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Homework Help: Cross Section Calculation

  1. Jan 10, 2012 #1
    1. The problem statement, all variables and given/known data

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

    diag.jpg

    where [itex]\phi[/itex] is a massive neutral scalar, N is a massive Majorana neutrino and [itex]\nu[/itex]L is the normal SM neutrino.

    2. Relevant equations

    N/A

    3. The attempt at a solution
    Apparently the answer should be something like: [tex] \frac{g^4}{4 \pi} \frac{m_N^2}{ {(m_\phi^2+m_N^2)}^2 } \>, [/tex]
    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 [tex] \sigma \cdot k [/tex] term (particularly when calculating the invariant amplitude squared)?

    Any help would be appreciated,
    Thanks!
     
    Last edited: Jan 10, 2012
  2. jcsd
  3. Jan 12, 2012 #2
    So, I've attempted to do the calculation. Does this look correct? (there are lots of steps I'm unsure about):

    blargleb.jpg
     
    Last edited: Jan 12, 2012
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