Majorana neutrino masses by D-brane instanton effects in magnetized orbifold models

Abstract

We study Majorana neutrino masses induced by D-brane instanton effects in magnetized orbifold models. We classify possible cases, where neutrino masses can be induced. Three and four generations are favored in order to generate neutrino masses by D-brane instantons. Explicit mass matrices have specific features. Their diagonalizing matrices correspond to the bimaximal mixing matrix in the case with even magnetic fluxes, independently of the modulus value $\tau$. On the other hand, for odd magnetic fluxes, diagonalizing matrices correspond nearly to the tri-bimaximal mixing matrix near $\tau =i$, while they become the bimaximal mixing matrix for larger $\mathrm{Im}\tau$. For even fluxes, neutrino masses are modular forms of the weight 1 on $T^2/{\mathbb{Z}}_2$, and they have symmetries such as $S_4^{\prime }$ and ${\Delta }^{\prime }(96)\times {\mathbb{Z}}_3$.

Comments: 32 pages, 8 figures