Mass difference corresponding to atmospheric oscillations

[krishna mohan]

Hi,

In arXiv:hep-ph/0307149v2, it is mentioned that atmospheric mass-squared difference is not uniquely defined and that the convention that is going to be used is that it is the largest possible mass-squared difference.

I know that the smallest mass difference is identified with solar neutrino oscillations.

So there m1 and then there is m2 which is heavier..

Then we have m3...If we place it above m2, we get normal hierarchy..and if we place it below m1, we get inverted hierarchy...

In either case, we might not be currently able to say whether it is m3- m1 mass difference or m2-m1 mass difference which is identified in atmospheric oscillations...

But with better data, won't we able to make a unique identification? Or is it again somehow a convention dependent thing...like identifying m2 to be bigger than m1...

 

[AndyW]

Hello,

Thank you for bringing up this interesting topic! The atmospheric mass-squared difference is indeed not uniquely defined, as it depends on the convention used. However, as you mentioned, the convention typically used is to take the largest possible mass-squared difference. This convention is based on the fact that in neutrino oscillations, the mass-squared difference is the physical quantity that determines the oscillation frequency.

As for the identification of the mass-squared difference in atmospheric oscillations, it is true that with better data, we may be able to make a more precise determination. However, it is important to keep in mind that the values of the mass-squared differences are not arbitrary, but are determined by the underlying physics of the neutrino oscillations. So even with better data, we may still have some uncertainty in the exact values.

As for the hierarchy of the masses, it is currently unknown whether the normal hierarchy (m1 < m2 < m3) or the inverted hierarchy (m3 < m1 < m2) is the correct one. This is an active area of research and future experiments may shed more light on this question.

Overall, while conventions and uncertainties may exist, it is important to remember that the study of neutrino oscillations is a constantly evolving field and with continued research and advancements in technology, we may be able to make more precise and definitive conclusions about the properties of neutrinos. Thank you for your interest in this topic!