Examples of PDF Uncertainty

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4/ Examples of PDF Uncertainty
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Estimate the uncertainty on the predicted cross
section for ppbar ? WX at the Tevatron collider.
global c2
local c2s
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Each experiment defines a prediction and a
range. This figure shows the Dc2 1 ranges.
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This figure shows broader ranges for each
experiment based on the 90 confidence level
(cumulative distribution function of the rescaled
c2).
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The final result is an uncertainty range for the
prediction of sW.
Survey of sw?Bln predictions (by R. Thorne)
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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 nb Orange MRST
prediction 2.69?0.11 nb Green Latest CDF value
2.780?0.014?0.060?0.167 nb Purple Latest D0
value 2.865?0.008?0.075?0.186 nb
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The error ellipse for W and Z production at the
Tevatron, Run 2
Red 1 40 e.v. basis sets Purple Full
uncertainty range (error ellipse) Blue
Uncorrelated ranges, roughly ?3 each
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Error ellipse for W and Z production at the LHC
Red 1 40 e.v. basis sets Blue uncorrelated
ranges Purple Full uncertainty range (error
ellipse)
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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.
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How well can we determine the value of aS( MZ )
from Global Analysis?
For each value of aS, find the best global fit.
Then look at the c2 value for each experiment as
a function of aS.
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Each experiment defines a prediction and a
range. This figure shows the Dc2 1 ranges.
Particle data group (shaded strip) is 0.117?0.002.
The fluctuations are larger than expected for
normal statistics. The vertical lines have
Dc2global100, as(MZ)0.1165?0.0065
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Uncertainties of LHC parton-parton luminosities
Provides simple estimates of PDF uncertainties at
the LHC.
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PDF uncertainty for inclusive jet production at
CDF and D0
Run 1 data CTEQ6.1 the 40 eigenvector basis sets
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(D-T)/T for Run 1 data CTEQ6.1 the 40
eigenvector basis sets
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The 40 eigenvector basis sets used to calculate
PDF uncertainty in the Hessian method
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Predictions for Run 2 at CDF and D0 The
boundaries are the full uncertainty range from
the Master Formula.
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CTEQ6.1 The u-quark PDf and its full uncertainty
band. (This representation is potentially
misleading because low-x and high-x are
correlated!)
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Comparison of MRST and CTEQ6 u-quark
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Comparison of MRST and CTEQ6 u-quark
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CTEQ6.1 The gluon PDf and its full uncertainty
band. (This representation is potentially
misleading because low-x and high-x are
correlated!)
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Comparison of MRST and CTEQ6 gluon
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Comparison of MRST and CTEQ6 gluon
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• Theoretical uncertainties may also be important,
  but are more difficult to assess.
• Parameterization of f(x,Q0) at Q01.3 GeV a
  nonperturbative function
• Higher order QCD corrections ( NNLO perturbation
  theory)

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5/ Outlook
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• ? 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.

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• HERA2LHC and TEV4LHC
• New Data to include in the global analysis
• NuTeV, HERA II, Tevatron Run 2
• Extend the accuracy of the global analysis to
  NNLO perturbation theory.