Quantum Field Theory-Mass spectrum of Lagrangian

[jgarrel]

Homework Statement

We are given the Lagrangian density:
$$ \mathcal{L}=\partial^\mu \phi ^* \partial_\mu \phi - m\phi^* \phi +\sum_{\alpha =1} ^2 (
\overline{\psi}^\alpha (i\gamma^\mu \partial_\mu -m)\psi^\alpha -g\overline{\psi}^\alpha\psi^\alpha \phi^* \phi) $$
, where $\phi$ is a complex scalar field, $\psi ^1$ $\psi ^2$ are Dirac fields and m,g are constants.

We are asked to find the mass and the spin of the particles that this theory describes.

Homework Equations

The Attempt at a Solution

I thouht about using spontaneous symmetry breaking and the Higgs mechanism, but I don't know how to deal with the kind of coupling presented in this problem.

 

[Asim Riaz]

I also thought about using the Feynman rules to calculate the propagators, but I don't think this is the right approach either. Any help would be appreciated.