A Complex Operator Z = M + iQ : Advantages for QCD and the SM

In quantum field theory, the distinction between dynamical (real‐valued) quantities like masses or coupling constants and topological or “phase‐like” contributions such as θ‐terms, anomalies, or topological charges has long been fundamental. Recent work in various corners—supersymmetric gauge theories, lattice QCD, analyses of nonperturbative running couplings, and Grand Unification‐scale physics—shows that combining these into holomorphic or “complexified” objects often yields deeper symmetry properties, better analytic control, and conceptual unification.