[Paper Review] Higgs-mass predictions in the MSSM and beyond

P. Slavich, S. Heinemeyer+37 more|arXiv (Cornell University)|Jan 1, 2020

Particle physics theoretical and experimental studies429 references15 citations

TL;DR

This comprehensive review synthesizes advances in Higgs mass predictions within supersymmetric models, particularly the MSSM and NMSSM, through fixed-order, effective field theory (EFT), and hybrid calculation approaches. It consolidates results from the Precision SUSY Higgs Mass Calculation Initiative (KUTS), delivering state-of-the-art theoretical accuracy and uncertainty estimates crucial for LHC Higgs physics and model exclusion.

ABSTRACT

Predictions for the Higgs masses are a distinctive feature of supersymmetric extensions of the Standard Model, where they play a crucial role in constraining the parameter space. The discovery of a Higgs boson and the remarkably precise measurement of its mass at the LHC have spurred new efforts aimed at improving the accuracy of the theoretical predictions for the Higgs masses in supersymmetric models. The 'Precision SUSY Higgs Mass Calculation Initiative' (KUTS) was launched in 2014 to provide a forum for discussions between the different groups involved in these efforts. This report aims to present a comprehensive overview of the current status of Higgs-mass calculations in supersymmetric models, to document the many advances that were achieved in recent years and were discussed during the KUTS meetings, and to outline the prospects for future improvements in these calculations.

Motivation & Objective

• To provide a unified, up-to-date overview of theoretical Higgs mass calculations in supersymmetric extensions of the Standard Model.
• To document key advances made by the KUTS initiative in improving the precision and reliability of Higgs mass predictions.
• To compare and contrast the performance and consistency of fixed-order, EFT, and hybrid calculation frameworks.
• To quantify and compare theoretical uncertainties across different calculation methods, especially in scenarios with large mass hierarchies.
• To support experimental constraints on supersymmetric models by delivering accurate, reliable Higgs mass predictions with well-estimated uncertainties.

Proposed method

• Systematic comparison of three main calculation frameworks: fixed-order (FO), effective field theory (EFT), and hybrid approaches.
• Implementation of two-loop radiative corrections in the MSSM and NMSSM, including handling of the 'Goldstone Boson Catastrophe' in non-vanishing momentum limits.
• Use of EFT matching at multiple scales to resum large logarithmic corrections, particularly in split-SUSY and high-scale scenarios.
• Development and integration of public codes (e.g., FeynHiggs, FlexibleSUSY, SARAH, NMSSMCALC) supporting FO, EFT, and hybrid methods.
• Application of semi-analytic solvers for boundary value problems in highly constrained models like the CNMSSM and CE6SSM.
• Quantification of parametric and higher-order uncertainties using scale variation and matching scale dependence in EFT and hybrid schemes.

Experimental results

Research questions

• RQ1 How do fixed-order, EFT, and hybrid Higgs mass calculation methods compare in accuracy and consistency across different SUSY scenarios?
• RQ2 What are the dominant higher-order corrections (e.g., three-loop) in the MSSM, and how do they affect Higgs mass predictions?
• RQ3 How can effective field theory be systematically applied to predict Higgs masses in models with large mass hierarchies, such as split-SUSY?
• RQ4 What are the main sources of theoretical uncertainty in Higgs mass predictions, and how can they be reliably estimated and reduced?
• RQ5 To what extent do different renormalization schemes and input parameter definitions affect Higgs mass predictions in the MSSM and NMSSM?

Key findings

• The two-loop Higgs mass calculation in the vanilla MSSM has been completed with full analytical and numerical consistency, resolving long-standing discrepancies.
• Dominant three-loop corrections in the MSSM are estimated to contribute approximately 1–2 GeV to the lightest CP-even Higgs mass, with significant dependence on stop masses and tanβ.
• EFT-based calculations achieve NLL resummation of large logarithmic corrections in hierarchical scenarios, with results consistent with FO calculations within uncertainties.
• Hybrid approaches combining FO and EFT methods show improved stability and accuracy, particularly in models with high-scale SUSY breaking and split-SUSY limits.
• Theoretical uncertainties in Higgs mass predictions are now estimated at the level of 1–2 GeV for the MSSM in typical benchmark scenarios, with better control in EFT and hybrid frameworks.
• Public codes such as FeynHiggs, FlexibleSUSY, and SARAH now support all three calculation methods, enabling cross-validation and broad application in phenomenological studies.