1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    3. The attempt at a solution

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


    which gives

    self-energy.jpg .

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


    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:


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

    Any help would be appreciated.

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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook