How the Higgs potential got its shape
Abstract
Stringlocalized quantum field theory allows renormalizable couplings involving massive vector bosons, without invoking negativenorm 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 Smatrix are not affected. This is an instance of the "LV formalism"  a novel modelindependent scheme that can be used as a tool to "renormalize the nonrenormalizable" by adding a total derivative to the interaction.
 Publication:

Nuclear Physics B
 Pub Date:
 February 2023
 DOI:
 10.1016/j.nuclphysb.2023.116109
 arXiv:
 arXiv:2209.06133
 Bibcode:
 2023NuPhB.98716109M
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 31 pages. v2: 33 pages, comments on relation to BRST, general presentation improved, references added