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Since a few days I've been confused about the seesaw mass matrix explaining neutrino masses. It is the following matrix:

[itex]\begin{pmatrix} 0 & m\\ m & M \\ \end{pmatrix}[/itex].

As can easily be checked it has two eigenvalues which are given by [itex]M[/itex] and [itex]-m^2/M[/itex] in the limit [itex]M>>m[/itex] (the limit doesn't really matter one is always negative when M and m are positive). It seems really weird to me that you would have a negative mass.

As a lot of papers on the subject (Y. Chikashige, R.N. Mohapatra and R.D. Peccei, Phys. Lett. B98 (1981) 265 and others) will tell you the "mass eigenstates" have masses [itex]M[/itex] and [itex]m^2/M[/itex] without the minus sign. This makes me feel like I'm missing something that makes the sign irrelevant. Could anyone help me with this?

Thanks in advance!

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# Seesaw mass matrix and neutrino masses

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