Abstract
We discuss how to apply the Hessian method (i) to predict the impact of a new data set (or sets) on the parton distribution functions (PDFs) and their errors, by producing an updated best-fit PDF and error PDF sets, such as the CTEQ-TEA PDFs; (ii) to predict directly the effect of a new data set on the PDF errors of any other set of observables, without the need to recalculate using the new error PDFs; and (iii) to transform the original set into a reduced set of error PDFs which is optimized for a specific set of observables to reproduce the PDF-induced uncertainties to any specified precision. We present a software package, ePump (Error PDF Updating Method Package), that can be used to update or optimize a set of PDFs, including the best-fit PDF set and Hessian eigenvector pairs of PDF sets (i.e., error PDFs), and to update any other set of observables. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the Large Hadron Collider. Special care is given to discuss the assumptions made and the limitations of this theoretical framework compared to a treatment by the full global-analysis program.
Highlights
Predictions for high-energy cross sections at the Large Hadron Collider and other colliders require the use of parton distribution functions (PDFs), which supply the long-distance hadronic contribution
We extend the method proposed in Ref. [13] and develop a software package called EPUMP (Error PDF Updating Method Package) to be used to updated any Hessian PDF sets obtained from an earlier global analysis
In the typical QCD global analysis of PDFs, the long computing time that is necessary to obtain preliminary results can slow down the improvement of the PDFs, even when just including a few LHC jet, high mass Drell-Yan, W, Z, and top quark data sets in the fits at the next-to-next-toleading order (NNLO) accuracy in QCD interaction
Summary
Predictions for high-energy cross sections at the Large Hadron Collider and other colliders require the use of parton distribution functions (PDFs), which supply the long-distance hadronic contribution. A version of this method has been included in the XFITTER package [15], in which it is called Hessian profiling The advantage of this Hessian updating method over the Monte Carlo reweighting method is that it directly works with the (small set of) Hessian PDFs and it is a simpler and much faster way to estimate the effects of the new data. This method directly calculates the minimum of the χ2 function within the Hessian approximation and was shown by Paukkunen and Zurita to be equivalent to the Monte Carlo reweighting method, if the Giele-Keller weights [7] (appropriately scaled to include the tolerance criterion) are used in that method.
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