# A3b: Precision predictions for Higgs boson properties as a probe for New Physics

Principal investigators
Prof. Margarete Muehlleitner Karlsruhe Institute of Technology
Prof. Matthias Steinhauser Karlsruhe Institute of Technology

### Subject

Higgs boson masses and self-couplings determine shape and stability of the Higgs potential. Their precise knowledge is mandatory for the correct interpretation of the experimental data. In supersymmetric models they are not independent; higher-order corrections are crucial. The Higgs self-couplings are important for the understanding of electroweak symmetry breaking. Trilinear Higgs self-couplings are accessible in Higgs boson pair production and in Higgs decays into a pair of lighter Higgs bosons. The goals of this project are: NLO corrections to Higgs boson pair production with the exact mass dependence of all particles in the SM and the MSSM and approximations for large and small top quark masses up to N$^3$LO in the SM; NLO electroweak corrections to Higgs-to-Higgs decays in various attractive extensions of the Standard Model.

### Topics

1. Higgs Boson Pair Production: Higher order corrections to Standard Model pair production up to N$^3$LO QCD in the heavy top mass limit. The Pad\'e method is applied at NNLO.
2. NLO corrections including the full mass dependences of all loop particles in the Standard Model and in the MSSM for neutral Higgs pairs, $gg \to hh, HH, hH,AA$, if time permits also $hA, HA$.
3. Higgs-to-Higgs Decay: electroweak corrections in the CP-violating Two-Higgs-Doublet Model (C2HDM) and the next-minimal supersymmetric model (NMSSM); comparative analysis of Higgs to Higgs decays in the Next-Minimal 2HDM (N2HDM), C2HDM and NMSSM; all models allow for sequences of Higgs-to-Higgs decays.
4. Higgs Boson Mass in the MSSM and NMSSM: Higgs Boson Mass in the MSSM and NMSSM; three-loop corrections of order $\alpha_b \alpha_s^2$ ; $\alpha_{t,b}^2 \alpha_s$, $\alpha_{t,b}^3$ to MSSM Higgs masses; two-loop corrections to NMSSM Higgs masses in different renormalization schemes, including singlet coupling $\lambda$, $\kappa$ contributions: order $\alpha_t \alpha_\lambda$, $\alpha_\lambda^2$, $(\alpha_t + \alpha_\kappa)^2$.
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