Anatomy of the Higgs fits: a first guide to statistical treatments of the theoretical uncertainties

TL;DR

This paper provides a comprehensive statistical framework for incorporating theoretical uncertainties into Higgs boson coupling fits, analyzing Bayesian and frequentist methods, and exploring the impact on Standard Model predictions with LHC data.

Contribution

It introduces a unified formalism for treating theoretical uncertainties in Higgs fits, including analytical marginal likelihoods, correlation effects, and bias approaches, advancing the statistical analysis of Higgs data.

Findings

Theoretical uncertainties significantly influence Higgs coupling fit regions.

Gaussian priors naturally emerge from error combination methods.

Standard Model predictions are consistent within 68% or 95% confidence levels depending on the statistical approach.

Abstract

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.