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arXiv · 2008.07813

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

D. Dudal·D. M. van Egmond·M. S. Guimaraes·L. F. Palhares·G. Peruzzo·S. P. Sorella
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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 $R_{\xi}$-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.

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D. Dudal, D. M. van Egmond, M. S. Guimaraes, L. F. Palhares, G. Peruzzo, S. P. Sorella. 2020-08-18. Spectral properties of local gauge invariant composite operators in the $SU(2)$ Yang--Mills--Higgs model. https://arxiv.org/abs/2008.07813

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