Spectral properties of local gauge invariant composite operators in the SU(2) Yang–Mills–Higgs model

The spectral properties of a set of local gauge (BRST) invariant composite operators are investigated in theSU(2) Yang–Mills–Higgs model with a single Higgs field in the fundamental representation, quantized in the ’t Hooft$$R_{\xi }$$Rξ-gauge. These operators can be thought of as a BRST invariant version of the elementary fields of the theory, the Higgs and gauge fields, with which they share a gauge independent pole mass. The two-point correlation functions of both BRST invariant composite operators and elementary fields, as well as their spectral functions, are investigated at one-loop order. It is shown that the spectral functions of the elementary fields suffer from a strong unphysical dependence from the gauge parameter$$\xi $$ξ, and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.