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

Authors :
Capri, M. A. L.
Justo, I. F.
Palhares, L. F.
Peruzzo, G.
Sorella, S. P.
Source :
Phys. Rev. D 102, 033003 (2020)
Publication Year :
2020

Abstract

The renormalization properties of two local BRST invariant composite operators, $(O,V_\mu)$, 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 $V_\mu$ mixes with the gauge invariant quantity $\partial_\nu F_{\mu\nu}$, 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.<br />Comment: 36 pages, 6 figures

Subjects

Subjects :
High Energy Physics - Theory

Details

Database :
arXiv
Journal :
Phys. Rev. D 102, 033003 (2020)
Publication Type :
Report
Accession number :
edsarx.2007.01770
Document Type :
Working Paper
Full Text :
https://doi.org/10.1103/PhysRevD.102.033003