Question Concerning Neutrino Mass Hierarchy

In summary, the issue of determining the mass hierarchy of neutrino oscillations is complicated due to the dependence on the mass squared differences of the mass eigenstates. There are two possible hierarchies, the "normal" and "inverted" hierarchy, with the latter indicating a greater mass for v2 than v1. The paper referenced discusses the positive mass squared difference for solar neutrinos, which is attributed to the solar mixing angle θ12 lying in the first octant. This refers to the direction of emission from the sun, specifically 0 < θ12 < π/4. Further research is needed to fully understand the relationship between octants and neutrino parameters.
  • #1
Appity
9
0
I've been reading up on neutrino oscillations and I have come across this issue. I know that oscillations are dependent on the mass squared differences of the mass eigenstates, which is why determining things like the absolute masses of the eigenstates and the hierarchy of the eigenstates is difficult.

When I see possible mass hierarchies, there are usually two options presented; the "normal" hierarchy (v1 < v2 < v3) and the "inverted" hierarchy (v3 < v1 < v2). This means that we know v2 is greater than v1. When I tried to look for an explanation, the closest I got was a description in the following paper: http://arxiv.org/abs/hep-ph/0407155

At the bottom of page 2, it states that "For the solar neutrinos, the mass squared difference [tex]\Delta[/tex] m[tex]^{2}_{21}[/tex] is known to be positive, since the solar mixing angle θ12 lies in the first octant."

I've tried looking up what it means by "octant" and how it relates to the neutrino parameters, but no luck. Can anyone explain or offer any sources discussing the matter? Thanks in advance!
 
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  • #2
Appity said:
I've been reading up on neutrino oscillations and I have come across this issue. I know that oscillations are dependent on the mass squared differences of the mass eigenstates, which is why determining things like the absolute masses of the eigenstates and the hierarchy of the eigenstates is difficult.

When I see possible mass hierarchies, there are usually two options presented; the "normal" hierarchy (v1 < v2 < v3) and the "inverted" hierarchy (v3 < v1 < v2). This means that we know v2 is greater than v1. When I tried to look for an explanation, the closest I got was a description in the following paper: http://arxiv.org/abs/hep-ph/0407155

At the bottom of page 2, it states that "For the solar neutrinos, the mass squared difference [tex]\Delta[/tex] m[tex]^{2}_{21}[/tex] is known to be positive, since the solar mixing angle θ12 lies in the first octant."

I've tried looking up what it means by "octant" and how it relates to the neutrino parameters, but no luck. Can anyone explain or offer any sources discussing the matter? Thanks in advance!

I believe they are referring to direction of emission from the sun, not a property of neutrinos themselves. http://en.wikipedia.org/wiki/Octant
 
  • #3
I think it just means [tex]0 < \theta_{12} < \pi/4.[/tex]
 

1. What is the question concerning neutrino mass hierarchy?

The question concerning neutrino mass hierarchy is whether neutrinos have a hierarchical mass pattern, meaning that they have distinct mass values that follow a specific order, or whether they have a non-hierarchical or degenerate mass pattern, meaning that their mass values are relatively similar to each other.

2. Why is the question of neutrino mass hierarchy important in science?

The question of neutrino mass hierarchy is important because it can provide valuable insights into the fundamental properties of neutrinos and their role in the universe. It can also help us understand the fundamental laws of physics and potentially lead to new discoveries.

3. How do scientists study the neutrino mass hierarchy?

Scientists study the neutrino mass hierarchy using a variety of techniques, including experiments that measure the oscillation of neutrinos between different types, measurements of the energy distribution of neutrinos, and observations of cosmic events such as supernovae.

4. What are the current theories about the neutrino mass hierarchy?

The most widely accepted theory is the three-neutrino framework, which suggests that there are three types of neutrinos with different masses. Within this framework, there are two main theories: the normal hierarchy, where the neutrinos have a hierarchical mass pattern, and the inverted hierarchy, where the neutrinos have a non-hierarchical mass pattern.

5. What are the potential implications of discovering the neutrino mass hierarchy?

Discovering the neutrino mass hierarchy could have many implications for our understanding of the universe. It could help us understand the origin of mass in the universe, the nature of dark matter, and the asymmetry between matter and antimatter. It could also have practical applications in fields such as energy production and medical imaging.

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