All Fermion Masses and Mixings in an Intersecting D-brane World

It is shown that neutrino mixing angles which are consistent with current experimental observations may be naturally obtained in a Pati-Salam model constructed from intersecting D6 branes on a $T^6/(Z_2 \times Z_2)$ orientifold. The Dirac mass matrices in the model are naturally the same as those which are obtained by imposing a $\mathbf{\Delta(27)}$ flavor symmetry, which allows for near-tribimaximal mixing in the neutrino sector. In addition, it is possible to obtain the correct mass matrices for quarks and charged leptons, as well as nearly the correct CKM matrix. An RGE analysis of the neutrino mass parameters, including the seesaw mechanism assuming a specific form for the right-handed neutrino mass matrix is performed, and it is found that the neutrino mixing angles at the electroweak scale are $\theta_{12}=35.0^{\circ}$, $\theta_{23}=47.1^{\circ}$, and $\theta_{13}=8.27^{\circ}$. In addition,the neutrino mass-squared differences are found to be $\Delta m^2_{32} = 0.00252$ eV$^2$ and $\Delta m^2_{21} = 0.0000739$ eV$^2$ with $m_1=0.0146$ eV, $m_2=0.0170$ eV, and $m_3=0.0530$ eV.