On the breaking of μ–τ permutation symmetry

In view of the observation of a relatively large 𝜃13, one has to break the μ–τ permutation symmetry properly which would otherwise result in a vanishing 𝜃13 (as well as 𝜃23 = π/4). Motivated by this, we study in a thorough way the various symmetry-breaking patterns and in particular whether an approximate this symmetry can lead to viable consequences. Furthermore, the symmetry-breaking effects arising from some specific physics (e.g. the renormalization group running effect) are discussed as well.