Higgs boson masses of the general two-Higgs-doublet model in the Minkowski-space formalism

We study the masses of the Higgs bosons in the most general two-Higgs-doublet model in a basis-independent approach. We adapt the recently developed Minkowski-space formalism to this problem and calculate traces of any power of the mass matrix in a compact and reparametrization-invariant form. Our results can be used to gain insight into the dynamics of the scalar sector of the general two-Higgs-doublet model.