# Cross Section Calculation

1. Jan 10, 2012

### ryanwilk

1. The problem statement, all variables and given/known data

Hi. I'm trying to calculate the cross section for this process:

where $\phi$ is a massive neutral scalar, N is a massive Majorana neutrino and $\nu$L is the normal SM neutrino.

2. Relevant equations

N/A

3. The attempt at a solution
Apparently the answer should be something like: $$\frac{g^4}{4 \pi} \frac{m_N^2}{ {(m_\phi^2+m_N^2)}^2 } \>,$$
where g is the coupling constant.

There’s a similar case in http://zippy.physics.niu.edu/spinors/DHMspinors.pdf, page 45. However, I’m not sure which part of Eq. (4.5.13) corresponds to the diagram above and I don’t know how to deal with the $$\sigma \cdot k$$ term (particularly when calculating the invariant amplitude squared)?

Any help would be appreciated,
Thanks!

Last edited: Jan 10, 2012
2. Jan 12, 2012

### ryanwilk

So, I've attempted to do the calculation. Does this look correct? (there are lots of steps I'm unsure about):

Last edited: Jan 12, 2012