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arXiv · 2209.06133

How the Higgs potential got its shape

Jens Mund·Karl-Henning Rehren·Bert Schroer
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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.

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Jens Mund, Karl-Henning Rehren, Bert Schroer. 2022-09-13. How the Higgs potential got its shape. https://doi.org/10.1016/j.nuclphysb.2023.116109

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