I am wondering... And I may be wrong but please correct me...(adsbygoogle = window.adsbygoogle || []).push({});

In general we have some constraints on the masses of the 3 flavored neutrinos [itex] m_{\nu_e}, m_{\nu_\mu} , m_{\nu_\tau}[/itex] and so there must be some constrain on the values of the 3 neutrino masses [itex]m_1, m_2, m_3[/itex]. Am I right?

Also the probability of flavor change is oscillating with distance with a frequency that's proportional to [itex]\Delta m_{ij}^2 [/itex] (i,j in [1,3] ).

My question is what happens if there is a 4th sterile neutrino, of the acceptable mass of [itex]m_\nu \sim 50~\text{GeV}[/itex] ?

I'd think then that the additional [itex]m_4[/itex] that we would have to introduce would have to be very large as well (so that its combination with [itex]m_i[/itex] is large)....and finally [itex]\frac{\Delta m _{4i}^2}{E} \approx \frac{m_4^2}{E} = \frac{2500 ~\text{GeV}^2}{5 \cdot 10^{-3}~\text{GeV}} = 5 \cdot 10^5~\text{GeV}[/itex]

Is this right so long? I'd guess then that a reasonable distance for oscillation to occur would be at approximately [itex]L \sim 10^{-21} m[/itex]?

http://pdg.lbl.gov/2011/reviews/rpp2011-rev-neutrino-mixing.pdf

(used 13.15 together with 13.12)

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# Neutrino masses and sterile neutrinos

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