Common origin of soft μ−τ and CP breaking in neutrino seesaw and the origin of matter

Abstract

Neutrino oscillation data strongly support µ−τ symmetry as a good approximate flavor symmetry of the neutrino sector, which has to appear in any viable theory for neutrino mass-generation. The µ−τ breaking is not only small, but also the source of Dirac CP-violation. We conjecture that both discrete µ−τ and CP symmetries are fundamental symmetries of the seesaw Lagrangian (respected by interaction terms), and they are only softly broken, arising from a common origin via a unique dimension-3 Majorana mass-term of the heavy right-handed neutrinos. From this conceptually attractive and simple construction, we can predict the soft µ−τ breaking at low energies, leading to quantitative correlations between the apparently two small deviations θ 23 − 45 • and θ 13 − 0 • . This nontrivially connects the on-going measurements of mixing angle θ 23 with the upcoming experimental probes of θ 13 . We find that any deviation of θ 23 − 45 • must put a lower limit on θ 13 . Furthermore, we deduce the low energy Dirac and Majorana CP violations from a common soft-breaking phase associated with µ−τ breaking in the neutrino seesaw. Finally, from the soft CP breaking in neutrino seesaw we derive the cosmological CP violation for the baryon asymmetry via leptogenesis. We fully reconstruct the leptogenesis CP-asymmetry from the low energy Dirac CP phase and establish a direct link between the cosmological CP-violation and the low energy Jarlskog invariant. We predict new lower and upper bounds on the θ 13 mixing angle,• . In addition, we reveal a new hidden symmetry that dictates the solar mixing angle θ 12 by its group-parameter, and includes the conventional tri-bimaximal mixing as a special case, allowing deviations from it.

Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos

“…Further, the formulation of a viable scheme of baryogenesis via leptogenesis within this scenario is a challenging task. There has also been a substantial amount of work with discrete flavor symmetries of the light neutrino Majorana mass matrix: specifically real µτ permutation symmetry [22][23][24][25][26][27][28][29][30][31] and its complex (CP) extension [32][33][34] as well as real µτ permutation antisymmetry [35] but not the complex (CP) extension of that. This last mentioned topic will be the subject of our attention in this paper with the aim of predicting the neutrino CP phases.…”

Spontaneous mirror parity violation, common origin of matter and dark matter, and the LHC signatures

“…We expect that m 1 should be the typical mass scale of light neutrinos, around m 1 = O(10 −1 −10 −2 ) eV. With the seesaw formalisms [35,36], we will derive m 1 and m ′ 1 explicitly, which also justify the conditions m 1 > m * and m ′ 1 > m ′ * , for the application of κ f formula (3.25) and its extension to κ ′ f . The µ−τ symmetry is a Z 2 invariance of the light neutrino mass-matrix M ν under the exchange ν µ ↔ ν τ .…”

“…In this subsection, we will extend two of our seesaw constructions [35,36] to the present visible and mirror neutrino sectors, where the µ − τ and CP symmetry breakings naturally arise from a common origin. With these, we show how the common origin of visible and dark matter geneses are explicitly realized in the seesaw formalism.…”

“…[37], which are all within 10 • range. A vanishing θ 13 also enforces the absence of Dirac CP violation, so under the attractive conjecture that all CP violations arise from a common origin in the neutrino seesaw, it is deduced that all CP violations share a common origin with µ−τ breaking [35,36].…”

“…In the first case, we found that the common origin of µ−τ and CP violations can be formulated as the unique soft breaking via dimension-3 mass-term of heavy singlet Majorana neutrinos [35]; while in the second case (called µ − τ blind seesaw), we found that this common breaking can be uniquely formulated in the Dirac mass term from Yukawa interactions [36].…”