Spectral properties of local gauge invariant composite operators in the SU(2) Yang–Mills–Higgs model
David Dudal, Duifje Maria van Egmond, M. S. Guimarães, L. F. Palhares, G. Peruzzo, S. P. Sorella
Abstract
Abstract 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 $$R_{\xi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mi>ξ</mml:mi></mml:msub></mml:math> -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 $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ξ</mml:mi></mml:math> , and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.