Seesaw mass matrix and neutrino masses

  • Thread starter rruben
  • Start date
  • #1
4
0

Main Question or Discussion Point

Hi

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!
 

Answers and Replies

  • #2
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,554
6,316
The sign is not irrelevant, it is related to the Majorana phase of the eigenstate. The mass of the particle is the absolute value of the eigenvalue.

Edit: You will notice that also the Dirac mass matrix
$$
\begin{pmatrix}
0 & m \\
m & 0
\end{pmatrix}
$$
has one positive and one negative eigenvalue.
 
  • #3
4
0
Thanks for your reply. I will look into it a bit more.
 

Related Threads for: Seesaw mass matrix and neutrino masses

  • Last Post
Replies
2
Views
4K
Replies
7
Views
1K
Replies
1
Views
580
Replies
9
Views
2K
Replies
2
Views
3K
Replies
2
Views
5K
  • Last Post
Replies
2
Views
689
Replies
5
Views
2K
Top