# Seesaw mass matrix and neutrino masses

• rruben
In summary, the conversation revolves around the seesaw mass matrix for neutrinos and the presence of a negative mass. The speaker is confused about this and is seeking clarification. It is explained that the negative mass is related to the Majorana phase of the eigenstate and the mass of the particle is the absolute value of the eigenvalue. The speaker is advised to look into the Dirac mass matrix which also has a positive and negative eigenvalue.
rruben
Hi

Since a few days I've been confused about the seesaw mass matrix explaining neutrino masses. It is the following matrix:
$\begin{pmatrix} 0 & m\\ m & M \\ \end{pmatrix}$.

As can easily be checked it has two eigenvalues which are given by $M$ and $-m^2/M$ in the limit $M>>m$ (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 $M$ and $m^2/M$ without the minus sign. This makes me feel like I'm missing something that makes the sign irrelevant. Could anyone help me with this?

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.

rruben
Thanks for your reply. I will look into it a bit more.

## 1. What is a seesaw mass matrix?

A seesaw mass matrix is a mathematical framework used to explain the extremely small masses of neutrinos, which are subatomic particles that have no electric charge and very little mass. In this framework, the masses of heavy and light neutrinos are related through a seesaw mechanism, with the heavy neutrinos having masses much larger than the light neutrinos.

## 2. How does the seesaw mass matrix relate to neutrino masses?

The seesaw mass matrix provides a theoretical explanation for the extremely small masses of neutrinos. It proposes that the masses of heavy and light neutrinos are related through a seesaw mechanism, in which the heavy neutrinos have masses much larger than the light neutrinos. This mechanism allows for the light neutrino masses to be extremely small, in contrast to the masses of other subatomic particles.

## 3. What is the significance of the seesaw mass matrix?

The seesaw mass matrix is significant because it provides a theoretical framework for understanding the extremely small masses of neutrinos. It also allows for the possibility of explaining other phenomena related to neutrinos, such as their ability to oscillate between different types, or flavors.

## 4. How is the seesaw mass matrix related to the Standard Model of particle physics?

The seesaw mass matrix is not explicitly part of the Standard Model of particle physics, but it is a proposed extension to the model that can potentially explain the masses of neutrinos. It is still an area of active research and is not yet fully accepted as part of the Standard Model.

## 5. How is the seesaw mass matrix tested experimentally?

One way to test the seesaw mass matrix is through experiments that measure the properties of neutrinos, such as their masses and flavor oscillations. These experiments may involve particle colliders or large-scale detectors, such as the Super-Kamiokande experiment in Japan. Additionally, theoretical predictions based on the seesaw mass matrix can be compared to experimental results to test its validity.

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