The scalar partner of Majorana particle in SUSY

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Discussion Overview

The discussion revolves around the properties of the right-handed sneutrino as a scalar partner of Majorana particles in supersymmetry (SUSY). Participants explore its mathematical representation, decay processes, and implications for particle states.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that the right-handed sneutrino can decay into both (s)leptons and anti-(s)leptons, indicating it is its own anti-particle and questions its mathematical representation.
  • Another participant questions whether the superpartner of the right-handed neutrino (νR) could be a single state, proposing it might be a real scalar.
  • A different participant challenges the notion that νR's superpartner could be a real scalar, arguing that a real scalar cannot have a non-zero number density based on calculations involving the scalar field.
  • One participant rephrases the question regarding the plane wave solution of the scalar field, suggesting that its anti-particle cannot be itself unless it is real, which contradicts the number density argument.
  • Another participant corrects the terminology used by a previous contributor, stating that what was referred to as number density is actually charge density and suggests reviewing the Klein-Gordon equation.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the sneutrino and its superpartner, with no consensus reached on whether it can be classified as a real scalar or the implications of its decay properties.

Contextual Notes

There are unresolved assumptions regarding the definitions of number density and charge density, as well as the implications of the Klein-Gordon equation in this context.

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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)...
 
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I don't understand. νR is just a single state. So wouldn't its superpartner be a single state also, i.e. a real scalar?
 
Bill_K said:
I don't understand. νR 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 [tex]n = -i(\phi\dot\phi^*-\dot\phi\phi^*)[/tex], a real scalar cannot have a non-zero number density.

Let me rephrase this question: Think about the plane wave solution of this scalar [tex]\phi=Ae^{-i\rm{px}}[/tex]. So its anti-particle [tex]\phi=Ae^{i\rm{px}}[/tex] cannot be itself, unless it is real. But in this case, it cannot have a number density.
 
What you're calling the number density is actually the charge density. Better read up on the Klein-Gordon equation!
 

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