May 2005CTEQ Summer School25 4/ Examples of PDF Uncertainty.
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May 2005CTEQ Summer School25 4/ Examples of PDF Uncertainty
May 2005CTEQ Summer School26 Estimate the uncertainty on the predicted cross section for pp bar W+X at the Tevatron collider. global 2 local 2 ’s
May 2005CTEQ Summer School27 Each experiment defines a “prediction” and a “range”. This figure shows the 2 = 1 ranges.
May 2005CTEQ Summer School28 This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled 2 ).
May 2005CTEQ Summer School29 The final result is an uncertainty range for the prediction of W. Survey of w B l predictions (by R. Thorne) … PDF setenergy s w B ln [nb] PDF uncert AlekhinTevatron2.73 0.05 MRST2002Tevatron2.59 0.03 CTEQ6Tevatron2.54 0.10 AlekhinLHC21.5 0.6 MRST2002LHC20.4 0.4 CTEQ6LHC20.5 0.8
May 2005CTEQ Summer School30 Inclusive W production at the Tevatron, Run 2 (K factor for NNLO/NLO = 1.037 has been applied) Red: 1 + 40 e.v. basis setsBlue: 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
May 2005CTEQ Summer School31 Red: 1 + 40 e.v. basis sets Purple: Full uncertainty range (error ellipse) Blue: Uncorrelated ranges, roughly 3% each The error ellipse for W and Z production at the Tevatron, Run 2
May 2005CTEQ Summer School32 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)
May 2005CTEQ Summer School33 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.
May 2005CTEQ Summer School34 How well can we determine the value of S ( M Z ) 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.
May 2005CTEQ Summer School35 Each experiment defines a “prediction” and a “range”. This figure shows the 2 = 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 2 global =100, s (MZ)=0.1165 0.0065
May 2005CTEQ Summer School37 Uncertainties of LHC parton-parton luminosities Provides simple estimates of PDF uncertainties at the LHC.
May 2005CTEQ Summer School38 PDF uncertainty for inclusive jet production at CDF and D0 Run 1 data CTEQ6.1 – the 40 eigenvector basis sets
May 2005CTEQ Summer School39 (D-T)/T for Run 1 data CTEQ6.1: the 40 eigenvector basis sets
May 2005CTEQ Summer School40 The 40 eigenvector basis sets – used to calculate PDF uncertainty in the Hessian method
May 2005CTEQ Summer School41 Predictions for Run 2 at CDF and D0 The boundaries are the full uncertainty range from the “Master Formula”.
May 2005CTEQ Summer School42 CTEQ6.1 The u-quark PDf and its full uncertainty band. (This representation is potentially misleading because low-x and high-x are correlated!)
May 2005CTEQ Summer School43 Comparison of MRST and CTEQ6 … u-quark
May 2005CTEQ Summer School44 Comparison of MRST and CTEQ6 … u-quark
May 2005CTEQ Summer School45 CTEQ6.1 The gluon PDf and its full uncertainty band. (This representation is potentially misleading because low-x and high-x are correlated!)
May 2005CTEQ Summer School46 Comparison of MRST and CTEQ6 … gluon
May 2005CTEQ Summer School47 Comparison of MRST and CTEQ6 … gluon
May 2005CTEQ Summer School48 Theoretical uncertainties may also be important, but are more difficult to assess. Parameterization of f(x,Q 0 ) at Q 0 =1.3 GeV – a nonperturbative function Higher order QCD corrections ( NNLO perturbation theory)
May 2005CTEQ Summer School50 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.
May 2005CTEQ Summer School51 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.