A curious model of the Higgs field: a complex scalar finite field meets the Monster symmetry

TL;DR

This paper proposes a novel finite field model for the Higgs field using a large finite group related to the Monster group, achieving a Higgs mass prediction with 99.7% accuracy and linking group theory to particle physics.

Contribution

It introduces a complex scalar finite field model based on a large finite group of Lie type, connecting phase transition critical points to the Monster group and predicting the Higgs mass.

Findings

Higgs mass calculated with 99.7% agreement to experimental value

Finite group order estimated close to the Monster group

Mass relations linking finite field properties to particle physics

Abstract

As a small step toward understanding the nature of the Higgs field, a curious observation is reported that calculates the mass of the Higgs boson with a 99.7 % agreement to its experimentally measured value. Particularly, motivated by the desire to avoid infinities, a complex scalar finite field that aims to describe the Higgs field is proposed as the underlying field of an extremely huge finite group of Lie type. Then, the occurrence of a critical point of the phase transition in that finite field is explained, and the mass of its bosons is computed employing the Klein-Gordon equation. Next, in a backward analysis, to curiously estimate magnificence of that finite group of Lie type, the mass of Higgs boson is inputted to the obtained mass relation, and a huge order close to the order of the Monster group is outputted. Supported by such a clue as well as the fact that the Monster group is critical among the sporadic groups, it is therefore assumed that the critical order of the corresponding symmetry group (of Lie type), at which its underlying finite field reaches the critical point of a phase transition, is the order of the Monster group. Based on this assumption, the main observation is reported as M_H/M_P = D m_(q^*)/m_2, where M_H, M_P, m_(q^*), m_2, and D, are respectively, the mass of Higgs boson, the reduced Planck mass, the mass of bosons of the finite field, the mass of field with two elements, and the number of spatial dimensions which perfectly match the central charge (i.e., number of degrees of freedom) in the Monster conformal field theory.