Heavy sterile neutrino decay into Z bosons. (Feynman Diagram)

[HypnoFunk]

Hello there,

I am looking at the decays of Heavy sterile neutrinos in the their mass states to Z bosons.

Using the feynman rules, how would I go about calculating the decay amplitude. I have only ever seen cases where the Z boson is a propagator. Would my expression look something like this:

$M = \kappa\frac{g}{2\cos\theta_{W}}\overline{\nu_{1}}(2)\gamma^{\mu}P_{L}N_{m}(1)\epsilon_{\mu}^{*}(3)$

where $\kappa$ is some constant. Essentially the Feynman diagram looks like a standard weak vertex between two neutrinos. The only difference is that one of them is Heavy (GeV-TeV) scale. However my question really is about whether I just take the standard vertex and include the $\epsilon^{*\mu}$ vector for the outgoing Z-boson.

The standard vertex factor reads
$-i\frac{g}{2\cos\theta_{W}}\kappa\gamma^{\mu}P_{L}$

Is it enough for me to just add $\epsilon^{\mu *}$ for the outgoing Z boson?

Thank you to anyone who can help.

 

[SuperStringboy]

i think the part of z (ϵμ∗ )boson is correct but there is a problem in vertex. Because sterile neutrino does not interact in weak interaction so it will not couple to z boson. so you need to do something different here. You can check Mahapotro's " Massive neutrinos in physics and astrophysics " . check out the chapter on Left right symmetric model. there check sections like FCNC and heavy neutrino decay. I think you can find your answer there. So check if possible.

 

[Vanadium 50]

I think that's right - if it's sterile, the vertex is 0, right?

More realistically, you will have to have to define your couplings and decide how sterile is sterile.

 

[Parlyne]

Vanadium, in my experience, sterile neutrino models (well, interesting ones at least) generally have small mixings between the sterile and active neutrinos. I think that's what Hypnofunk's $\kappa$ is intended to quantify.