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arXiv · 2007.01770

Study of the renormalization of BRST invariant local composite operators in the $U(1)$ Higgs model

M. A. L. Capri·I. F. Justo·L. F. Palhares·G. Peruzzo·S. P. Sorella
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Abstract

The renormalization properties of two local BRST invariant composite operators, $(O,V_μ)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the $U(1)$ Higgs model by means of the algebraic renormalization setup. Their renormalization $Z$'s factors are explicitly evaluated at one-loop order in the $\overline{\text{MS}}$ scheme by taking into due account the mixing with other gauge invariant operators. In particular, it turns out that the operator $V_μ$ mixes with the gauge invariant quantity $\partial_νF_{μν}$, which has the same quantum numbers, giving rise to a $2 \times 2$ mixing matrix. Moreover, two additional powerful Ward identities exist which enable us to determine the whole set of $Z$'s factors entering the $2 \times 2$ mixing matrix as well as the $Z$ factor of the operator $O$ in a purely algebraic way. An explicit check of these Ward identities is provided. The final setup obtained allows for computing perturbatively the full renormalized result for any $n$-point correlation function of the scalar and vector composite operators.

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M. A. L. Capri, I. F. Justo, L. F. Palhares, G. Peruzzo, S. P. Sorella. 2020-07-03. Study of the renormalization of BRST invariant local composite operators in the $U(1)$ Higgs model. https://doi.org/10.1103/physrevd.102.033003

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