Parametrisation and dictionary for CP violating Higgs boson interactions

Searches for charge-parity (CP) violating interactions of the Standard Model (SM) Higgs boson are a key priority of the LHC physics program. Experimental results from ATLAS and CMS are often reinterpreted within a variety of theoretical parametrisations, the most commonly used being the Higgs basis, $\kappa$'s and angles, CP fractions and effective field theories (EFT) such as the SMEFT and the Higgs EFT. However, differing conventions and assumptions across the literature make the translation between these parametrisations nontrivial and prone to inconsistencies. In this paper, we provide a unified framework and construct explicit dictionaries connecting these different approaches. This facilitates a transparent comparison between theoretical studies and experimental analyses, enabling more robust interpretations of CP violating effects in Higgs boson interactions.