Fermion masses and mixing in SO(10) GUT with a universal two-zero texture

We apply a universal two-zero texture (UTZT) to all mass matrices for matters in their flavour space in SO(10) GUT framework. This texture can be realised by assigning different charge for each family in a $Z_6$ symmetry. By fixing charged fermion masses at their best-fit values, we fit the rest 9 precisely measured observables (three angles and one CP-violating phase in the quark mixing, three angles in the lepton mixing, and two neutrino mass-squared differences) with seven model parameters. The model fits all data of fermion masses and mixing very well and the leptonic CP-violating phase is predicted in the range $(90^\circ, 230^\circ)$. The model further predicts the right-handed neutrino masses, with the lightest and heaviest of order $10^9$ and $10^{12}$ GeV, respectively. Gauge unification and proton decay have been checked with the assumption of a breaking chain with two intermediate symmetries above the electroweak scale. It indicates that $\alpha_{\rm GUT}$ ranges in (0.022,0.032) as long as the assumption of economical choice of Higgs contents, and $M_{\rm GUT}$ should be bigger than $4.5\times 10^{15}$ GeV to meet the Super-K bound. We show effective mass $m_{ee}$ for neutrinoless double beta decay, which provides us with a possibility to test grand unification with neutrinoless double beta decay experiments.