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Constructing a Feynman loop integral

  1. Dec 2, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to construct the Feynman loop integral for the following diagram:

    loop.jpg (*)

    where [itex]\nu[/itex]L is the left-handed neutrino, [itex]\phi[/itex] is a scalar particle and N is a heavy neutrino with a Majorana mass.

    2. Relevant equations

    N/A

    3. The attempt at a solution

    I'm trying to determine it by comparing it to the self-energy of the electron:

    200px-SelfE.svg.png

    which gives

    self-energy.jpg .

    1) Since there's a scalar propagator ([itex]\phi[/itex]) in (*), do I need to use these Feynman rules?:

    yukawa.jpg

    where m = m[itex]\phi[/itex] in this case. (Taken from http://bolvan.ph.utexas.edu/~vadim/Classes/2011f/QED.pdf).

    2) How do I deal with the fact that the neutrinos are left-handed? Do I just add factors of (1-γ5)/2 in the (-igδβα) terms?

    3) For Dirac particles, the propagator is:

    dirac.jpg

    But how does this change if the particle (in this case, N) is Majorana?


    Any help would be appreciated.

    Thanks!
     
    Last edited: Dec 2, 2011
  2. jcsd
  3. Dec 2, 2011 #2

    fzero

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    Have you been given a Lagrangian? It would be much better to work out the Feynman rules from that rather than try to guess at bits and pieces that might not quite fit what you want.
     
  4. Dec 2, 2011 #3
    The Lagrangian is:

    L = L[itex]\varphi[/itex] + LSM where

    L[itex]\varphi[/itex] = [itex]\frac{1}{2}[/itex]∂μ[itex]\phi[/itex]+μ[itex]\phi[/itex] + [itex]\frac{m^2}{2}[/itex][itex]\phi[/itex]+[itex]\phi[/itex] + [itex]\frac{λ}{4}[/itex]([itex]\phi[/itex]+[itex]\phi[/itex])2 + g[itex]\phi[/itex][itex]\overline{N_R}[/itex][itex]\nu[/itex]L + [itex]\frac{m_N}{2}[/itex]NRTCNR + h.c.

    (g = coupling constant, N = Majorana neutrino, [itex]\phi[/itex] = Neutral scalar, [itex]\nu[/itex]L = LH neutrino),

    However, I was told just to construct it from Feynman rules. Also, I have no idea how to go from this complicated Lagrangian to the integral =/.
     
    Last edited: Dec 2, 2011
  5. Dec 3, 2011 #4
    Anyone? :frown:
     
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