[Paper Review] Measuring the Higgs boson couplings

Michael Rauch|arXiv (Cornell University)|Oct 6, 2011

Particle physics theoretical and experimental studies19 references3 citations

TL;DR

This paper presents a comprehensive analysis of Higgs boson coupling measurements at the LHC using the SFitter framework, projecting experimental data onto a weak-scale effective theory with generalised Higgs couplings. It demonstrates that the $WWH$ coupling is best constrained (10–20% error), while top-quark and loop-induced couplings are significantly affected by dimension-five operators, leading to degeneracies in fitting that require high luminosity to resolve.

ABSTRACT

Once a Higgs boson has been discovered, it is also important to know what are its properties, in particular its couplings to the other particles. At the LHC, there will be many observable channels that can be used to measure the relevant parameters. Using the SFitter framework, we project these measurements onto a weak-scale effective theory with general Higgs boson couplings. Thereby, our analysis profits from the error treatment and the parameter determination tools already used for new-physics searches. We use this to study both the individual couplings and their associated errors as well as correlations between them.

Motivation & Objective

• To assess the precision of Higgs boson coupling measurements at the 14 TeV LHC with 30 fb⁻¹ luminosity.
• To evaluate the impact of theoretical uncertainties, including statistical, systematic, and theory errors (RFit scheme), on coupling determinations.
• To investigate how dimension-five operators affect the determination of Higgs couplings, especially for loop-induced processes.
• To study the degeneracy in fitting solutions for new-physics models like the Higgs portal and SILH (MCHM5), and the conditions under which they can be resolved.

Proposed method

• Uses the SFitter framework to construct a full-dimensional log-likelihood map of the Higgs coupling parameter space.
• Parametrizes deviations from SM couplings via $\Delta_{jjH}$, with additional dimension-five contributions $\Delta_{jjH}^{\text{SM}} + \Delta_{jjH}$ for loop-induced couplings.
• Applies Bayesian and frequentist techniques (marginalisation and profile likelihood) to reduce the likelihood map to one- or two-dimensional distributions.
• Simulates ATLAS data at 14 TeV with 30 fb⁻¹, smears results across 10,000 toy experiments to extract error distributions.
• Treats theory errors via the RFit scheme, modeling them as box-shaped uncertainties.
• Analyzes both SM-like couplings and new-physics models (Higgs portal, MCHM5) by fitting to simulated measurements and assessing fit degeneracies.

Experimental results

Research questions

• RQ1 What is the expected precision on Higgs boson couplings to vector bosons, fermions, and gauge bosons at the LHC with 30 fb⁻¹ at 14 TeV?
• RQ2 How do dimension-five operators affect the determination of Higgs couplings, particularly for top-quark and loop-induced processes?
• RQ3 In models like the Higgs portal and MCHM5, what causes multiple fitting solutions for the same observed rate, and under what conditions can they be resolved?
• RQ4 How do correlations and error structures (statistical, systematic, theory) influence the sensitivity to deviations from the Standard Model?
• RQ5 Can the SM Higgs coupling be excluded at 95% CL in scenarios with invisible decays or modified couplings?

Key findings

• The $WWH$ coupling is the best-determined coupling, with 68% CL errors ranging from 10% to 20%, depending on the Higgs mass.
• The $bbH$ coupling has larger errors around 150 GeV due to reduced branching ratios, though it still significantly affects the total width.
• Top-quark Yukawa coupling errors are strongly influenced by dimension-five operators, which can compensate for changes in tree-level couplings, making it degenerate without top-associated Higgs production.
• In the Higgs portal model with $\cos^2\chi_{\text{th}} = 0.6$, the SM coupling (\cos^2\chi = 1) is excluded at 95% CL across the entire Higgs mass range.
• In the MCHM5 model, multiple fitting solutions emerge for $\xi \gtrsim 0.4$, indicating statistical degeneracy rather than true theoretical degeneracy, which can only be resolved with higher luminosity.
• For gluon-fusion Higgs production with $H \to \gamma\gamma$, each theoretical $\xi$ value leads to two possible fitted solutions, demonstrating a statistical ambiguity that requires increased data to resolve.