Symmetries and generalisations of tri-bimaximal neutrino mixing

Tri-bimaximal mixing is a specific lepton mixing ansatz, which has been shown to account very successfully for the established neutrino oscillation data. Working in a particular basis (the ‘circulant basis’), we identify three independent symmetries of tri-bimaximal mixing, which we exploit to set the tri-bimaximal hypothesis in context, alongside some simple, phenomenologically interesting CP-conserving and CP-violating generalisations.