Towards a Refined Understanding of Non-holomorphic Soft SUSY-Breaking Effects on the Higgs Boson Mass Spectra

We study the impact of the non-holomorphic (NH) soft supersymmetry-breaking terms $ T_{33}^{\prime D} $ and $ \mu^\prime $, which introduce additional SUSY-breaking effects beyond the holomorphic structure of the superpotential, on the Higgs boson mass spectrum in the NH Minimal Supersymmetric Standard Model (NHSSM). 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 (CCB) 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 $\cal CP$-even Higgs boson mass, $ M_h $, from $ \mu^\prime $ and $ T_{33}^{\prime D} $ can reach up to $ 1.4 \,\, \mathrm{GeV} $ and $ 90 \,\, \mathrm{MeV} $, respectively. For the heavy $\cal CP$-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 \,\, \mathrm{GeV} $ for $ M_H $ and $ 42 \,\, \mathrm{GeV} $ for $ M_{H^{\pm}} $ due to $ \mu^\prime $, and up to $ 60 \,\, \mathrm{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.