Dirac, Majorana & a missing factor of 2

[EL]

A question concerning Feynman rules for Dirac vs Majorana neutrinos.

Take e.g. the scattering process:
electron + positron -> electron neutrino + electron antineutrino.

Following the electroweak Feynman rules we can calculate an expression for the unpolarized differential cross section.
The total cross section is then obtained by integrating over the angels, and, in the case of identical particles in the final state (as would be the case for Majorana neutrinos which are their own antiparticles), multiply by the symmetry factor 1/2.

So, to me it seems this procedure would give different results for Majorana and Dirac neutrinos. I'm definitely missing something here, since obviously this cannot be the case. (E.g. the number of neutrino species predicted from data from measurements of the Z width should hold no matter if the neutrinos are Majorana or Dirac.)

Where is the missing factor of 2?

 

[LightHero]

The missing factor of 2 is due to the fact that Majorana neutrinos are their own antiparticle. This means that when we calculate the differential cross section for the scattering process described above, we need to double the result to account for the two ways the scattering can occur: electron + positron -> electron neutrino + electron antineutrino, and electron + positron -> electron antineutrino + electron neutrino. Since the neutrino is its own antiparticle, these two processes are indistinguishable from one another.

 

[sir-pinski]

The missing factor of 2 in the Feynman rules for Dirac vs Majorana neutrinos arises due to the fact that Majorana neutrinos are their own antiparticles, while Dirac neutrinos have separate particles and antiparticles. This difference leads to a different interpretation of the Feynman diagrams and the calculation of the cross section for the scattering process mentioned.

In the case of Majorana neutrinos, the Feynman diagram would represent the exchange of a single particle, while for Dirac neutrinos it would represent the exchange of both a particle and its antiparticle. This means that in the case of Majorana neutrinos, the symmetry factor of 1/2 should not be applied when calculating the total cross section, as there is only one particle involved in the interaction.

Furthermore, the number of neutrino species predicted from data on the Z width should indeed hold regardless of whether the neutrinos are Majorana or Dirac. This is because the Z boson interacts with both neutrinos and antineutrinos, so the distinction between Majorana and Dirac neutrinos does not affect the measurements of the Z width.

In summary, the missing factor of 2 in the Feynman rules for Dirac vs Majorana neutrinos arises due to the different interpretations of the Feynman diagrams and the number of particles involved in the interaction. It is important to consider this distinction when calculating cross sections and interpreting experimental data.