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4/ Examples of PDF Uncertainty

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.

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4/ Examples of PDF Uncertainty

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  1. 4/ Examples of PDF Uncertainty CTEQ Summer School

  2. Estimate the uncertainty on the predicted cross section for ppbar W+X at the Tevatron collider. global c2 local c2’s CTEQ Summer School

  3. Each experiment defines a “prediction” and a “range”. This figure shows the Dc2 = 1 ranges. CTEQ Summer School

  4. This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled c2). CTEQ Summer School

  5. The final result is an uncertainty range for the prediction of sW. Survey of swBlnpredictions (by R. Thorne) … 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 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 CTEQ Summer School

  7. 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 CTEQ Summer School

  8. 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) 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. CTEQ Summer School

  10. 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. CTEQ Summer School

  11. 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 Dc2global=100, as(MZ)=0.11650.0065 CTEQ Summer School

  12. CTEQ Summer School

  13. Uncertainties of LHC parton-parton luminosities Provides simple estimates of PDF uncertainties at the LHC. CTEQ Summer School

  14. PDF uncertainty for inclusive jet production at CDF and D0 Run 1 data CTEQ6.1 – the 40 eigenvector basis sets CTEQ Summer School

  15. (D-T)/T for Run 1 data CTEQ6.1: the 40 eigenvector basis sets CTEQ Summer School

  16. The 40 eigenvector basis sets – used to calculate PDF uncertainty in the Hessian method CTEQ Summer School

  17. Predictions for Run 2 at CDF and D0 The boundaries are the full uncertainty range from the “Master Formula”. CTEQ Summer School

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

  19. Comparison of MRST and CTEQ6 … u-quark CTEQ Summer School

  20. Comparison of MRST and CTEQ6 … u-quark CTEQ Summer School

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

  22. Comparison of MRST and CTEQ6 … gluon CTEQ Summer School

  23. Comparison of MRST and CTEQ6 … gluon 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) CTEQ Summer School

  25. 5/ Outlook 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. CTEQ Summer School

  27. 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. CTEQ Summer School

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