Parton Distributions with Theory Uncertainties: General Formalism and First Phenomenological Studies

Abstract

We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of prescriptions for constructing a theory covariance matrix using scale variations, which can be used in global fits of data from a wide range of different processes, based on choosing a set of independent scale variations suitably correlated within and across processes. We set up an algebraic framework for the choice and validation of an optimal prescription by comparing the estimate of MHOU encoded in the next-to-leading order (NLO) theory covariance matrix to the observed shifts between NLO and NNLO predictions. We perform a NLO PDF determination which includes the MHOU, assess the impact of the inclusion of MHOUs on the PDF central values and uncertainties, and validate the results by comparison to the known shift between NLO and NNLO PDFs. We finally study the impact of the inclusion of MHOUs in a global PDF determination on LHC cross-sections, and provide guidelines for their use in precision phenomenology. In addition, we also compare the results based on the theory covariance matrix formalism to those obtained by performing PDF determinations based on different scale choices.

NNNPDF3.0: Evidence for a modified partonic structure in heavy nuclei

“…One could also account for missing higher-order corrections as additional correlated uncertainties, e.g. by means of the method developed in [69,70]. Even if the fit quality of nNNPDF3.0 is overall very good, the precision of forthcoming LHC measurements is expected to increase with the higher luminosity achieved in Run III.…”

“…Notably, a shortcoming of this approach is that it becomes necessary to exclude the reference pp data from the proton baseline which enters the nPDF fit. The extension of the perturbative accuracy of the fit to NNLO QCD and/or including theoretical uncertainties (as in [69,70]) would allow one to consider absolute distributions instead of ratios for these selected processes. As a note, these ratios are constructed in the pp CoM frame.…”

A new generation of simultaneous fits to LHC data using deep learning

“…If we wanted to include also correlated sources of theoretical uncertainties, such as those associated with missing higher order uncertainties in the theory predictions, we could include them using the method outlined in Refs. [34][35][36]. Hidden layer 1 are Bjorken-x and its logarithm.…”

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

“…In the context of PDF fitting a similar recipe to take into account theoretical errors has recently been advocated in Refs. [3,4]. Note that there are no rigorous arguments favouring the assumption that theoretical errors are normally distributed; it is nonetheless a useful working assumption, and a definite improvement compared to ignoring the theoretical errors altogether.…”

“…In the context of fitting parton distribution functions there are potentially missing higher order uncertainties (MHOUs) from using fixed order perturbative calculations as part of the forward map. MHOUs have been included in parton distribution fits [3,4] and in the future these should be included in the closure test, however this is beyond the scope of the study presented here, since MHOUs are still not included in the NNPDF methodology by default. In the results presented in the rest of this paper we do include nuclear and deuteron uncertainties, as presented in [8,9,10], since they are to be included in NNPDF fits by default.…”