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Register a new userAnatomy of the Higgs fits: a first guide to statistical treatments of the theoretical uncertainties
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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.
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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.
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 develop a technique to present Higgs coupling measurements, which decouple the poorly defined theoretical uncertainties associated to inclusive and exclusive cross section predictions. The technique simplifies the combination of multiple measurements and can be used in a more general setting. We illustrate the approach with toy LHC Higgs coupling measurements and a collection of new physics models.
We examine the exclusion limits set by the CDF and D0 experiments on the Standard Model Higgs boson mass from their searches at the Tevatron in the light of large theoretical uncertainties on the signal and background cross sections. We show that when these uncertainties are consistently taken into account, the sensitivity of the experiments becomes significantly lower and the currently excluded mass range $M_H=158$-175 GeV would be entirely reopened. The necessary luminosity required to recover the current sensitivity is found to be a factor of two higher than the present one.
The remaining theoretical uncertainties from unknown higher-order corrections in the prediction for the light Higgs-boson mass of the MSSM are estimated. The uncertainties associated with three different approaches that are implemented in the publicly available code FeynHiggs are compared: the fixed-order diagrammatic approach, suitable for low SUSY scales, the effective field theory (EFT) approach, suitable for high SUSY scales, and the hybrid approach which combines the fixed-order and the EFT approaches. It is demonstrated for a simple single-scale scenario that the result based on the hybrid approach yields a precise prediction for low, intermediate and high SUSY scales with a theoretical uncertainty of up to $sim 1.5$ GeV for large stop mixing and $sim 0.5$ GeV for small stop mixing. The uncertainty estimate of the hybrid calculation approaches the uncertainty estimate of the fixed-order result for low SUSY scales and the uncertainty estimate of the EFT approach for high SUSY scales, while for intermediate scales it is reduced compared to both of the individual results. The estimate of the theoretical uncertainty is also investigated in scenarios with more than one mass scale. A significantly enhanced uncertainty is found in scenarios where the gluino is substantially heavier than the scalar top quarks. The uncertainty estimate presented in this paper will be part of the public code FeynHiggs.
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