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

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.

62 pages, 10 figures

References in corpus (22)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Big-Bang Nucleosynthesis
• Bayes in the sky: Bayesian inference and model selection in cosmology
• Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV
• Higgs boson gluon-fusion production in N3LO QCD
• The PDF4LHC Working Group Interim Recommendations
• Measurement of Higgs boson production in the diphoton decay channel in $pp$ collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector
• Measurements of Higgs boson production and couplings in the four-lepton channel in $pp$ collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector
• Search for the Standard Model Higgs boson produced in association with top quarks and decaying into $b\bar{b}$ in pp collisions at $\sqrt{s}$ = 8 TeV with the ATLAS detector
• An update of the constraints on the phenomenological MSSM from the new LHC Higgs results
• Search for $H\to \gamma \gamma$ produced in association with top quarks and constraints on the Yukawa coupling between the top quark and the Higgs boson using data taken at 7 TeV and 8 TeV with the ATLAS detector
• Electroweak Symmetry Breaking and the Higgs Boson: Confronting Theories at Colliders
• Fiducial and differential cross sections of Higgs boson production measured in the four-lepton decay channel in $pp$ collisions at $\sqrt{s}$=8 TeV with the ATLAS detector
• Constraining extra-fermion(s) from the Higgs boson data
• Les Houches 2013: Physics at TeV Colliders: New Physics Working Group Report
• Higgs production at the LHC in warped extra-dimensional models
• The apparent excess in the Higgs to di-photon rate at the LHC: New Physics or QCD uncertainties?
• The Tevatron Higgs exclusion limits and theoretical uncertainties: a critical appraisal
• The Higgs Legacy of the LHC Run I
• New likelihoods for shape analysis
• Clarifications on the impact of theoretical uncertainties on the Tevatron Higgs exclusion limits

Cited by in corpus (23)

• Scenarii for interpretations of the LHC diphoton excess: two Higgs doublets and vector-like quarks and leptons
• Precision Higgs Physics at CEPC
• The Gauge-Higgs Legacy of the LHC Run I
• The Gauge-Higgs Legacy of the LHC Run II
• Current and future constraints on Higgs couplings in the nonlinear Effective Theory
• Learning from Higgs Physics at Future Higgs Factories
• Standard Model Extended by a Heavy Singlet: Linear vs. Nonlinear EFT
• Vector-like top/bottom quark partners and Higgs physics at the LHC
• Search for single production of the vector-like top partner at the 14 TeV LHC
• Search for single production of vector-like top partners at the Large Hadron Electron Collider
• Composite Higgs theory
• Search for single production of the heavy vectorlike $T$ quark with $T\to th$ and $h\to \gamma \gamma$ at the high-luminosity LHC
• Constraining SMEFT operators with associated $h\gamma$ production in Weak Boson Fusion
• The correlation matrix of Higgs rates at the LHC
• Modelling theoretical uncertainties in phenomenological analyses for particle physics
• On new physics searches with multidimensional differential shapes
• Taming systematic uncertainties at the LHC with the central limit theorem
• To Profile or To Marginalize -- A SMEFT Case Study
• Higgs Factories: Higgs-Strahlung versus W-Fusion
• Adding Pseudo-Observables to the Four-Lepton Experimentalist's Toolbox
• Higgs Effective Field Theories - Systematics and Applications
• Diboson resonances within a custodially protected warped extra-dimensional scenario
• Is there new particle running in the loop-induced $H\gamma \gamma$ and $Hgg$ vertex?