1
$\begingroup$

The neutrino mass hierarchies are made of two hypotheses/scenarios:

  • the normal hierarchy: $m1<m2<m3$
  • the inverted hierarchy: $m3<m1<m2$

Why neutrino mass hierarchy scenario do not include also the cases:

  • $m2<m1<m3$?

  • $m3<m2<m1$?

I have seen the post: Neutrino mass hierarchy

but two people are in contradiction and there was no conclusion on who is right. @SRS is saying in this thread that it is a convention to have $m_1<m_2$. Is he right? wrong? Is there a proof of the convention from a statement in a document?

| cite | improve this question | | | | |
$\endgroup$
2
$\begingroup$

We know that $m_1$ is less than $m_2$ from solar neutrino measurements of the MSW effect. Here's a quote from a paper that addresses this

Solar neutrinos allow to fix the sign of $\Delta m^2_{21}$for the standard value of $V_e$. The sign determines the resonance channel (neutrino or antineutrino) and the mixing in matter. The facts that due to smallness of the 1-3 mixing the problem is reduced approximately to the $2\nu$-problem and that suppression of signal averaged over the oscillations at high energies is stronger than 1/2, selects $\Delta m^{2}_{21} > 0 $.

-- Solar neutrinos and neutrino physics, Maltoni & Smirnov.

Put simply we measure the survival probability of solar neutrinos to be (more or less) like this... survival probability Image from Wikipedia.

Where the probability at low energies is ~60% and at high energies is about 30%. If $\Delta m^{2}_{21}$ were negative you would see at high energies the survival probability dip to some value of ~50% at ~1MeV then go back up to ~60% at higher energies. (Caveat, most of the numbers above are made up, take them with a grain of salt).

| cite | improve this answer | | | | |
$\endgroup$
  • $\begingroup$ Is m1 < m3 < m2 ruled out? $\endgroup$ – JollyJoker Feb 25 at 9:12
  • 1
    $\begingroup$ Yes, that possibility is ruled out by the fact that $\Delta m^{2}_{21}$ is ~$10^{-5}$ eV$^2$ and $\Delta m^{2}_{31}$ is around $10^{-3}$ eV$^2$. I.e the mass difference between the $m_{1}$ state and the $m_{3}$ state is very large compared to the difference between the $m_{1}$ state and the $m_{2}$ state. So the only remaining possibilities are $m_{1} < m_{2} < m_{3}$ or $m_{3} < m_{1} < m_{2}$. $\endgroup$ – mze Feb 26 at 18:04
1
$\begingroup$

I was also trying to find a concrete answer to this question and just came across this quote from https://arxiv.org/abs/1801.04946;

Note that the observation of matter effects in the Sun constrains the product $\Delta m_{21}^2 \cos 2θ_{12}$ to be positive. Therefore, depending on the convention chosen to describe solar neutrino oscillations, matter effects either fix the sign of the solar mass splitting $\Delta m_{21}^2$ or the octant of the solar angle $θ_{12}$, with $\Delta m_{21}^2$ positive by definition.

So the answer appears to be both. Though I have seen more documents fixing the octant of the angle than the sign of the splitting.

| cite | improve this answer | | | | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.