The Higgs resonance in fermionic pairing

The Higgs boson in fermionic condensates with the BCS pairing interaction describes the dynamics of the pairing amplitude. I show that the existence and properties of this mode are sensitive to the energy dispersion of the interaction. Specifically, when the pairing is suppressed at the Fermi level, the Higgs mode may become unphysical (virtual) state or a resonance with finite lifetime, depending on the details of interaction. Conversely, the Higgs mode is discrete for the pairing interaction enhanced at the Fermi level. This work illustrates conceptual difficulties associated with introducing collective variables in the many-body pairing dynamics.