How the Higgs potential got its shape
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Publication:6410627
DOI10.1016/J.NUCLPHYSB.2023.116109arXiv2209.06133MaRDI QIDQ6410627
Bert Schroer, Jens Mund, Karl-Henning Rehren
Publication date: 13 September 2022
Abstract: String-localized quantum field theory allows renormalizable couplings involving massive vector bosons, without invoking negative-norm states and compensating ghosts. We analyze the most general coupling of a massive vector boson to a scalar field, and find that the scalar field necessarily comes with a quartic potential which has the precise shape of the shifted Higgs potential. In other words: the shape of the Higgs potential has not to be assumed, but arises as a consistency condition among fundamental principles of QFT: Hilbert space, causality, and covariance. The consistency can be achieved by relaxing the localization properties of auxiliary quantities, including interacting charged fields, while observable fields and the S-matrix are not affected. This is an instance of the "L-V formalism" - a novel model-independent scheme that can be used as a tool to "renormalize the non-renormalizable" by adding a total derivative to the interaction.
Localization and completion in homotopy theory (55P60) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Renormalization group methods applied to problems in quantum field theory (81T17) (S)-matrix theory, etc. in quantum theory (81U20) Bosonic systems in quantum theory (81V73)
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