# Neutrino Oscillation in matter

• ChrisVer
In summary, the conversation is about deriving \Delta m_M^2 as given in equation 35 from the provided link. The individual tries to derive the eigenvalues of H_M (equation 33) but only obtains one eigenvalue. They seek help understanding the definition of \Delta m_M^2, which is defined as \Delta m_i^2 \times |m|. The solution provided involves the derivation of m_{1M}^2 and m_{2M}^2 using the equations m_{1M} = m_1 + m and m_{2M} = m_2 - m, resulting in \Delta m_M^2 = \Delta m^2 + 2 m (\Sigma m).
ChrisVer
Gold Member
Hi, I have some problem in deriving $\Delta m_M^2$ as given in eq.35 here:
http://www.slac.stanford.edu/econf/C040802/papers/L004.PDF

When I tried to derive the eigenvalues of $H_M$ (eq.33) I got:

$m^2 = (\cos 2 \theta -x)^2 + \sin^2 2 \theta$
which is only one eigenvalue. Any help? In particular it seems he defines:
$\Delta m_M^2 = \Delta m_i^2 \times |m|$

Here's my solution

#### Attachments

• neutrino in matter.pdf
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If I say:
$m_{1M} = m_1 + m \Rightarrow m_{1M}^2 = m_1^2 + m^2 + 2 m_1 m$
$m_{2M} = m_2 -m \Rightarrow m_{2M}^2 = m_2^2 + m^2 - 2 m_2 m$
Then:
$\Delta m_M^2 =m_{1M}^2 - m_{2M}^2 = (m_1^2 - m_2^2 ) + 2 m (m_1 +m_2 ) = \Delta m^2 + 2 m (\Sigma m)$

## 1. What are neutrino oscillations in matter?

Neutrino oscillations in matter refer to the phenomenon in which neutrinos, which are elementary particles with very little mass and no electric charge, change from one type to another as they travel through matter. This is due to the interaction of neutrinos with the electrons, protons, and neutrons in matter.

## 2. Why do neutrinos oscillate in matter?

Neutrinos oscillate in matter because they have different masses and flavors. As they travel through matter, they interact with the particles in the matter, causing them to change their flavor. This process is known as neutrino oscillation.

## 3. How is neutrino oscillation in matter detected?

Neutrino oscillation in matter is detected through experiments that use large detectors, such as underground neutrino observatories or particle accelerators. These detectors are able to detect the different types of neutrinos and their interactions with matter, providing evidence of neutrino oscillation.

## 4. What impact does neutrino oscillation in matter have on particle physics?

Neutrino oscillation in matter has a significant impact on particle physics as it provides evidence for the existence of neutrino mass and the violation of the conservation of lepton flavor. It also has implications for our understanding of the Standard Model of particle physics and the role of neutrinos in the universe.

## 5. Can neutrino oscillation in matter be controlled or manipulated?

Neutrino oscillation in matter cannot be controlled or manipulated as it is a natural phenomenon that occurs due to the properties of neutrinos. However, scientists continue to study and understand neutrino oscillation in order to improve our understanding of the fundamental particles and forces in the universe.

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