Sterile neutrino oscillations in MINOS and hadron production in pC collisions Page: 29 of 237
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2.3 Neutrino oscillations
VeV I vAm
Normal Hierarchy Inverted Hierarchy
Figure 2.1: Schematic of the two allowed mass orderings given fixed Am2tm and Am . The
diagram on the left is for the normal mass ordering, while the diagram on the right is for
the inverted mass ordering. The colours show the approximate flavour content of each mass
state. The figure is taken from .
Figure 2.1 shows the two possible mass orderings for the three-neutrino case that allow
Amatm > Am. They are usually referred to as the "normal" and the "inverted" mass
hierarchy. Note that the mass ordering for Am (with m2 > nil) has already been
established by the oscillations in matter, as will be explained in section 2.4.1.
In the MINOS experiment, studied in this thesis, a beam of v1, is produced and, after
allowing for neutrino propagation, neutrinos of the same flavour are detected. The survival
probability can be written, expanding equation (2.16):
P(v, - vl) = 1 - 41U,3 2 1U,12 sin2 A31
-41U,3 2 1U22 sin2 A32 - 4U, 2 121U,12 sin2 A21. (2.19)
MINOS is designed to precisely measure Am2 but has no sensitivity to Am2, because
of the ratio between the baseline and the neutrino energy chosen. Consequently the mass
states nil and m2 can be treated as degenerate. Equation (2.19) can be rewritten as:
P(v, -1 v/) = 1 - 4 U/3 2(1 - U3A2) sin2 As, + O(A2i) (2.20)
Am 2 L/4E. A., is the effective atmospheric Am2
where I U,32 =3 2 3 and A,,
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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/m1/29/: accessed April 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.