= Solution
In four spacetime dimensions, canonical <mass dimensions> are
$$
[\phi]=[\Phi]=1,\quad[\psi]=\frac32,\quad[F]=2,\quad[\theta]=-\frac12,\quad[d^2\theta]=1,\quad[d^4\theta]=2.
$$
Since a <Lagrangian> has mass dimension four, a power-counting <renormalizable quantum field theory> requires $[K]=2$ and $[W]=3$, with couplings of nonnegative mass dimension. Up to a positive constant kinetic matrix, field redefinitions and <Kähler transformations>, the renormalizable ungauged kinetic term is canonical. Holomorphic additions to $K$ integrate to a boundary term. The general renormalizable <superpotential> is
$$
\boxed{W=W_0+a_i\Phi_i+\frac12m_{ij}\Phi_i\Phi_j+\frac16y_{ijk}\Phi_i\Phi_j\Phi_k.}
$$
The coefficients have dimensions $3,2,1,0$, respectively; $m_{ij}$ and $y_{ijk}$ may be taken symmetric. The constant $W_0$ does not affect a global chiral theory. Higher polynomial degree in $W$, nontrivial higher-degree terms in $K$, or higher-derivative interactions are <nonrenormalizable interactions> and can instead be retained in an <effective field theory>.
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