Sterile neutrino oscillations in MINOS and hadron production in pC collisions Page: 36 of 237
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2.3 Neutrino oscillations
(2Ev2GFN6)/Am1, that is known as the MSW resonance (after Mikheyev-Smirnov-
* The oscillation probability loses its symmetry in 0 about fr/4 due to the cos(20) term.
* Except at the maximal mixing given by sin2(20) = 1, the oscillation probability
depends on the sign of Am2, giving sensitivity to the mass ordering. For the resonant
condition to occur it is necessary that Amj1 > 0, bounding m2 > Hi1.
* The potential energy for neutrinos and antineutrinos has a different sign: the matter
effect resonant condition could occur either for neutrinos or antineutrinos. This asym-
metry could be exploited to determine the neutrino mass hierarchy from atmospheric
neutrinos, as suggested in , by studying the transition v, --i v1, and T, -> T, that
could be resonant in matter.
2.3.4 Oscillation into sterile neutrinos
The measurement of the width of the Z0 boson bounds the number of light active neutrinos
to three. Nevertheless, as some experiments have suggested, some additional types of
neutrinos may not couple with the Z0 boson and are referred as "sterile". In this section
the formalism for four neutrino mass states is given.
The mixing between the three active neutrino flavours and one sterile neutrino requires
the addition of one mass eigenstate, expanding the PMNS mixing matrix in equation (2.17)
to a 4x4 matrix. The expanded mixing matrix contains six mixing angles and six phases,
with three of the phases being Majorana phases that are not relevant to oscillation experi-
ments. The matrix can be written as a product of six independent rotation matrices about
the Euler axes Ri, where 1j refers to the plane in which a particular rotation takes place,
following the formalism in .
As MINOS is designed to precisely measure Am21 but has no sensitivity to Am21, the
mass states nil and m12 can be treated as degenerate. As a consequence, the corresponding
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Tinti, Gemma Maria & U., /Oxford. Sterile neutrino oscillations in MINOS and hadron production in pC collisions, thesis or dissertation, July 1, 2010; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1015233/m1/36/: accessed April 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.