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Register a new userCorrelation of Theoretical Uncertainties in PDF Fits and Theoretical Uncertainties in Predictions
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We show how to account for correlations between theoretical uncertainties incorporated in parton distribution function (PDF) fits, and the theoretical uncertainties in the predictions made using these PDFs. We demonstrate by explicit calculations, both analytical and numerical, that these correlations can lead to corrections to the central values of the predictions, and reductions in both the PDF uncertainties and the theoretical uncertainties in the prediction. We illustrate our results with predictions for top production rapidity distributions and the Higgs total cross-section at the LHC, using the NLO NNPDF3.1 PDF set which incorporates missing higher order uncertainties. We conclude that the inclusion of correlations can increase both the accuracy and precision of predictions involving PDFs, particularly for processes with data already included in the PDF fit.
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With present and future observations becoming of higher and higher quality, it is timely and necessary to investigate the most significant theoretical uncertainties in the predictions of inflation. We show that our ignorance of the entire history of the Universe, including the physics of reheating after inflation, translates to considerable errors in observationally relevant parameters. Using the inflationary flow formalism, we estimate that for a spectral index $n$ and tensor/scalar ratio $r$ in the region favored by current observational constraints, the theoretical errors are of order $Delta n / | n - 1| sim 0.1 - 1$ and $Delta r /r sim 0.1 - 1$. These errors represent the dominant theoretical uncertainties in the predictions of inflation, and are generically of the order of or larger than the projected uncertainties in future precision measurements of the Cosmic Microwave Background. We also show that the lowest-order classification of models into small field, large field, and hybrid breaks down when higher order corrections to the dynamics are included. Models can flow from one region to another.
There is now a rapidly growing body of experimental data relevant to the question of whether the standard model CKM quark mixing matrix is a correct description of CP-violation as well as of non--CP-violating flavor decay processes. In the detailed comparisons with theoretical predictions that are required to investigate this, a key challenge has been the representation of non-statistical uncertainties, especially those arising in theoretical calculations. The analytical procedures that have been used to date require procedural value judgments on this matter that color the interpretation of the quantitative results they produce. Differences arising from these value judgments in the results obtained from the various global CKM fitting techniques in the literature are of a scale comparable to those arising from the other uncertainties in the input data and therefore cannot be ignored. We have developed techniques for studying and visualizing the sensitivity of global CKM fits to non-statistical uncertainties and their parameterization, as well as techniques for visual evaluation of the consistency of experimental and theoretical inputs that minimize the implicit use of such value judgments, while illuminating their effects. We present these techniques and the results of such studies using recently updated theoretical and experimental inputs, discuss their implications for the interpretation of global CKM fits, and illustrate their possible future application as the uncertainties on the inputs are improved over the next several years.
We consider the problem of assigning a meaningful degree of belief to uncertainty estimates of perturbative series. We analyse the assumptions which are implicit in the conventional estimates made using renormalisation scale variations. We then formulate a Bayesian model that, given equivalent initial hypotheses, allows one to characterise a perturbative theoretical uncertainty in a rigorous way in terms of a credibility interval for the remainder of the series. We compare its outcome to the conventional uncertainty estimates in the simple case of the calculation of QCD corrections to the e+e- -> hadrons process. We find comparable results, but with important conceptual differences. This work represents a first step in the direction of a more comprehensive and rigorous handling of theoretical uncertainties in perturbative calculations used in high energy phenomenology.
The studies of the Higgs boson couplings based on the recent and upcoming LHC data open up a new window on physics beyond the Standard Model. In this paper, we propose a statistical guide to the consistent treatment of the theoretical uncertainties entering the Higgs rate fits. Both the Bayesian and frequentist approaches are systematically analysed in a unified formalism. We present analytical expressions for the marginal likelihoods, useful to implement simultaneously the experimental and theoretical uncertainties. We review the various origins of the theoretical errors (QCD, EFT, PDF, production mode contamination...). All these individual uncertainties are thoroughly combined with the help of moment-based considerations. The theoretical correlations among Higgs detection channels appear to affect the location and size of the best-fit regions in the space of Higgs couplings. We discuss the recurrent question of the shape of the prior distributions for the individual theoretical errors and find that a nearly Gaussian prior arises from the error combinations. We also develop the bias approach, which is an alternative to marginalisation providing more conservative results. The statistical framework to apply the bias principle is introduced and two realisations of the bias are proposed. Finally, depending on the statistical treatment, the Standard Model prediction for the Higgs signal strengths is found to lie within either the $68%$ or $95%$ confidence level region obtained from the latest analyses of the $7$ and $8$ TeV LHC datasets.
The problem of estimating the effect of missing higher orders in perturbation theory is analyzed with emphasis in the application to Higgs production in gluon-gluon fusion. Well-known mathematical methods for an approximated completion of the perturbative series are applied with the goal to not truncate the series, but complete it in a well-defined way, so as to increase the accuracy - if not the precision - of theoretical predictions. The uncertainty arising from the use of the completion procedure is discussed and a recipe for constructing a corresponding probability distribution function is proposed.
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