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.
Highlights
The gauge parameter independence of the pole masses of both transverse W and Z bosons as well as of the Higgs field two-point correlation functions are understood by means of the so-called Nielsen identities [7,8,9,10,11,12,13], which follow from the Slavnov–Taylor identities encoding the exact BRST symmetry of quantized non
We have explicitly shown that the correlation functions of the composite operators display a well defined positive and gauge independent Källén–Lehmann spectral representation, a feature not shared by the two-point correlation functions of the elementary fields which, as in the explicit case of the Higgs field, i.e. h( p)h(− p), display an unphysical dependence from the gauge parameter ξ, becoming even negative depending on the value of ξ
4 One-loop evaluation of the correlation function of the local BRST invariant composite operators d = 4 −, we find that the divergent part of the one-loop correction is given by
Summary
We have worked out the one-loop corrections to the two-point functions in Eq (1) corresponding to the Higgs and Abelian gauge fields and we have shown that they have the same gauge independent pole masses of the corresponding elementary two-point correlation functions. We have explicitly shown that the correlation functions of the composite operators display a well defined positive and gauge independent Källén–Lehmann spectral representation, a feature not shared by the two-point correlation functions of the elementary fields which, as in the explicit case of the Higgs field, i.e. h( p)h(− p) , display an unphysical dependence from the gauge parameter ξ , becoming even negative depending on the value of ξ. The local composite BRST invariant operators corresponding to the gauge bosons transform as a triplet under the custodial symmetry, a property which will imply useful relations for their two-point correlation functions.
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