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## What is the neutrino mass hierarchy? Figure 1: Neutrino mass hierarchy. Though the value of the individual masses m1,m2,and m3 are unknown, there are two possible orderings. [click to enlarge]

Though there are three neutrino types, until recently they were thought to be massless. With the discovery of “neutrino oscillations,” however, a phenomenon in which neutrinos change their type in flight, it is now known that not only do they have mass, but the masses of the three types (m1,m2,m3) are different.

Experiments observing the oscillations of neutrinos produced in the sun have determined the squared difference of the masses m1 and m2, m12-m22, and the squared difference between the masses m1 and m3 has been measured using the oscillations of neutrinos produced in the Earth’s atmosphere. However, since oscillation experiments can only probe the squared difference of the masses, the absolute values of m1, m2, and m3 as well as the question of whether or not m2 is heavier than m3 remain unknown. The latter question is known as the “neutrino mass hierarchy problem.” If m2 is lighter than m3, the hierarchy is said to be “normal,” but if it is heavier the hierarchy is called “inverted” (Figure 1).

## Why is the mass hierarchy important?

It turns out that neutrinos and their masses have deep connections with the other elementary particles and nuclei.

Though there are four forces that govern our world (the strong, weak, electromagnetic, and gravitational forces), it is thought that they were unified into a single force under the tremendous temperatures present at the birth of the universe. Theories that seek to explain this “unification” of the forces often predict that the neutrino mass hierarchy is normal. At the same time there are theories that explain the origins of the universe and its particles but which also predict an inverted mass hierarchy. Since it is not possible to recreate the conditions present at the beginning of the universe with modern technology, resolving the neutrino mass hierarchy problem is critical to understanding the early universe using these theories.

Resolving the mass hierarchy also plays a role in understanding the present-day universe. Indeed, it has deep connections to efforts to determine whether or not the neutrino is its own antiparticle. While the particles and antiparticles of all leptons other than neutrinos are known to be different from one another, if there is a lepton whose particle is indistinguishable from its antiparticle, the only possible candidate is the neutrino. For this reason if it could be determined that the neutrino is its own antiparticle it would be a discovery of profound significance. Further, the neutrino mass hierarchy is known to have a strong influence on the number and types of isotopes produced when a star ends its life with a supernova explosion.

Finally, by measuring the differences between the oscillations of neutrinos and antineutrinos it may be possible to solve the long standing mystery of why the present universe is filled with only particles and almost no antiparticles, even though both were thought to exist in equal numbers at its birth. However, if the neutrino mass hierarchy is not known it can obscure the differences in these oscillations and thereby hamper the measurement. Determining the neutrino mass hierarchy is essential to overcoming this difficulty.

## Determining the mass hierarchy at Hyper-Kamiokande Figure 2: Determining the neutrino mass hierarchy at Hyper-Kamiokande. The difference in the expected number of events relative to the expectation assuming no oscillations is shown for the normal (red) and inverted (blue) mass hierarchy. The number of events from the opposite side of the Earth (“upward-going”) that oscillate into electron neutrinos is larger for the normal mass hierarchy. [click to enlarge]

Hyper-Kamiokande will observe large numbers of neutrinos produced by the collisions of cosmic rays with nuclei in the atmosphere. Those which are produced in the atmosphere on the opposite side of the Earth will be influenced by its matter on their way to the detector. Accordingly, the oscillations of such muon neutrinos into electron neutrinos as well as the oscillations of muon antineutrinos into electron antineutrinos will be affected. However, the extent of these effects depends upon the mass hierarchy such that for a normal hierarchy oscillations into electron neutrinos are enhanced, while for an inverted hierarchy oscillations into electron antineutrinos are enhanced. For this reason, the number of events coming from the opposite side of the Earth that oscillate into electron neutrinos will be larger if the hierarchy is normal than if it is inverted (Figure 2). On the other hand, the number of events that oscillate into electron antineutrinos will be larger for the inverted hierarchy than for the normal hierarchy. Though the change in the event rate due to the mass hierarchy is only between about 5 and 15%, because Hyper-Kamiokande is so large it will be able to detect even this small difference.