A3a: Extended Higgs sectors at the LHC

Extended Higgs sectors are a generic feature of many new physics models. We can accomodate e.g. dark matter or the baryon-antibaryon asymmetry through enlarged Higgs sectors with light new states, motivating their search at the LHC. Given the experimental and theoretical constraints, LHC signals for extended Higgs sectors can be small and require {\bf highest precision}. This has to be carried over both, into the analysis of theoretical constraints and of all available data on these sectors. We systematically analyse extended Higgs sectors guided by three principles: properties of the electroweak vacuum, precision predictions for the LHC, and phenomenology.

1. Precision studies of the electroweak vacuum: vacuum stability of the 2HDM and the NMSSM at next-to-leading order; symmetry structure of extended Higgs sectors with dark matter candidates; non-perturbative evolution of the Higgs potential ; machine learning methods in the numerical evolution.
2. Precision predictions for LHC phenomenology: corrections to Higgs decays, e.g. electroweak corrections in the CP-violating 2HDM, SUSY-NLO corrections for charged Higgs in the CP-violating NMSSM, NLO SUSY-QCD corrections to gluon fusion into the MSSM pseudoscalar; impact of higher-order corrections on model parameters.
3. Phenomenology and analysis: information geometry of new light scalar, matrix element method for complex phase space configurations, generative adversarial networks for phase space mapping, impact of precision predictions on global analysis.