The scalar partner of Majorana particle in SUSY

[Accidently]

For example, the right-handed sneutrino. It can decay into both (s)leptons and anti-(s)leptons, so it is also the anti-particle of itself. I wonder how it looks like mathematically. If it is the same as normal scalar field, we can still distinguish its anti-particle (the complex conjugate)...

 

[Bill_K]

I don't understand. ν_R is just a single state. So wouldn't its superpartner be a single state also, i.e. a real scalar?

 

[Accidently]

I don't understand. ν_R is just a single state. So wouldn't its superpartner be a single state also, i.e. a real scalar?

I don't think it can be a real scalar. When we calculate the number density of the scalar $$n = -i(\phi\dot\phi^*-\dot\phi\phi^*)$$, a real scalar cannot have a non-zero number density.

Let me rephrase this question: Think about the plane wave solution of this scalar $$\phi=Ae^{-i\rm{px}}$$. So its anti-particle $$\phi=Ae^{i\rm{px}}$$ cannot be itself, unless it is real. But in this case, it cannot have a number density.

 

[Bill_K]

What you're calling the number density is actually the charge density. Better read up on the Klein-Gordon equation!