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 the SU(2) Yang-Mills-Higgs model with a single Higgs field in the fundamental representation, quantized in the 't Hooft R-xi-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, and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.

Automated summary

The spectral properties of a set of local gauge invariant composite operators in the SU(2) Yang-Mills-Higgs model with a single Higgs field in the fundamental representation were investigated. It was found that the spectral functions of elementary fields are strongly dependent on the gauge parameter and can exhibit unphysical behavior, whereas the BRST invariant local operators exhibit a well-defined positive spectral density.