Predictive flavour symmetries of the neutrino mass matrix

Unless flavour symmetries are assumed, particle masses and mixings are generally undetermined in gauge theories. Understanding mass and mixing constitutes one of the biggest challenges in elementary particle physics. Current observations do not determine all elements of the effective neutrino mass matrix Mν completely and this will be a great challenge even for future experiments. Therefore theoretical ideas restricting the structure of Mν are needed in order to guide future searches. One such input studied extensively is the assumption that some entries in the neutrino mass matrix vanish [1]. While the phenomenological implications of the assumed zeros in the texture of Mν are straightforward to derive [2], it is a non-trivial task to produce a good symmetry leading to such zeros and a diagonal charged lepton mass matrix simultaneously. Although for any desired texture structure of the mass matrices such a symmetry is in principle always present, this symmetry and the associated Higgs content are sometimes discouragingly complex [3].