D. Casey

Uncertainties of predictions from parton distribution functions. II. The Hessian method

We develop a general method to quantify the uncertainties of parton distribution functions and their physical predictions, with emphasis on incorporating all relevant experimental constraints. The method uses the Hessian formalism to study an effective chi-squared function that quantifies the fit between theory and experiment. Key ingredients are a recently developed iterative procedure to calculate the Hessian matrix in the difficult global analysis environment, and the use of parameters defined as components along appropriately normalized eigenvectors. The result is a set of 2D eigenvector basis parton distributions (where

Uncertainties of Predictions from Parton Distribution Functions I: the Lagrange Multiplier Method

densuremath{approx}16

tt̄ production cross section in pp̄ collisions at √s = 1.8 TeV

is the number of parton parameters) from which the uncertainty on any physical quantity due to the uncertainty in parton distributions can be calculated. We illustrate the method by applying it to calculate uncertainties of gluon and quark distribution functions, W boson rapidity distributions, and the correlation between W and Z production cross sections.

Limits on [Formula Presented] and [Formula Presented] couplings from [Formula Presented] boson pair production

We apply the Lagrange Multiplier method to study the uncertainties of physical predictions due to the uncertainties of parton distribution functions (PDFs), using the cross section for W production at a hadron collider as an archetypal example. An effective chi-squared function based on the CTEQ global QCD analysis is used to generate a series of PDFs, each of which represents the best fit to the global data for some specified value of the cross section. By analyzing the likelihood of these alterative hypotheses, using available information on errors from the individual experiments, we estimate that the fractional uncertainty of the cross section due to current experimental input to the PDF analysis is approximately 4% at the Tevatron, and 8-10% at the LHC. We give sets of PDFs corresponding to these up and down variations of the cross section. We also present similar results on Z production at the colliders. Our method can be applied to any combination of physical variables in precision QCD phenomenology, and it can be used to generate benchmarks for testing the accuracy of approximate methods based on the error matrix.

Limits on anomalous [Formula Presented] and [Formula Presented] couplings

Results are presented on a measurement of the t (t) over bar pair production cross section in p (p) over bar collisions at roots=1.8 TeV from nine independent decay channels. The data were collected by the D empty set experiment during the 1992-1996 run of the Fermilab Tevatron Collider. A total of 80 candidate events is observed with an expected background of 38.8+/-3.3 events. For a top quark mass of 172.1 GeV/c(2), the measured cross section is 5.69+/-1.21(stat)+/-1.04(syst) pb.Results are presented on a measurement of the ttbar pair production cross section in ppbar collisions at sqrt{s} = 1.8 TeV from nine independent decay channels. The data were collected by the Dzero experiment during the 1992-1996 run of the Fermilab Tevatron Collider. A total of 80 candidate events are observed with an expected background of 38.8 +- 3.3 events. For a top quark mass of 172.1 GeV/c^2, the measured cross section is 5.69 +- 1.21 (stat) +- 1.04 (sys) pb.

Uncertainties of Parton Distribution Functions and Their Implications on Physical Predictions

The results of a search for W boson pair production in pp collisions at √s=1.8TeV with subsequent decay to eμ, ee, and μμ channels are presented. Five candidate events are observed with an expected background of 3.1±0.4 events for an integrated luminosity of approximately 97pb -1 . Limits on the anomalous couplings are obtained from a maximum likelihood fit of the E T spectra of the leptons in the candidate events. Assuming identical WWγ and WWZ couplings, the 95% C.L. limits are -0.62<Δκ<0.77 (λ=0) and -0.53<λ<0.56 (Δκ=0) for a form factor scale Λ=1.5TeV.