On the systematic construction of basis invariants

We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies) between mutually dependent BIs. Due to the novel use of orthogonal hermitian projection operators, we obtain the shortest possible invariants and their interrelations. The substructure of non-linear BIs is fully resolved in terms of linear, basis-covariant objects. The substructure distinguishes real (CP-even) and purely imaginary (CP-odd) BIs in a simple manner. As an illustrative example, we construct the full ring of BIs of the scalar potential of the general Two-Higgs-Doublet model.