Common origin of reactor and sterile neutrino mixing

If the hints for light sterile neutrinos from short-baseline anomalies are to be taken seriously, global fits indicate active-sterile mixings of a magnitude comparable to the known reactor mixing. We therefore study the conditions under which the active-sterile and reactor mixings could have the same origin in an underlying flavour model. As a starting point, we use $\mu-\tau$ symmetry in the active neutrino sector, which (for three neutrinos) yields a zero reactor neutrino angle and a maximal atmospheric one. We demonstrate that adding one sterile neutrino can change this setting, so that the active-sterile mixing and non-zero $\theta_{13}$ can be generated simultaneously. From the phenomenological perspective, electron (anti)neutrino disappearance can be easily accommodated, while muon neutrino disappearance can vanish. It is, however, difficult to reconcile the LSND results with this scenario. From the theory perspective, the setting requires the misalignment of some of the flavon vacuum expectation values, which may be achieved in an $A_4$ or $D_4$ flavour symmetry model using extra dimensions.