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 = has been applied) Red: e.v. basis setsBlue: full uncertainty range 2.63  0.09 nb Orange: MRST prediction 2.69  0.11 nb Green: Latest CDF value    nb Purple: Latest D0 value    nb

May 2005CTEQ Summer School31 Red: 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: 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  The fluctuations are larger than expected for normal statistics. The vertical lines have  2 global =100,  s (MZ)= 

May 2005CTEQ Summer School36

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 School49 5/ Outlook

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.