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Take a canonical Kähler potential $K={\Phi }^{†}\Phi$ and the Wess–Zumino model superpotentialThe F-term component givesEliminating the auxiliary field by $F=-\overline{W^{\prime }(\varphi )}$ gives the F-term scalar potential $V=|W^{\prime }(\varphi ){|}^2$. ConsequentlyThis is the supersymmetric relation between quartic and Yukawa couplings: there is one holomorphic parameter $g$, with the quartic coefficient $|g{|}^2$ and the Yukawa coupling $g$ in the displayed normalization. For real $g$ the quartic coefficient is the $g^2$ of the question. They cannot be varied independently while retaining this canonical supersymmetry.

The relation produces the supersymmetric cancellation of quadratic divergences. Bosonic and fermionic Feynman diagrams correcting a scalar mass have equal ultraviolet quadratic coefficients and opposite signs, so the mass is not driven directly to the ultraviolet cutoff scale. In a theory with soft supersymmetry breaking, residual corrections instead have the schematic sizewith coefficients and logarithms depending on the spectrum. Thus superpartner masses near the electroweak scale can stabilize the Higgs boson mass against a much larger cutoff, addressing the radiative part of the hierarchy problem. Heavy sparticles leave a corresponding residual sensitivity; the cancellation does not by itself explain every mass scale.