uncertainty band.(This representation is potentially misleading because low-x and high-x are correlated!)


Comparison of MRST and CTEQ6… gluon


Comparison of MRST and CTEQ6… gluon


Theoretical uncertainties may also be important, but are more difficult to assess.

Parameterization of f(x,Q0) at Q0=1.3 GeV – a nonperturbative function

Higher order QCD corrections ( NNLO perturbation theory)


5/Outlook


Parton distribution functions are a necessary theoretical infrastructure for hadron colliders.

Tools now exist to assess the PDF uncertainties.

Certain advances will be important for making accurate predictions for the LHC.


HERA2LHC and TEV4LHC

New Data to include in the global analysisNuTeV, HERA II, Tevatron Run 2

Extend the accuracy of the global analysis to NNLO perturbation theory.

May 2005CTEQ Summer School25 4/ Examples of PDF Uncertainty.

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