= Mass spectrum of the quadratic-cubic O'Raifeartaigh model
{title2=$W=\lambda X(Z^2-\mu^2)+MYZ$}
For positive real $M,\mu,\lambda$ with $M^2>2\lambda^2\mu^2$, minimizing $V=\lambda^2|z^2-\mu^2|^2+M^2|z|^2+|2\lambda xz+My|^2$ gives $z=y=0$ with arbitrary $x$. Around $x=0$, the real scalar squared masses are $0,0,M^2,M^2,M^2-2\lambda^2\mu^2,M^2+2\lambda^2\mu^2$, while the three <Weyl spinor> masses are $0,M,M$. Their weighted <supertrace> vanishes. The massless $\psi_X$ is the <goldstino>; the two real $x$ modes form a tree-level <pseudomodulus>. The stability bound follows from $|z^2-\mu^2|^2\ge(|z|^2-\mu^2)^2$, after minimizing the final square over $y$.
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