A Casimir trick for neutrinos

1. Jun 27, 2017

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.

Last edited: Jun 27, 2017
2. Jun 27, 2017

Orodruin

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

3. Jun 27, 2017

cipi

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

4. Jun 27, 2017

Orodruin

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

5. Jun 27, 2017

cipi

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.

Last edited: Jun 27, 2017