  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.
