The Natural TeV Cutoff of the Higgs Field from the Multiplicative Lagrangian

TL;DR

This paper introduces a multiplicative Lagrangian for a complex scalar field, leading to a natural TeV-scale cutoff for the Higgs field, with implications for Higgs physics and fundamental problems in particle physics.

Contribution

It constructs a novel multiplicative Lagrangian for scalar fields and applies it to Higgs physics, revealing a natural TeV cutoff and independence of the Higgs vev from Fermi coupling.

Findings

Higgs vev becomes independent of Fermi coupling after symmetry breaking.

Higgs field acquires a natural TeV-scale cutoff.

Discussed implications for Higgs mass, strong CP problem, and cosmological constant.

Abstract

The various types of the non-standard Lagrangian can be added to the standard Lagrangian with the invariant of the equation of motion in the low energy limit. In this paper, we construct the multiplicative Lagrangian of a complex scalar field giving the approximated Klein-Gordon equation from the inverse problem of the calculus of variation. Then, this multiplicative Lagrangian with arbitrary high cutoff is applied to the toy model of the Higgs mechanism in U(1)-gauge symmetry in order to study the simple effects in the Higgs physics. We show that, after spontaneous symmetry breaking happens, the Higgs vev is free from the Fermi-coupling constant and the Higgs field gets the natural cutoff in TeV scale. The other relevant coupling constants, the UV-sensitivity of Higgs mass due to the loop correction, some applications on the strong CP problem as well as anomalous small fermion mass, and the cosmological constant problem are also discussed.