  With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion
and a right-handed fermion both expressed as the quaternion makes an octonion,
and the gauge field can be treated as self-dual, we calculate the axial current
and two vector currents triangle diagram of Bardeen, which yields the
contribution of the axial anomaly.
  The octonion possesses the triality symmetry, and there are 5 symmetry
operations $G_{ij}$ and $G_{ijk}$ ($ijk=123)$, in which mixing of spinors and
vectors occur. $G_{23}$ does not mix vectors and spinors, but mismatch of the
spinor and vector fields occurs. Hence, electro magnetic (EM) wave emitted from
galaxies transformed by the five transformations would not be detected by EM
detectors in our galaxy, and the source would be regarded as dark matter.
  The axial anomaly appears as a reflection of the symmetry of the matter field
and not as a reflection of the symmetry of the pure vacuum, which is consistent
with recent arguments on condensates and confinement.
