Sterile neutrino oscillations in MINOS and hadron production in pC collisions Page: 27 of 237

                                
2.3 Neutrino oscillations

of three mixing angles 012, 023 and 013 and a phase 6 as:

[UI U2 U,31
U   =    Up1 Up2    Up3
U,1 U,2 U,3
C12C13
=    -12C23 - C12823s13ei6
s12823 - C12C23s136i6
1    0     0       c13
=         C c23  823     0
0  -s23   C23    -813i6

s12C13         s130      1   0    0
C12C23 - 812823s13C    s 823c13  0  C a  0
-C12823 - s12c23s13Ci6  c23c13   0   0  e i
0  s13i6e     C12   812 0    1   0    0
1     0      -s12 C12 0      0        l 0
0    C13       0         0  1  0  0 Ci/

where sij = sin 0i and cij = cos Oij. The unitarity constraint on U removes nine free
parameters, and five of the remaining are relative phases between the six lepton fields
which can be absorbed by those fields. This leaves four free parameters in U. A Dirac
phase 6 allows for the possibility of CP violation in the lepton sector. The two Majorana
phases a and # are unobservable in neutrino oscillation experiments. Consequently, these
phases are ignored here, but Majorana phases play an important role in neutrinoless double
# decay search experiments. The last equality does not apply any conceptual modification,
but the mixing matrix is decomposed into terms that can be associated with different classes
of experiments. The leftmost of the matrices, involving 023 is studied by those experiments
concerned with the atmospheric Aflatm. The second-to-rightmost matrix involving 012 is
studied by those experiments interested in the solar Am2. Finally, the matrix involving
013 and 6 is the current most interesting topic in the neutrino sector and will be intensively
studied by future experiments.
Under the assumption of CPT being conserved, the first of the two equalities in equa-

(2.17)

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