= Holomorphic need for two Higgs chiral doublets
A renormalizable <MSSM> <superpotential> is a <holomorphic function> of <chiral superfields> and cannot use their conjugates. Gauge-invariant up-type <Yukawa couplings> require $H_u$ of <hypercharge> $+1/2$, while down-type and charged-lepton <Yukawa couplings> require $H_d$ of <hypercharge> $-1/2$. A single doublet and its conjugate cannot play both roles in the <superpotential>. This is distinct from <higgsino anomaly cancellation>.
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