A Clifford Algebra Approach to Chiral Symmetry Breaking and Fermion Mass Hierarchies

TL;DR

This paper introduces a novel Clifford algebra framework to model chiral symmetry breaking and fermion mass hierarchies, proposing composite Higgs bosons from fermion condensates and exploring their phenomenological implications.

Contribution

It develops a Clifford algebra-based model for fermion masses and symmetry breaking, predicting multiple composite Higgs bosons and their potential experimental signatures.

Findings

Three composite Higgs bosons from fermion condensates.

Fermion mass hierarchies explained by four-fermion condensations.

Predicted detection of tau neutrino Higgs via charm decay.

Abstract

We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu-Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.