# Constructing a Feynman loop integral

1. Dec 2, 2011

### ryanwilk

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

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

(*)

where $\nu$L is the left-handed neutrino, $\phi$ 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:

which gives

.

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

where m = m$\phi$ 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.

Thanks!

Last edited: Dec 2, 2011
2. Dec 2, 2011

### fzero

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.

3. Dec 2, 2011

### ryanwilk

The Lagrangian is:

L = L$\varphi$ + LSM where

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

(g = coupling constant, N = Majorana neutrino, $\phi$ = Neutral scalar, $\nu$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
4. Dec 3, 2011

Anyone?