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Geometric Neutrino Mass Hierarchy and Leptogenesis in the Minimal Seesaw Model

This work explores the concept of a universal geometric neutrino mass hierarchy and its implications for leptogenesis within the framework of the minimal seesaw model (MSM). We discuss the role of right-handed neutrinos, the preservation of gauge symmetry, and the generation of baryon asymmetry through leptogenesis. Using phenomenological approaches, we link neutrino oscillations and baryon asymmetry, examining the possible configurations of lepton mass matrices inspired by Fritzsch textures. The study provides insights into the connection between neutrino physics and cosmological observations, offering a comprehensive view of neutrino mixing and mass scales.

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Geometric Neutrino Mass Hierarchy and Leptogenesis in the Minimal Seesaw Model

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  1. Geometric -Mass Hierarchy & Leptogenesis Zhi-zhong Xing (IHEP, Beijing) A Conjecture + An Ansatz Seesaw + Leptogenesis -Mixing + Baryogenesis Z.Z.X., Phys. Rev. D 70, 071301 (2004)

  2. Motivation: the new minimal SM Davoudiasl, Kitano, Li, Murayama, hep-ph/0405097 NMSM = MSM + New Physics (Minimal number of new degrees of freedom) Experimental/Observational Evidence for NP: •Dark Matter •Dark Energy •Cosmic Inflation •Cosmic Baryon Asymmetry •Atmospheric & Solar Neutrino Oscillations

  3. Can one stone kill two big birds? The minimal seesaw model: Frampton, Glashow, Yanagida,hep-ph/0208157; …… 2 Right-handed neutrinos added: •Principle of minimal particle content •SU(2)U(1) gauge symmetry preserved { Neutrino Oscillations Baryon Asymmetry Seesaw+Leptogenesis

  4. Is there special -mass hierarchy? 3 Right-handed neutrinos more freedom Conjecture:Universal Geometric Neutrino Mass Hierarchy Z.Z.X.,hep-ph/0406047 (for both light and heavy ); Kaus, Meshkov,hep-ph/0410024 (for light ); Tsujimoto,hep-ph/0501023 (for heavy ). Light Heavy ? Quarks

  5. A plot of fermion mass spectrum (a nomal neutrino mass hierarchy is assumed) Gaps:eV— MeV; and TeV — RH-mass scale

  6. Leptogenesis m m m M M M 1 3 2 10 2 2 1 3 10 GeV 10 GeV Quantum correction Seesaw Oscillations A phenomenological picture:

  7. Atm Sun Geometric -mass hierarchy: at electroweak scale

  8. Renormalization-group equations Minimal SM case Further Conjecture: at the seesaw scale

  9. Seesaw-invariant Fritzsch texture Seesaw relation: Conjecture:Y_ and M_RFritzsch Texture Phase condition Seesaw invariance!

  10. MNS lepton flavor mixing matrix Charged leptons: at the seesaw scale The MNS matrix V arises from mismatch between the diagonalizations of Y_l and Y_ . Due to the normal hierarchy of m_i , RGE effects on V is negligibly small from seesaw to electroweak scales. At low scales, the Fritzsch-like texture of lepton mass matrices is found to be compatible with the present neutrino data at the 3 level. (Z.Z.X.02; Z.Z.X., S. Zhou04)

  11. Isomeric textures and FTY seesaw If M_l and M_ take a parallel and Fritzsch-like form, there are 6 different combinations. Their consequences on lepton flavor mixing are exactly the same --- an isomeric feature! (This feature is also true when the leptogenesis is concerned.) A seesaw ansatz with Fritzsch form of M_l and M_D , but M_R = 1 (3 degenerate heavy neutrinos) by Fukugita, Tanimoto, Yanagida (93, 03): At low scales: better fit to current neutrino oscillations; At seesaw scale:no leptogenesisdue to N-degeneracy.

  12. Leptogenesisatthe seesaw scale Lepton-number-violating decays: CP violation Fukugita, Yanagida86

  13. Baryogenesis via Leptogenesis Out of thermal equilibrium and N_1 decay Net lepton asymmetry Net baryon asymmetry via sphaleron Observation:

  14. CP asymmetry in our ansatz where { (A) Dilution factor (B) in which

  15. The allowed ranges of M_1 and w Input M1, w random

  16. L

  17. Some further comments: •The cosmological baryon asymmetry and the present -oscillation data can simultaneously be interpreted in this phenomenological ansatz •YBcan be extended to the MSSM for •TheCP-violating asymmetry has no direct connection with the low-energy CP violation in neutrino oscillations •Replace by The result is stable, but more free parameters.

  18. Concluding question Leibniz:why is there something rather than nothing? Thanks

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