The Higgs resonance in fermionic pairing

TL;DR

This paper investigates how the properties of the Higgs mode in fermionic condensates depend on the energy dispersion of the pairing interaction, revealing conditions under which it becomes a resonance or remains discrete.

Contribution

It demonstrates the sensitivity of the Higgs mode's nature to the energy dependence of the pairing interaction in fermionic systems.

Findings

Higgs mode can become virtual or resonant depending on interaction details.

Discreteness of the Higgs mode is linked to enhanced pairing at the Fermi level.

Conceptual challenges in defining collective variables in pairing dynamics.

Abstract

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.