Why Does Casimir's Trick Include Nonphysical Neutrino Helicities?

[cipi]

Hello

I was reading in Griffiths that in the case of electron neutrino scattering, one can apply Casimir's trick to sum over input and output spin states, including the neutrinos. My question is, how come you are allowed to include in the sum the nonphysical right handed helicity state ? And, yes, I understand that the final average takes into account that there is only one neutrino spin. But how does the nonphysical helicity not contribute mathematically, since it is included ?

Thank you.

 

[Orodruin]

The interaction vertex contains a projection onto the left-handed states.

 

[cipi]

The interaction vertex contains a projection onto the left-handed states.

Thank you for answering, but trying to understand your answer, given that the vertex is γ^μ (1-γ⁵), in a world where only right handed states interacted, what would the vertex change to ?

 

[Orodruin]

Thank you for answering, but trying to understand your answer, given that the vertex is γ^μ (1-γ⁵), in a world where only right handed states interacted, what would the vertex change to ?

$\gamma^\mu (1+\gamma^5)$

 

[cipi]

$\gamma^\mu (1+\gamma^5)$

Great, I wished missing logic links like this were better explained in the book for leisure readers like myself. Thanks.

I noticed 15 pages later that the book sort of explains it.