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October 2004CTEQ Meeting1 Parton distribution uncertainty and W and Z production at hadron colliders Dan Stump Department of Physics and Astronomy Michigan State University

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October 2004CTEQ Meeting2 PDF uncertainty and inclusive jet production

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October 2004CTEQ Meeting3 PDF uncertainty and the cross section for inclusive jet production at the Tevatron. Run 1: CTEQ6.1, central fit and 40 Eigenvector Basis Sets

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October 2004CTEQ Meeting4 Comparing the CDF data (Run 1) and the NLO calculation with CTEQ6.1 Green: 1 + 40 alternative sets; Red: full uncertainty range

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October 2004CTEQ Meeting5 The “master equation” for the Hessian method asymmetric errors, or one could use the Sullivan-Nadolsky formula

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October 2004CTEQ Meeting6 Inclusive jet cross section for Run 2, in 5 rapidity bins, predicted by CTEQ6.1. Red: central prediction; Blue: full uncertainty range

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October 2004CTEQ Meeting7 Inclusive jet cross section for the LHC, predicted by CTEQ6.1. central prediction + 40 alternatives

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October 2004CTEQ Meeting8 PDF uncertainty — the method

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October 2004CTEQ Meeting9 Uncertainties of Parton Distribution Functions —a major challenge for global analysis The total cross sections for W and Z production were among the first examples to which we applied the new methods of uncertainty analysis. W and Z were good test cases.

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October 2004CTEQ Meeting10 Estimate the uncertainty on the predicted cross section for pp bar W+X at the Tevatron collider. global 2 local 2 ’s

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October 2004CTEQ Meeting11 Each experiment defines a “prediction” and a “range”. This figure shows the 2 = 1 ranges.

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October 2004CTEQ Meeting12 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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October 2004CTEQ Meeting13 The final result is an uncertainty range for the prediction of W. Survey of w B l predictions (by R. Thorne, 2002) PDF setenergy w B ln [nb] PDF uncert AlekhinTevatron2.73 0.05 MRST2002Tevatron2.59 0.03 CTEQ6Tevatron2.54 0.10 AlekhinLHC215. 6. MRST2002LHC204. 4. CTEQ6LHC205. 8.

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October 2004CTEQ Meeting14 Each experiment defines a “prediction” and a “range”. This figure shows the 2 = 1 ranges for the value of S. 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 (M Z )=0.1165 0.0065.

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October 2004CTEQ Meeting15 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.

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October 2004CTEQ Meeting16 PDF uncertainty for W/Z production

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October 2004CTEQ Meeting17 Inclusive Z production at the Tevatron, Run 2 (K factor for NNLO/NLO = 1.045 has been applied) Red: 1 + 40 alternativesBlue: full uncertainty range 0.258 0.008 nb Green: Latest CDF value Purple: Latest D0 value 0.2539 0.0033 0.0046 0.0152 nb 0.2649 0.0039 0.0099 0.0172 nb

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October 2004CTEQ Meeting18 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

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October 2004CTEQ Meeting19 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

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October 2004CTEQ Meeting20 Are the “up” and “down” displacements along the eigenvector directions symmetric?

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October 2004CTEQ Meeting21 Z production at the LHC Red: 1 + 40 e.v. basis setsBlue: Full uncertainty range 1.95 0.07 nb

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October 2004CTEQ Meeting22 W production at the LHC Red: 1 + 40 e.v. basis setsBlue: Full uncertainty range 19.5 0.8 nb Orange: MRST prediction 20.0 0.8 nb

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October 2004CTEQ Meeting23 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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October 2004CTEQ Meeting24 ratio The PDF uncertainty in the ratio Z / W is very small possible test for new physics.

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October 2004CTEQ Meeting25 Why calculations don’t agree

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October 2004CTEQ Meeting26 W production at the Tevatron; MRST calculations from their paper on Theoretical Errors CTEQ 2.63 0.09 nb

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October 2004CTEQ Meeting27 W production at the LHC; MRST calculations from their paper on Theoretical Errors CTEQ 19.5 0.8 nb

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October 2004CTEQ Meeting28 Other theoretical uncertainties Branching ratio Treatment of W width (off shell W) EW parameter values, e.g., CKM matrix Treatment of heavy quark mass effects may lead to differences of order 1 %

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October 2004CTEQ Meeting29 A survey of results from different programs (Pavel Nadolsky, C P Yuan) ProgramCross sec (nb)CTEQ6MMRST2002 Tev’n Run 2 SigmaTot1 (W -> l 25262548 wttot (W) 0.1068 25392562 wttot (W) 0.1084 25772601 ResBos (W -> l 2588 62606 6 MRST’02 (W) 0.1068 2600 LHC SigmaTot1 (W -> l 2002219944 wttot (W) 0.1068 2013720066 wttot (W) 0.1084 2043920367 ResBos (W -> l 20616 5220690 52 MRST’02 (W) 0.1068 20400 s = 1.96 TeV s = 14 TeV

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October 2004CTEQ Meeting30 P T dependence of vector boson production Collins, Soper and Sterman (CSS) formalism for p T resummation, schematically, BLNY parametrization (Brock, Landry, Nadolsky, Yuan) i.e., 4 N.P. parameters (g 1,g 2,g 3,b max )

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October 2004CTEQ Meeting31 The BLNY fit to E288, E605, CDF Z, and D0 Z data

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October 2004CTEQ Meeting32 Standard 2 = 1 parameter errors … but are such small uncertainties realistic?

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October 2004CTEQ Meeting33 Reassess the parameter uncertainties, using the methods that we have used for PDF uncertainties. The most interesting parameter, and which should have the largest uncertainty, is g 2. Method Scan the BLNY fit versus g 2 values. For a range of g 2 values, construct the best fit to g 1 and g 3. Then look how 2 varies with g 2.

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October 2004CTEQ Meeting34 A 2 “parabola” for each experiment… … implies an allowed range for the value of g 2 for each experiment. b max = 0.5 GeV -1

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October 2004CTEQ Meeting35 A 2 “parabola” for each experiment… … implies an allowed range for the value of g 2 for each experiment. b max = 1.12 GeV -1

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October 2004CTEQ Meeting36 Comparison of CDF Z and D0 Z data (Run 1) to resummation calculation with BLNY parametrization

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October 2004CTEQ Meeting37 More work needs to be done to obtain a final uncertainty range for g 2. Our larger goal is to include p T cross sections in the global analysis; i.e., simultaneously to fit PDF parameters and resummation parameters, for both W and Z production.

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