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

October 2004CTEQ Meeting2 PDF uncertainty and inclusive jet production

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

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

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

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

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

October 2004CTEQ Meeting8 PDF uncertainty — the method

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.

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

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

October 2004CTEQ Meeting12 This figure shows broader ranges for each experiment based on the “90% confidence level” (cumulative distribution function of the rescaled  2 ).

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.

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  The fluctuations are larger than expected for normal statistics. The vertical lines have  2 global =100;  s (M Z )= 

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.

October 2004CTEQ Meeting16 PDF uncertainty for W/Z production

October 2004CTEQ Meeting17 Inclusive Z production at the Tevatron, Run 2 (K factor for NNLO/NLO = has been applied) Red: alternativesBlue: full uncertainty range  nb Green: Latest CDF value Purple: Latest D0 value    nb    nb

October 2004CTEQ Meeting18 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

October 2004CTEQ Meeting19 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

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

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

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

October 2004CTEQ Meeting23 Error ellipse for W and Z production at the LHC Red: e.v. basis sets Blue: uncorrelated ranges Purple: Full uncertainty range (error ellipse)

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

October 2004CTEQ Meeting25 Why calculations don’t agree

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

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

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 %

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  wttot  (W)  wttot  (W)  ResBos  (W -> l  2588   6 MRST’02  (W)  LHC SigmaTot1  (W -> l  wttot  (W)  wttot  (W)  ResBos  (W -> l    52 MRST’02  (W)   s = 1.96 TeV  s = 14 TeV

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 )

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

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

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.

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

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

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

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.