Higgs mode in $2+1$ dimensional $O(2)$ model

TL;DR

This paper analyzes the spectral functions of the Higgs mode in a 2+1 dimensional O(2) model, revealing peaks in susceptibilities and discussing limitations in explaining experimental observations.

Contribution

It provides a detailed 2-loop calculation of spectral functions in the O(2) model at zero temperature, highlighting features of the Higgs mode relevant to experiments.

Findings

Peaks appear in spectral functions of both susceptibilities.

The model cannot explain the disappearance of the response at weak interactions.

A possible lower peak at about 2m_sigma is observed.

Abstract

We investigate the spectral functions of the Higgs mode in $O(2)$ model, which can be experimentally realized in a 2D Bose gas. Zero temperature limit is considered. Our calculation fully includes the 2-loop contributions. Peaks show up in the spectral functions of both the longitudinal and the scalar susceptibilities. Thus this model cannot explain the disappearance of the response at the weak interaction limit. Neither it can explain the similarity between the longitudinal and the scalar susceptibilities in the visibility of the Higgs mode. A possible lower peak at about $2m_{\sigma}$ is also noted.