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We conjecture that all CP violations (both Dirac and Majorana types) arisefrom a common origin in neutrino seesaw. With this conceptually attractive andsimple conjecture, we deduce that mu-tau breaking shares the common origin withall CP violations. We study the common origin of mu-tau and CP breaking in theDirac mass matrix of seesaw Lagrangian (with right-handed neutrinos beingmu-tau blind), which uniquely leads to inverted mass-ordering of lightneutrinos. We then predict a very different correlation between the two smallmu-tau breaking observables theta_{13}-0 and theta_{23}-45, which can saturatethe present experimental upper limit on theta_{13}. This will be tested againstour previous normal mass-ordering scheme by the on-going oscillationexperiments. We also analyze the correlations of theta_{13} with Jarlskoginvariant and neutrinoless double-beta-decay observable. From the common originof CP and mu-tau breaking in the neutrino seesaw, we establish a direct linkbetween the low energy CP violations and the cosmological CP violation forbaryon asymmetry. With these we further predict a lower bound on theta_{13},supporting the on-going probes of theta_{13} at Daya Bay, Double Chooz and RENOexperiments. Finally, we analyze the general model-independent Z_2 x Z_2symmetry structure of the light neutrino sector, and map it into the seesawsector, where one of the Z_2's corresponds to the mu-tau symmetry and anotherthe hidden symmetry Z_2^s (revealed in our previous work) which dictates thesolar mixing angle \theta_{12}. We derive the physical consequences of thisZ_2^s and its possible partial violation in the presence of mu-tau breaking(without or with neutrino seesaw), regarding the theta_{12} determination andthe correlation between mu-tau breaking observables.

Common Origin of mu-tau and CP Breaking in Neutrino Seesaw, Baryon Asymmetry, and Hidden Flavor Symmetry