Rearranging neutrino expression in see-saw maths

In summary, the conversation discusses the equality of two expressions involving the conjugation of fields in the see-saw mechanism. The first expression is incorrect as the fields on the right are not conjugated while those on the left are. The correct expression is obtained by adding the hermitian conjugate on both sides. The proof is provided, showing the equality between the two expressions.
  • #1
venus_in_furs
19
1
Hello

I'm working through the see-saw mechanism.
This is currently from the one-generation section.
(I haven't got to the three generation workings yet... although I'm guessing I'll come across something very similar in the three generation model)

Could someone please tell me if it is correct or not that
[itex] \bar{\nu_R} \nu_R^c = \bar{\nu_R^c} \nu_R [/itex]

and if it is, could I please have a hint as to why / how to prove this.

Thank you in advance!
 
Physics news on Phys.org
  • #2
It is not true, the fields on the right are not conjugated while those on the left are. You might want to add the hermitian conjugate on both sides.
 
  • #3
ahhhhh thankyou, I think I have it ...

[itex] \overline{ \nu_R^c} \nu_R + h.c. = \overline{ \nu_R} \nu_R^c + h.c. [/itex]

[itex] (1) + h.c. = (2) + h.c. [/itex]

[itex] (1)^{\dagger} +h.c. = (2) + h.c. [/itex]Proof

[itex] (1)^{\dagger} = ( \overline{ \nu_R^c} \nu_R )^{\dagger} [/itex]

[itex] = ( - \nu_R^T C ^{\dagger} \nu_R )^{\dagger} [/itex]

[itex] = \nu_R^{\dagger} C \nu_R^{\ast} [/itex]

[itex] = \nu_R^{\dagger}\gamma^0 C \gamma^0 \nu_R^{\ast} [/itex]

[itex] = \overline{\nu_R} C \gamma^0 \nu_R^{\ast} [/itex]

[itex] = \overline{\nu_R} C \overline{\nu_R^{T} } [/itex]

[itex] = \overline{\nu_R} \nu_R^{c} = (2) [/itex]
 

1. What is the see-saw mechanism in neutrino physics?

The see-saw mechanism is a theoretical framework used to explain the small mass of neutrinos compared to other elementary particles. It proposes that there are two types of neutrinos - light and heavy - and that they interact with each other to produce the observed mass of neutrinos.

2. How does the see-saw mechanism explain the mass of neutrinos?

The see-saw mechanism proposes that the heavy neutrinos have a very large mass and the light neutrinos have a very small mass. When the two interact, the heavy neutrino's mass is transferred to the light neutrino, resulting in the observed small mass of neutrinos.

3. What is the role of rearranging neutrino expressions in see-saw maths?

Rearranging neutrino expressions in see-saw maths is a common technique used to simplify and solve complex equations related to the see-saw mechanism. This allows scientists to better understand the relationship between the different types of neutrinos and their masses.

4. Can the see-saw mechanism be tested experimentally?

Yes, the see-saw mechanism can be tested through various experiments such as studying the energy spectrum of neutrinos and measuring their oscillation patterns. These experiments provide evidence for the existence of heavy neutrinos and support the validity of the see-saw mechanism.

5. How does rearranging neutrino expressions in see-saw maths impact our understanding of the universe?

Rearranging neutrino expressions in see-saw maths allows scientists to further explore and analyze the properties of neutrinos, which are fundamental particles in the universe. This understanding can contribute to our knowledge of the early universe and the fundamental laws of physics.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
6
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
3
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
  • Advanced Physics Homework Help
Replies
1
Views
733
  • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
Replies
1
Views
837
Replies
3
Views
641
  • Set Theory, Logic, Probability, Statistics
Replies
12
Views
5K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
2K
Back
Top