Hierarchy spectrum of SM fermions: from top quark to electron neutrino

TL;DR

This paper explores how four-fermion operators from quantum gravity could explain the fermion mass hierarchy, neutrino masses, and phase transitions in the Standard Model, proposing a unified framework for fermion masses and new physics phenomena.

Contribution

It introduces a novel approach linking quantum gravity-induced four-fermion operators to the fermion mass hierarchy, neutrino masses, and phase transitions in the Standard Model.

Findings

Hierarchical patterns of fermion masses and mixing matrices are qualitatively derived.

Light Majorana neutrino masses are consistent with oscillation data.

A phase transition at TeV scale addresses the fine-tuning problem.

Abstract

In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy functions. The study is motivated by the speculation that these four-fermion operators are probably originated due to the quantum gravity that provides the natural regularization for chiral-symmetric gauge field theories. In the chiral-gauge symmetry breaking phase, as to achieve the energetically favorable ground state, only the top-quark mass is generated via the spontaneous symmetry breaking, and other fermion masses are generated via the explicit symmetry breaking induced by the top-quark mass, four-fermion interactions and fermion-flavor mixing matrices. A phase transition from the symmetry breaking phase to the chiral-gauge symmetric phase at TeV scale occurs and the drastically fine-tuning problem can be resolved. In the infrared fixed-point domain of the four-fermion coupling for the SM at low energies, we qualitatively obtain the hierarchy patterns of the SM fermion Dirac masses, Yukawa couplings and family-flavor mixing matrices with three additional right-handed neutrinos $\nu^f_R$. Large Majorana masses and lepton-symmetry breaking are originated by the four-fermion interactions among $\nu^f_R$ and their left-handed conjugated fields $\nu^{fc}_R$. Light masses of gauged Majorana neutrinos in the normal hierarchy ($10^{-5}-10^{-2}$ eV) are obtained consistently with neutrino oscillations. We present some discussions on the composite Higgs phenomenology and forward-backward asymmetry of $t\bar t$-production, as well as remarks on the candidates of light and heavy dark matter particles (fermions, scalar and pseudoscalar bosons).