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

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.