Implications of hadron collider observables on parton distribution function uncertainties

Abstract

Standard parton distribution function sets do not have rigorously quantified uncertainties. In recent years it has become apparent that these uncertainties play an important role in the interpretation of hadron collider data. In this paper, using the framework of statistical inference, we illustrate a technique that can be used to efficiently propagate the uncertainties to new observables, assess the compatibility of new data with an initial fit, and, in case the compatibility is good, include the new data in the fit.

Neural network determination of parton distributions: the nonsinglet case

“…An interesting suggestion [7] is to use Bayesian inference based on the data in order to update the existing prior knowledge of PDFs, as summarized e.g. by a Monte Carlo sample based on an existing parton set.…”

“…The basic idea is to combine a Monte Carlo sampling of the probability measure on the space of functions that one is trying to determine (as in the approach of ref. [7]) with the use of neural networks as universal unbiased interpolating functions. In a Monte Carlo approach, the function with error -the up quark distribution, say -is given as a Monte Carlo sample of replicas of the function, so that any statistical property of the underlying distribution can be derived from the given sample.…”

“…Now, the simultaneous progress in higher-order theoretical calculations and experimental results has made this simple-minded approach obsolete: a bona fide estimate of the error on PDFs has become necessary. This is a difficult problem, not only because of the usual difficulties in accounting properly for theoretical uncertainties (such as higher order perturbative corrections) which are non-gaussian and hard to estimate, and in collecting and propagating uncertainties contained in large experimental covariance matrices, but also because a PDF set is a set of functions, and therefore one is faced with the problem of constructing an error -a probability measure -on a space of functions [7]. This is clearly an ill-posed problem, because one is trying to infer an infinite amount of information from a finite set of data points: it can be made tractable only by introducing some theoretical assumptions.…”

A meta-analysis of parton distribution functions

“…When combining the PDF ensembles, one follows two common methods used for estimating the PDF uncertainty, the Hessian method [12,13] and the Monte Carlo (MC) sampling method [14,15]. We summarize the core relations of the two methods for completeness.…”

Next-to-leading order QCD and electroweak corrections to Higgs-strahlung processes at the LHC

“…Then we provide our numerical results for these processes at the LHC with center-of-mass energy 13 TeV using the Monte Carlo program HAWK [14] by adopting the NNPDF2.3qed, NNPDF3.0qed, MRST2004qed, CT14QEDinc, and NNLO LUXqed PDFs, as well as their reweighting photon PDFs. We obtain reweighting photon PDFs by using the reweighting method [15][16][17][18] and the LHC CMS 8 TeV data [19] as in Ref. [10].…”