Leptonic Dirac CP violation predictions from residual discrete symmetries

Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group G (f), and that G (f) is broken to specific residual symmetries G(e) and G(v) of the charged lepton and neutrino mass terms, we derive sum rules for the cosine of the Dirac phase delta of the neutrino mixing matrix U. The residual symmetries considered are: i) G(e) = Z(2) and G(v) = Z(n), n > 2 or Z(n) x Z(m), n,m >= 2; ii) G(e) = Z(n), n > 2 or Z(n) x Z(m), n, m >= 2 and G(v) = Z(2); iii) G(e) = Z(2) and G(v) = Z(2); iv) G(e) is fully broken and G(v) = Z(n), n > 2 or Z(n) x Z(m,) n, m >= 2; and v) G(e) = Z(n), n > 2 or Z(n) x Z(m), n, m >= 2 and G(v) is fully broken. For given G(e) and G(v), the sum rules for cos delta thus derived are exact, within the approach employed, and are valid, in particular, for any G (f) containing G(e) and G(v) as subgroups. We identify the cases when the value of cos delta cannot be determined, or cannot be uniquely determined, without making additional assumptions on unconstrained parameters. In a large class of cases considered the value of cos delta can be unambiguously predicted once the flavour symmetry G (f) is fixed. We present predictions for cos delta in these cases for the flavour symmetry groups G (f) = S-4, A(4), T' and A(5), requiring that the measured values of the 3-neutrino mixing parameters sin(2) theta(12), sin2 theta(13) and sin(2) theta(23), taking into account their respective 3 sigma uncertainties, are successfully reproduced. (C) 2015 The Authors. Published by Elsevier B.V.