How the Higgs potential got its shape
arXiv:2209.06133 · doi:10.1016/j.nuclphysb.2023.116109
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.
arXiv comment31 pages. v2: 33 pages, comments on relation to BRST, general presentation improved, references added
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- Positivity and causal localizability in higher spin quantum field theories
- Relations between positivity, localization and degrees of freedom: the Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity
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