Radiative corrections to Higgs-boson-mass sum rules in the minimal supersymmetric extension to the standard model

The mass sum rules involving Higgs bosons that arise in supersymmetric extensions to the standard model are renormalized. The general procedure for calculating radiative corrections to these relations is presented. The radiative corrections from loop contributions of quarks, leptons, and their supersymmetric partners to the mass relation $M_h^2+M_H^2=M_A^2+M_Z^2$ of the minimal supersymmetric extension to the standard model are derived. The results indicate that large corrections to the sum rules may arise from heavy matter fields. Squarks significantly heavier than their fermionic partners contribute large contributions when mixing occurs in the squark sector. These large corrections result from squark-Higgs-boson couplings that become large in this limit. Contributions to individual Higgs-boson masses that are quadratic in the squark masses cancel in the sum rule. Thus the naturalness constraint on Higgs-boson masses in hidden in the sum rule.