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 d=16 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.Comment: 30 pages, Latex. Reference added. Normalization of Hessian matrix
  changed to HEP standar

Brock, R.

Casey, D.

Huston, J.

Kalk, J.

Lai, H. L.

Pumplin, J.

Stump, D.

Tung, W. K.

English

arXiv

D. Stump

J. Pumplin

R. Brock

D. Casey

J. Huston

J. Kalk

H. L. Lai

W. K. Tung

Crossref

Physical Review D

Uncertainties of predictions from parton distribution functions. I. The Lagrange multiplier 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 d=16 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.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 d=16 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

Lai, H.L.

Tung, W.K.

CERN Document Server

Uncertainties of predictions from parton distribution functions: 2, the Hessian method

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

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 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.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 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

Uncertainties of Predictions from Parton Distribution Functions: 1, the Lagrange Multiplier Method

Uncertainties of predictions from parton distribution functions II: the
  Hessian method

Uncertainties of predictions from parton distribution functions II: the Hessian method

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