Future Tests of Parton Distributions

Abstract

The remarkable recent progress in the precision of Lattice QCD computations for several physical quantities relevant for flavour physics has motivated the introduction of isospin-breaking effects, including in particular electromagnetic corrections, to the computations. The isospin-breaking corrections are necessary to fully exploit this improved precision for the determination of the fundamental parameters of the Standard Model, including the CKM matrix elements, and to look for deviations from experimental measurements which might signal the presence of New Physics. Together with colleagues from Rome, we have developed and implemented a framework for including isospin-breaking corrections in leptonic decays P → ν (γ), where P is a pseudoscalar meson and a charged lepton, and the theoretical framework and numerical results are reviewed below. The status of our studies to extend this framework to semileptonic decays P 1 → P 2 ν (γ), where P 1,2 are pseudoscalar mesons, is also presented.

Correlation and combination of sets of parton distributions

“…Note also that the deviation of the S-correlation from 100% is much larger than the uncertainty due to the finite size of the replica sample, so the correlation loss cannot just be due to an insufficient number of replicas. The fact that the S-correlation of NNPDF3.1 PDFs is smaller than that of NNPDF4.0 PDFs is consistent with the fact [14,18,21] 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 [9,14]. 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.…”

“…Be all that as it may, our goal here is not to investigate the most efficient way to implement the weighted combination, but rather, to explore the implications of performing a correlated weighted PDF combination according to Eqs. (21)(22)(23). As discussed in Sect.…”

A data-based parametrization of parton distribution functions

“…To this end we utilize the "future test" technique introduced in Ref. [28], and used to validate the smallx extrapolation region of the NNPDF4.0 PDFs in Ref. [12].…”

Small $x$ extrapolation for parton distributions

“…In the extrapolation region, however, it is impossible to test the accuracy of a methodology on experimental data and the most reliable operation to test whether the PDF uncertainties can accommodate unseen data. In the NNPDF context this is done by means of the so-called "future test" [11] by which the same methodology is applied to subsets of data in order to check the faithfulness of the PDF uncertainties, however this tell us nothing -by definition -on the accuracy of the PDF where no data is available. One could use the techniques of the Closure Test to generate new data for the Future Test but a Closure Test needs a prior PDF as truth which trivializes the result.…”