# Exploring Conservation of Lepton Number in Electron & Muon Neutrino Mixing

• Urvabara
In summary, the conversation discusses a theory where electron and muon neutrinos mix in a way that conserves lepton number. The values for the neutrinos are not specified, but it is determined that the mass eigenstates are Dirac neutrinos. The theory also fits with observational data, but the exact procedure for calculating lepton number is unknown. The conversation ends with a request for assistance with this calculation.
Urvabara

## Homework Statement

In some theory the electron neutrinos and the muon neutrinos mix like this:
$$\mathcal{L}_{m} &= -\frac{1}{2}m\left(\overline{ \nu^{C}_{\mu\text{R}} }\nu_{\text{eL}} + \overline{ \nu^{C}_{\text{eR}} }\nu_{\mu\text{L}}\right) + \text{h.c.}$$

Show that there exists a conserving lepton number in this theory. What are the values for $$\nu_{\text{e}}$$ and $$\nu_{\mu}$$? Are the mass eigenstates Dirac neutrinos or Majorana neutrinos? Does the theory fit with the observational data?

## Homework Equations

$$\mathcal{L}_{m} = \dots = -\frac{1}{2}\left(m\overline{ \nu^{C}_{\mu\text{R}} }\nu_{\text{eL}} + m\overline{ \nu^{C}_{\text{eR}} }\nu_{\mu\text{L}}\right) - \frac{1}{2}\left(m\overline{ \nu_{\text{eL}} }\nu_{\mu\text{R}}^{C}+m\overline{ \nu_{\mu\text{L}} }\nu_{\text{eR}}^{C}\right).$$ Right?

## The Attempt at a Solution

Well, I was just thinking that it must be Dirac type mixing, if there exists a conserving lepton number. So the neutrinos are Dirac neutrinos. Right?

At least, the oscillation fits with the observational data, though in reality there are three types of neutrinos...

But I do not know how to calculate the lepton number. Maybe using the continuity equation and then constructing the Euler-Lagrange equation, but I do not know the exact procedure.

Can you help?

Thanks!

Anyone?

I think they are Dirac.
lepton number conservation? is there some kind of a global symmetry somewhere here?

## 1. What is the conservation of lepton number?

The conservation of lepton number is a fundamental principle in particle physics that states that the total number of leptons (electrons, muons, and their associated neutrinos) must remain constant in any reaction or interaction.

## 2. What is electron and muon neutrino mixing?

Electron and muon neutrino mixing refers to the phenomenon in which electron and muon neutrinos can transform into each other as they travel through space. This is due to the fact that neutrinos have mass and can therefore undergo flavor oscillations.

## 3. How is the conservation of lepton number explored in electron and muon neutrino mixing?

In order to explore the conservation of lepton number, scientists study the properties of neutrinos and their interactions with other particles. By measuring the rates of electron and muon neutrino mixing, scientists can confirm that lepton number is conserved in these processes.

## 4. What are the implications of violating the conservation of lepton number in electron and muon neutrino mixing?

Violating the conservation of lepton number in electron and muon neutrino mixing would indicate the existence of new physics beyond the Standard Model. This could lead to a better understanding of the fundamental forces and particles in the universe.

## 5. How is the conservation of lepton number related to other conservation laws in physics?

The conservation of lepton number is a part of the larger principle of conservation of total lepton number, which also includes the conservation of baryon number. These conservation laws are all related to the overall conservation of energy and matter in the universe.

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