4/ examples of pdf uncertainty
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4/ Examples of PDF Uncertainty. Estimate the uncertainty on the predicted cross section for pp bar W+X at the Tevatron collider. global c 2. local c 2 ’s. Each experiment defines a “prediction” and a “range”. This figure shows the Dc 2 = 1 ranges. - PowerPoint PPT PresentationTRANSCRIPT
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May 2005 CTEQ Summer School 1
4/Examples of PDF Uncertainty
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May 2005 CTEQ Summer School 2
Estimate the uncertainty on the predicted cross section for ppbar W+X at the Tevatron collider.
global 2
local 2’s
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May 2005 CTEQ Summer School 3
Each experiment defines a “prediction” and a “range”.This figure shows the 2 = 1 ranges.
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May 2005 CTEQ Summer School 4
This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled 2).
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May 2005 CTEQ Summer School 5
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
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May 2005 CTEQ Summer School 6
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
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May 2005 CTEQ Summer School 7
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
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May 2005 CTEQ Summer School 8
Error ellipse for W and Z production at the LHC
Red: 1 + 40 e.v. basis setsBlue: uncorrelated rangesPurple: Full uncertainty range(error ellipse)
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May 2005 CTEQ Summer School 9
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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May 2005 CTEQ Summer School 10
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.
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May 2005 CTEQ Summer School 11
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
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May 2005 CTEQ Summer School 12
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May 2005 CTEQ Summer School 13
Uncertainties of LHC parton-parton luminosities
212121 dxdxsxxsxfxfCsLum jiji
ij )ˆ()()()ˆ(,
Provides simple estimates of PDF uncertainties at the LHC.
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May 2005 CTEQ Summer School 14
PDF uncertainty for inclusive jet production at CDF and D0
Run 1 dataCTEQ6.1 – the 40 eigenvector basis sets
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May 2005 CTEQ Summer School 15
(D-T)/T for Run 1 dataCTEQ6.1: the 40 eigenvector basis sets
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May 2005 CTEQ Summer School 16
The 40 eigenvector basis sets – used to calculate PDF uncertainty in the Hessian method
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May 2005 CTEQ Summer School 17
Predictions for Run 2 at CDF and D0
The boundaries are the full uncertainty range from the “Master Formula”.
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May 2005 CTEQ Summer School 18
CTEQ6.1The 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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May 2005 CTEQ Summer School 19
Comparison of MRST and CTEQ6… u-quark
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May 2005 CTEQ Summer School 20
Comparison of MRST and CTEQ6… u-quark
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May 2005 CTEQ Summer School 21
CTEQ6.1The gluon PDf and its full uncertainty band.(This representation is potentially misleading because low-x and high-x are correlated!)
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May 2005 CTEQ Summer School 22
Comparison of MRST and CTEQ6… gluon
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May 2005 CTEQ Summer School 23
Comparison of MRST and CTEQ6… gluon
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May 2005 CTEQ Summer School 24
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)
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May 2005 CTEQ Summer School 25
5/Outlook
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May 2005 CTEQ Summer School 26
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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May 2005 CTEQ Summer School 27
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.