Quantum-hydrodynamical picture of the massive Higgs boson

The phenomenon of spontaneous symmetry breaking admits a physical interpretation in terms of the Bose-condensation process of elementary spinless quanta. In this picture, the broken-symmetry phase emerges as a real physical medium, endowed with a hierarchical pattern of scales, supporting two types of elementary excitations for k \to 0: a massive energy branch E_a(k) \to M_H, corresponding to the usual Higgs boson field, and a collective gap-less branch E_b(k) \to 0. This is similar to the coexistence of phonons and rotons in superfluid He-4 that, in fact, is usually considered the condensed-matter analog of the Higgs condensate. After previous work dedicated to the properties of the gap-less, phonon branch, in this paper we use quantum hydrodynamics to propose a physical interpretation of the massive branch. On the base of our results, M_H coincides with the energy-gap for vortex formation and a massive Higgs boson is like a roton in superfluid He-4. Within this interpretation of the Higgs particle, there is no "naturalness" problem since M_H remains a naturally intermediate, fixed energy scale, even for an ultimate ultraviolet cutoff Lambda \to \infty.