A Way to Understand the Mass Generation

TL;DR

This paper proposes a fundamental framework where the Standard Model and family gauge fields originate from a Minkowski space-time with specific gauge groups, predicting the Higgs mass and addressing divergence issues.

Contribution

It introduces a novel approach with built-in gauge groups and scalar fields, predicting the Higgs mass and exploring divergence management.

Findings

Predicts the SM Higgs mass as half the vacuum expectation value.

Suggests family gauge fields prevent Landau ghost and ensure asymptotic freedom.

Proposes a new perspective on the origin of mass and divergence handling.

Abstract

We believe that the quantum 4-dimensional Minkowski space-time with the force-fields gauge-group structure $SU_c(3) \times SU_L(2) \times U(1) \times SU_f(3)$ built-in from the very beginning is the background for everything. Thus, the self-repulsive, but ``related'', complex scalar fields $\Phi(1,2)$ (the Standard-Model Higgs), $\Phi(3,1)$ (the purely family Higgs), and $\Phi(3,2)$ (the mixed family Higgs), with the first family label and the second $SU_L(2)$ label, co-exist such that they generate all the masses if, and only if, necessary. Note that the ``ignition'' channel is on the elusive $\Phi(3,1)$ channel, yielding the prediction that the Standard-Model (SM) Higgs mass $m_{SM}$ is half of the SM vacuum expectation value $v$. Before the ``ignition'', there is no mass terms, including the Higgs, the quarks, and the leptons. Apart from the ``ignition'' term, all the couplings are dimensionless and thus the theory is determined by the quantum 4-dimensional Minkowski space-time. The multi-GeV or sub-sub-fermi $SU_f(3)$ family gauge fields protect the lepton world from the QED Landau ghost and make them asymptotically free. We try to discuss different ways to deal with infinities (ultraviolet divergences) for the resultant Standard Model (as the consistent and complete theory).