Next-to-leading order unitarity fits in Two-Higgs-Doublet models with soft Z2 breaking

We fit the next-to-leading order unitarity conditions to the Two-Higgs-Doublet model with a softly broken acurrency sign (2) symmetry. In doing so, we alleviate the existing uncertainty on how to treat higher order corrections to quartic couplings of its Higgs potential. A simplified approach to implementing the next-to-leading order unitarity conditions is presented. These new bounds are then combined with all other relevant constraints, including the complete set of LHC Run I data. The upper 95% bounds we find are 4.2 on the absolute values of the quartic couplings, and 235 GeV (100 GeV) for the mass degeneracies between the heavy Higgs particles in the type I (type II) scenario. In type II, we exclude an unbroken acurrency sign (2) symmetry with a probability of 95%. All fits are performed using the open-source code HEPfit.