Question Concerning Neutrino Mass Hierarchy

[Appity]

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 $$\Delta$$ m$$^{2}_{21}$$ 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!

 

[Frame Dragger]

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 $$\Delta$$ m$$^{2}_{21}$$ 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

 

[jeblack3]

I think it just means $$0 < \theta_{12} < \pi/4.$$