I have encountered some diagrams (like the example below) where two lines coming out of a single vertex (in this context, right-handed neutrino $N^c$) have opposite direction. In a usual diagram, a fermion propagator should have one direction only. Why is this different?
This propagator must come from Majorana fermion which satisfies the real condition i.e. there is only one kind of creation or annihilation operator in plane mode expansion: \begin{align} N^c=\int\overline{\mathrm{d}^3p}\left(e^{-ipx}\zeta a+e^{ipx}\eta a^{\dagger}\right)\, \end{align} where $\overline{\mathrm{d}^3k}$ is the one-particle covariant measure and $\zeta$ and $\eta $ are possible spinors which depend on representations.
As a consequence, $N^c$ could contract (Wick's contraction, recall that this contraction comes from $[a,a^\dagger]$) with $N^c$ itself, which generates this double arrow line.
But for Dirac fermion, there is only the contraction between $\psi$ and $\bar{\psi}$, which yields the one-way arrow from $\psi$ to $\bar{\psi}$ in the propagator.
There is the main difference between those two propagators in Feynman diagrams.
