Embedding Generalized CP Symmetry in One Zero Texture Neutrino Mass Models

In this study, we investigate one zero textures within the framework of generalized CP symmetry associated with the complex tribimaximal matrix. By combining these approaches, we derive predictive neutrino mass matrices and establish correlations between different parameters. Future long-baseline experiments, including NO$\nu$A, DUNE, and Hyper-Kamiokande, will provide a test of the predictions for the atmospheric mixing angle arising from this analysis. We also analyze the implications for neutrinoless double beta decay in the context of one-zero textures, in light of current and future experimental data. Our analysis indicates that the sum of the three neutrino masses in the inverted hierarchy is inconsistent with the cosmological bounds from Planck data ($\Sigma m_i < 0.12 \text{eV}$). In addition, constraints from the DESI/SDSS+Pantheon+DES-SN dataset ($\Sigma m_i < 0.17\text{eV}$) within the $\Lambda$CDM + Fluid DR + $\sum m_\nu$ framework at 95\% confidence level also disfavor the inverted hierarchy. In addition, constraints from the DESI experiment ($\Sigma m_i < 0.072$eV) may rule out all matrices in the $X_1$ case except $m_I$, and in the $X_2$ scenario except $m_I$, $m_{II}$, and $m_{III}$. Thus, the improved cosmological observations on $\Sigma m_i$ shall have decisive implications for viability of this class of model.