Future tests of parton distributions

Cruz-Martinez, Juan; Forte, Stefano; Nocera, Emanuele R.

doi:10.48550/arxiv.2103.08606

Cited by 7 publications

(11 citation statements)

References 47 publications

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“…The fact that the S-correlation of NNPDF3.1 PDFs is smaller than that of NNPDF4.0 PDFs is consistent with the fact [13,17,18] that the NNPDF4.0 methodology leads to smaller uncertainties than the NNPDF3.1 methodology, even though both can be shown to be faithful using closure tests [8,13]. Indeed, the only way PDF sets determined from the same underlying data can have different uncertainties is if one of the two has a smaller functional (i.e.…”

Section: The Data-induced S-correlation and Cross-correlationsupporting

confidence: 79%

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Correlation and Combination of Sets of Parton Distributions

Ball¹,

Forte²,

Stegeman³

2021

Preprint

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We study the correlation between different sets of parton distributions (PDFs). Specifically, viewing different PDF sets as distinct determinations, generally correlated, of the same underlying physical quantity, we examine the extent to which the correlation between them is due to the underlying data. We do this both for pairs of PDF sets determined using a given fixed methodology, and between sets determined using different methodologies. We show that correlations have a sizable component that is not due to the underlying data, because the data do not determine the PDF uniquely. We show that the data-driven correlations can be used to assess the efficiency of methodologies used for PDF determination. We also show that the use of data-driven correlations for the combination of different PDFs into a joint set can lead to inconsistent results, and thus that the statistical combination used in constructing the widely used PDF4LHC15 PDF set remains the most reliable method.

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Section: The Data-induced S-correlation and Cross-correlationsupporting

confidence: 79%

“…The expressions Eqs. (17,18) can be generalized straightforwardly to the combination of n PDF sets, by taking N/n replicas at random from each (always keeping N n of course): then…”

Section: The Pdf4lhc15 Combinationmentioning

confidence: 99%

Correlation and Combination of Sets of Parton Distributions

Ball¹,

Forte²,

Stegeman³

2021

Preprint

Self Cite

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“…, which have been computed only for NNPDF4.0 2 . The results here act both as a proof of principle of new estimators presented in this paper but also as part of a suite of methodological validation tools, see also the "future tests" [14], used to understand the PDF uncertainties of the recent NNPDF4.0 set of PDFs. For the purpose of understanding how the results here were produced, we will briefly describe the key features of the NNPDF4.0 methodology, but refer the reader to Ref.…”

Section: Numerical Setup and Resultsmentioning

confidence: 77%

Bayesian Approach to Inverse Problems: an Application to NNPDF Closure Testing

Del Debbio,

Giani,

Wilson

2021

Preprint

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We discuss the Bayesian approach to the solution of inverse problems and apply the formalism to analyse the closure tests performed by the NNPDF collaboration. Starting from a comparison with the approach that is currently used for the determination of parton distributions (PDFs) by the NNPDF collaboration, we discuss some analytical results that can be obtained for linear problems and use these results as a guidance for the more complicated non-linear problems. We show that, in the case of Gaussian distributions, the posterior probability density of the parametrized PDFs is fully determined by the results of the NNPDF fitting procedure. In the particular case that we consider, the fitting procedure and the Bayesian analysis yield exactly the same result. Building on the insight that we obtain from the analytical results, we introduce new estimators to assess the statistical faithfulness of the fit results in closure tests. These estimators are defined in data space, and can be studied analytically using the Bayesian formalism in a linear model in order to clarify their meaning. Finally we present numerical results from a number of closure tests performed with current NNPDF methodologies. These further tests allow us to validate the NNPDF4.0 methodology and provide a quantitative comparison of the NNPDF4.0 and NNPDF3.1 methodologies. As PDFs determinations move into precision territory, the need for a careful validation of the methodology becomes increasingly important: the error bar has become the focal point of contemporary PDFs determinations. In this perspective, theoretical assumptions and other sources of error are best formulated and analysed in the Bayesian framework, which provides an ideal language to address the precision and the accuracy of current fits.

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“…From a theoretical point of view, it will be necessary to have better control both from non-perturbative and perturbative aspects. The former require an increase knowledge of PDFs, with good prospects in the following years [35]. The latter concerns the development of innovative techniques to handle multiloop calculations, which may encompass the use of different regularizations methods.…”

Section: Discussionmentioning

confidence: 99%

A step towards a consistent treatment of chiral theories at higher loop order: the abelian case

Cherchiglia

2021

Preprint

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As recently pointed out, regularization schemes defined in four-dimensions may also face inconsistencies in the presence of chiral fermions. In this work, we extend this analysis to two-loop order. Adopting the implicit regularization as working arena, we obtain the one and two-loop coefficients of the gauge coupling β functions in the standard model, which agree with previous analysis performed in the context of dimensional methods. We discuss in detail how a consistent version of the method can be envisaged, and present many of the subtleties that appear at two-loop order using an abelian chiral model as working example.

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Future tests of parton distributions

Cited by 7 publications

References 47 publications

Correlation and Combination of Sets of Parton Distributions

Correlation and Combination of Sets of Parton Distributions

Bayesian Approach to Inverse Problems: an Application to NNPDF Closure Testing

A step towards a consistent treatment of chiral theories at higher loop order: the abelian case

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