We study the impact of the non-holomorphic (NH) soft supersymmetry-breaking terms $T_{33}^{\prime D}$ and ${\mu }^{\prime }$, which introduce additional supersymmetry-breaking effects beyond the holomorphic structure of the superpotential, on the Higgs boson mass spectrum in the NH Minimal Supersymmetric Standard Model. The term $T_{33}^{\prime D}$ modifies the scalar bottom-quark mass matrix and Higgs couplings, while ${\mu }^{\prime }$ affects the mass matrices of charginos and neutralinos. In our analysis, we incorporate constraints from charge- and color-breaking minima where we find that a portion of the parameter space is excluded by these constraints. Focusing on the allowed parameter space, the NH contributions to the light $\mathcal{C}\mathcal{P}$-even Higgs boson mass $M_h$ from ${\mu }^{\prime }$ and $T_{33}^{\prime D}$ can reach up to 1.4 GeV and 90 MeV, respectively. For the heavy $\mathcal{C}\mathcal{P}$-even Higgs boson mass $M_H$ and the charged Higgs boson mass $M_{H^{\pm }}$, these contributions can be substantially larger in certain regions of the parameter space, reaching up to 44 GeV for $M_H$ and 42 GeV for $M_{H^{\pm }}$ due to ${\mu }^{\prime }$ and up to 60 GeV due to $T_{33}^{\prime D}$ for both $M_H$ and $M_{H^{\pm }}$. These corrections are significantly larger than the expected future experimental precision for Higgs boson masses and should therefore be considered in precision analyses for future experiments.

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• Hypothetical particle physics models
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