Complex Action Support from Coincidences of Couplings

TL;DR

This paper reviews a complex action model in a path integral framework, explaining coincidences of couplings and predicting a small Higgs VEV and specific Yukawa coupling behavior, addressing the hierarchy problem.

Contribution

It introduces a model with complex action that explains unexplained coincidences and predicts the Higgs VEV and Yukawa couplings, offering a novel approach to the hierarchy problem.

Findings

Higgs field expectation value predicted to be very small

Top-Yukawa coupling near unity at the scale

Model explains scale problem and coupling coincidences

Abstract

Our model \cite{ownmMPP}\cite{SIMPP} with complex action in a functional integral formulation with path integrals extending over all times, past and future, is reviewed. Several numerical relations between coupling constants are presented as supporting evidence. The new evidence is that some more unexplained coincidences are explained in our model: 1) The "scale problem" is solved because the Higgs field expectation value is predicted to be very small compared to say some fundamental scale, that might be the Planck scale. 2) The Higgs VEV need not, however, to be just zero, but rather is predicted to be so that the running top-Yukawa coupling just is about to be unity at this scale; in this way the (weak) scale easily becomes "exponentially small". Instead of the top-Yukawa we should rather say the highest flavour Yukawa coupling here. These predictions are only achieved by allowing the principle of minimization of the imaginary part of the action SI(history) to to a certain extent adjust some coupling constants in addition to the initial conditions. If Susy-partners are not found in LHC, it would strengthen the need for "solution" of the hierarchy or rather scale problem along the lines of the present article.