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## CP Violation in the D4-D5-E6 model

Of the three symmetries of CPT,
C is not a fundamental spacetime symmetry,
but
P and T are.
P is reversal of the orientation of the 3 (or 7) space dimensions
of 4 (or 8) dimensional spacetime.
T is reversal of the 1 time dimension.
C is the charge (electic or color) of a particle.
C is related to P and T such that CPT = I, so that CP = T.
The D4-D5-E6 Lagrangian contains scalar, vector, and spinor fields.
The D4-D5-E6 scalar particles are single particles.
A scalar particle is invariant under P and T.
The D4-D5-E6 vector particles are single particles.
A vector particle is invariant under P and T.
After dimensional reduction, that is, below the Planck energy,
the D4-D5-E6 spinor particles are either:
single particles - first generation;
pairs of particles - second generation; or
triples of particles - third generation.
A single spinor particle has helicity, and so is NOT invariant under P.
The SU(2) weak bosons inherit P violation
from their interaction with spinor fermions.
Denote a first generation spinor single as 1.
1 is invariant under T.
Denote a second generation spinor pair by 1-2.
A transition from 1-2 to 1 can only proceed by one decay route,
the decay of 2,
and so is invariant under T.
Denote a third generation spinor triple by 1-2-3.
A transition from 1-2-3 to 1-2 can only proceed by one decay route,
the decay of 3,
and so is invariant under T.
A transition from 1-2-3 to 1 can proceed by two alternative decay routes,
the decay of 3 followed by the decay of 2, and
the decay of 2 followed by the decay of 3,
and so is NOT invariant under T.
The result is T = CP violation measured by a phase
in the Kobayashi-Maskawa mixing matrix for three generations.
Below the Higgs energy, some KM matrix elements can be determined by masses.
Above the Higgs energy, but below the Planck energy,
symmetries in the D4-D5-E6 model give the same values for those KM elements.
At the Planck energy,
before dimensional reduction so that spacetime is 8-dimensional,
the D4-D5-E6 model fermions have only one generation,
so that T and CP are conserved.

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