= Solution
Counting the <mass dimensions> of each interaction operator gives
$$
\boxed{[\lambda_a]=-1,\qquad[\lambda_b]=-3,\qquad[\lambda_\gamma]=-1.}
$$
Indeed $\Phi(\partial a)^2$ and $\Phi F^2$ have dimension five, whereas $\Phi b^2(\partial b)^2$ has dimension seven. These are interactions of an <effective field theory> with dimensionful <couplings>.
The direct one-vertex <decay channels> are $\Phi\to aa$, $\Phi\to bbbb$ and $\Phi\to\gamma\gamma$. Each leading <scattering amplitude> is linear in its corresponding <coupling>, and a <decay width> is quadratic in the amplitude. Therefore, holding the parent <mass> fixed,
$$
\boxed{\Gamma_{aa}\propto|\lambda_a|^2,\qquad\Gamma_{bbbb}\propto|\lambda_b|^2,\qquad\Gamma_{\gamma\gamma}\propto|\lambda_\gamma|^2.}
$$
There are no tree-level interference terms between these different final states.
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