= Tree-level supertrace mass sum rule
{title2=$\operatorname{STr}M^2=0$}
For canonical positive kinetic terms in global <supersymmetry>, $V=\sum_k|W_k|^2$ has mixed <Hessian matrix> $V_{i\bar j}=\sum_kW_{ki}\overline{W_{kj}}$ and holomorphic block $V_{ij}=\sum_k\overline{W_k}W_{kij}$. The $2n$ real scalar squared-mass sum is $2\operatorname{tr}(m^\dagger m)$ for the <chiral-superfield fermion mass matrix> $m=W_{ij}$. Each <Weyl spinor> contributes two states, giving the same fermion weighted sum. Thus their boson-minus-fermion <supertrace> vanishes even with <F-term> breaking. The holomorphic Hessian splits real scalar masses without changing their sum. Noncanonical <Kähler metrics>, <supergravity>, and radiative corrections require different formulas.
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