Higgs Decay to $Z\gamma$ in the Minimal Supersymmetric Standard Model and Its Nonholomorphic Extension

Recent measurements of $ h \rightarrow Z \gamma $ from CMS and ATLAS indicate an excess over Standard Model (SM) predictions, suggesting the presence of new physics. In this work, we investigate the $ h \rightarrow Z \gamma $ decay within the minimal supersymmetric standard model (MSSM) and its nonholomorphic extension, the NHSSM. Calculations are performed using the FeynArts/FormCalc setup, utilizing the pre-existing model file for MSSM and generating the NHSSM model file with the support of {\tt SARAH}. In the allowed parameter space, MSSM contributions to $h \rightarrow Z \gamma$ can significantly surpass SM predictions reaching to the value $\Gamma(h \rightarrow Z \gamma)= 9.77 \times 10^{-6} \text{GeV}$, thereby bringing $ \Gamma (h \rightarrow Z \gamma) $ closer to the experimental value. The SM predicted value deviates from the experimental value by $1.7 \sigma$. However, the MSSM contributions can reduce this deviation to less than $1 \sigma$. In contrast, NHSSM contributions remain negligible and do not produce sizable corrections to the $ h \rightarrow Z \gamma $ decay width.