Spectral function of the Higgs mode in 4-\varepsilon dimensions

TL;DR

This paper analyzes the spectral function of the Higgs mode in the relativistic O(N) model near the quantum critical point in 4-epsilon dimensions, revealing phase-dependent spectral features and the nature of the Higgs resonance.

Contribution

It provides a leading-order calculation of the universal spectral function near the quantum critical point in 4-epsilon dimensions, clarifying the Higgs mode's resonance behavior across phases.

Findings

Disordered phase shows no Higgs peak, only threshold behavior.

Ordered phase exhibits a well-defined Higgs resonance.

Resonance pole transitions from real to imaginary with dimensionality.

Abstract

We investigate the amplitude (Higgs) mode of the relativistic O(N) model in the vicinity of the Wilson-Fisher quantum critical point in D=4-epsilon spacetime dimensions. We compute the universal part of the scalar spectral function near the transition, to leading non-trivial order in the ordered phase, and to next to leading order in both the disordered phase and the quantum critical regime. We find that, in the disordered phase, the spectral function has a threshold behavior with no Higgs-like peak, whereas in the ordered phase, the Higgs mode appears as a well defined resonance. The pole associated with this resonance is purely real in the D->4 limit, evolving smoothly with dimensionality to become purely imaginary at D=3 in the N->infty limit. Our results complement previous studies of the scalar spectral function, and demonstrate that the resonance found in these studies can indeed be directly identified with the Higgs mode.