Gauge-invariant spectral description of the $U(1)$ Higgs model from local composite operators

TL;DR

This paper develops a gauge-invariant spectral framework for the $U(1)$ Higgs model using local composite operators, providing explicit one-loop spectral functions that reveal physical excitations independent of gauge choice.

Contribution

It introduces a gauge-invariant spectral description of the $U(1)$ Higgs model through local composite operators, overcoming limitations of elementary field approaches.

Findings

Spectral functions are explicitly calculated at one-loop order.

Correlation functions are gauge-parameter independent.

Positive spectral densities and gauge-invariant pole masses are confirmed.

Abstract

The spectral properties of a set of local gauge-invariant composite operators are investigated in the $U(1)$ Higgs model quantized in the 't Hooft $R_{\xi}$ gauge. These operators enable us to give a gauge-invariant description of the spectrum of the theory, thereby surpassing certain incommodities when using the standard elementary fields. The corresponding two-point correlation functions are evaluated at one-loop order and their spectral functions are obtained explicitly. As expected, the above mentioned correlation functions are independent from the gauge parameter $\xi$, while exhibiting positive spectral densities as well as gauge-invariant pole masses corresponding to the massive photon and Higgs physical excitations.