On the breaking of mu-tau flavor symmetry

In light of the observation of a relatively large ${\theta }_{13}^{}$, one has to consider breaking the $\mu$-$\tau$ symmetry properly which would otherwise result in a vanishing ${\theta }_{13}^{}$ (as well as ${\theta }_{23}^{}=\pi \mathrm{/}4$). Therefore, we investigate various symmetry-breaking patterns and accordingly identify those that are phenomenologically viable. Furthermore, the symmetry-breaking effects arising from some specific physics (e.g., the renormalization group equation running effect) are discussed as well.