[Paper Review] CERN Yellow Reports: Monographs, Vol 3 (2020): Theory for the FCC-ee: Report on the 11th FCC-ee Workshop, Theory and Experiments, 8–11 January 2019, CERN, Geneva

A. Blondel|arXiv (Cornell University)|May 13, 2019

Particle physics theoretical and experimental studies15 references23 citations

TL;DR

This paper presents a comprehensive theoretical framework for the FCC-ee, a proposed high-luminosity electron-positron collider at CERN, focusing on precision calculations of Standard Model and MSSM/ NMSSM Higgs boson decays. It details the required theoretical accuracy for measuring key parameters like αQED, αQCD, MW, and mt, and identifies critical uncertainties from higher-order corrections, loop effects, and Higgs mixing, with estimated uncertainties ranging from 4% to 50% depending on the decay channel and model context.

ABSTRACT

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments.

Motivation & Objective

• To establish the theoretical precision requirements for FCC-ee experiments, particularly for Z, W, Higgs, and top quark physics.
• To assess the impact of higher-order quantum corrections—especially QCD and electroweak NLO/NNLO effects—on Higgs decay widths in the NMSSM.
• To quantify theoretical uncertainties in Higgs decay predictions due to missing higher-order corrections, Higgs mixing approximations, and parametric errors.
• To evaluate the reliability of current one-loop calculations in the context of decoupling limits and heavy Higgs states.
• To guide the development of advanced theoretical tools and software for precision physics at FCC-ee, including handling of Sudakov logarithms and final-state interactions.

Proposed method

• Systematic evaluation of one-loop Higgs decay widths into SM particles in the NMSSM, including full QCD corrections in the heavy-quark limit.
• Comparison of results with SM predictions and existing codes (e.g., NMSSMCALC, FeynHiggs) to estimate missing NLO and NNLO effects.
• Use of multiple Higgs mixing matrices (Zmix, Um, U0) to assess uncertainty from mixing treatment in the decoupling limit.
• Estimation of theoretical uncertainty budgets by analyzing the sensitivity to input parameters, such as pole vs. MS quark masses.
• Incorporation of final-state interactions and Sudakov logarithms in threshold regions where free-particle approximations break down.
• Assessment of phenomenological impact of electroweak and SUSY corrections on rare and radiative decays (e.g., h→γγ, h→gg, h→γZ).

Experimental results

Research questions

• RQ1 What is the expected theoretical uncertainty in Higgs decay widths in the NMSSM, particularly for radiative and fermionic decays, at the required FCC-ee precision?
• RQ2 How do missing higher-order corrections (NLO, NNLO) in QCD and electroweak sectors affect the accuracy of Higgs decay predictions?
• RQ3 To what extent do different Higgs mixing matrix approximations (e.g., Zmix vs. U0) influence the predicted decay widths?
• RQ4 What is the impact of electroweak Sudakov logarithms and SUSY contributions on the theoretical uncertainty in heavy Higgs decays?
• RQ5 How do uncertainties in input parameters like mt, MW, αQED, and αQCD propagate into the final predictions for Higgs decays?

Key findings

• Theoretical uncertainty in Higgs decays into γγ is estimated at ≳4% due to missing electroweak NLO and QCD NNLO corrections, even with full QCD NLO corrections included.
• For Higgs decays into gluons, the uncertainty exceeds the SM estimate (3% from QCD) due to the use of the heavy-quark approximation and missing electroweak corrections.
• For h→γZ decays, the absence of QCD corrections leads to an uncertainty budget above ∼5%, higher than the SM estimate.
• In the decoupling limit, the uncertainty in the SM-like Higgs mass prediction remains at ∼2%, but higher-order corrections in the NMSSM introduce larger uncertainties.
• For heavy Higgs states (e.g., ∼1 TeV), theoretical uncertainties can reach 5–15% for fermionic and radiative decays, and up to 50% for WW/ZZ final states due to strong dependence on SUSY spectrum and Sudakov effects.
• The use of different quark mass definitions (pole vs. MS) at one-loop level leads to width shifts of ∼50%, indicating the need for two-loop consistency in precision calculations.