= Solution
The remaining non-derivative component term in the Lagrangian is the <Yukawa interaction>
$$
\mathcal L_{\rm fermion,pot}
=-\frac12W''(v+\widetilde\varphi)\psi\psi+\mathrm{h.c.}
=-\frac12(M_v+g\widetilde\varphi)\psi\psi+\mathrm{h.c.}
$$
Equivalently the interaction Hamiltonian has the opposite displayed sign. The first term is the two-component <fermion> mass, and the second its scalar-fermion interaction. A phase redefinition of $\psi$ makes the mass coefficient nonnegative, so the physical <Weyl spinor> mass is
$$
\boxed{m_{\rm fermion}=|M_v|=\sqrt{|m^2-2g\kappa|}.}
$$
It is again independent of $\alpha$, the choice of root and any sign of a real $M_v$. This distinguishes the complex bilinear coefficient from the nonnegative physical mass. In the pure-linear supersymmetry-breaking branch $W''=0$, the <fermion> is the massless <Goldstino>.
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