The involved scales are v L = 0.025 eV and v R = 2 v 2 u / ∆m 2 A ≃ 1.2 · 10 15 GeV. As a consequence of non - zero η , the zeroth - order values U e3 = 0 and θ 12 = θ 23 = π/4 are modified to |U e3 | ≃ B ǫ η/ √ 2 , tan 2 θ 23 ≃ 1 − 2 η and tan 2θ 12 ≃ 4 √ 2 B ǫ / η , where for simplicity also η is assumed to be real . The value sin 2 θ 12 = 1 3 is achieved for B ǫ = η/2 . The ratio of the neutrino mass squared differences ∆m 2 ⊙ /∆m 2 A is approximately 3 4 η ( 4 ǫ+η ) . A choice of parameters which leads to neutrino properties that agree with the data , and which we will use in what follows , is B = 1.1 , η = 0.1194 and ǫ = 0.0542 . The low energy phase φ is the Dirac - type CP violation phase which can influence neutrino oscillations .