Abstract
We discuss how seesaw neutrino models can be graphically represented in lepton flavour space. We examine various popular models and show how this representation helps understanding their properties and connection with experimental data showing in particular how certain texture zero models are ruled out. We also introduce a new matrix, the bridging matrix, that brings from the light to the heavy neutrino mass flavour basis, showing how this is related to the orthogonal matrix and how different quantities are easily expressed through it. We then show how one can randomly generate orthogonal and leptonic mixing matrices uniformly covering all flavour space in an unbiased way (Haar-distributed matrices). Using the isomorphism between the group of complex rotations and the Lorentz group, we also introduce the concept of Lorentz boost in flavour space for a seesaw model and how this has an insightful physical interpretation. Finally, as a significant application, we consider N2-leptogenesis. Using current experimental values of low energy neutrino parameters, we show that the probability that at least one flavoured decay parameter of the lightest right-handed neutrino is smaller than unity is about 49% (to be compared with the tiny probability that the total decay parameter is smaller than unity, P (KI< 1) ∼ 0.1%, confirming the crucial role played by flavour effects). On the other hand when m1 ≳ 0.1 eV this probability reduces to less than 5%, showing how also N2-leptogenesis disfavours degenerate light neutrinos.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Minkowski, μ → eγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. 67B (1977) 421 [INSPIRE].
T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, in Proceedings of the Workshop on Unified Theory and Baryon Number of the Universe, O. Sawada and A. Sugamoto eds., KEK, (1979), p. 95.
P. Ramond, The Family Group in Grand Unified Theories, in International Symposium on Fundamentals of Quantum Theory and Quantum Field Theory Palm Coast, Florida, February 25 - March 2, 1979, pp. 265-280, 1979, hep-ph/9809459 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex Spinors and Unified Theories, in Supergravity, P. van Niewwenhuizen and D. Freedman eds., North Holland, Amsterdam, (1979), Conf. Proc. C790927 p. 315, PRINT-80-0576.
R. Barbieri, D.V. Nanopoulos, G. Morchio and F. Strocchi, Neutrino Masses in Grand Unified Theories, Phys. Lett. 90B (1980) 91 [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
J.A. Casas and A. Ibarra, Oscillating neutrinos and μ → e, γ, Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [INSPIRE].
S. Lavignac, I. Masina and C.A. Savoy, Large solar angle and seesaw mechanism: A bottom up perspective, Nucl. Phys. B 633 (2002) 139 [hep-ph/0202086] [INSPIRE].
S. Blanchet, P. Di Bari, D.A. Jones and L. Marzola, Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations, JCAP 01 (2013) 041 [arXiv:1112.4528] [INSPIRE].
M. Plümacher, Baryogenesis and lepton number violation, Z. Phys. C 74 (1997) 549 [hep-ph/9604229] [INSPIRE].
E. Nezri and J. Orloff, Neutrino oscillations versus leptogenesis in SO(10) models, JHEP 04 (2003) 020 [hep-ph/0004227] [INSPIRE].
M. Fujii, K. Hamaguchi and T. Yanagida, Leptogenesis with almost degenerate Majorana neutrinos, Phys. Rev. D 65 (2002) 115012 [hep-ph/0202210] [INSPIRE].
E.K. Akhmedov, V.A. Rubakov and A. Yu. Smirnov, Baryogenesis via neutrino oscillations, Phys. Rev. Lett. 81 (1998) 1359 [hep-ph/9803255] [INSPIRE].
A. Anisimov and P. Di Bari, Cold Dark Matter from heavy Right-Handed neutrino mixing, Phys. Rev. D 80 (2009) 073017 [arXiv:0812.5085] [INSPIRE].
A. Yu. Smirnov, Seesaw enhancement of lepton mixing, Phys. Rev. D 48 (1993) 3264 [hep-ph/9304205] [INSPIRE].
W. Buchmüller and M. Plümacher, Baryon asymmetry and neutrino mixing, Phys. Lett. B 389 (1996) 73 [hep-ph/9608308] [INSPIRE].
F. Buccella, D. Falcone and F. Tramontano, Baryogenesis via leptogenesis in SO(10) models, Phys. Lett. B 524 (2002) 241 [hep-ph/0108172] [INSPIRE].
G.C. Branco, R. Gonzalez Felipe, F.R. Joaquim and M.N. Rebelo, Leptogenesis, CP-violation and neutrino data: What can we learn?, Nucl. Phys. B 640 (2002) 202 [hep-ph/0202030] [INSPIRE].
S.F. King, Neutrino mass models, Rept. Prog. Phys. 67 (2004) 107 [hep-ph/0310204] [INSPIRE].
P. Di Bari, Seesaw geometry and leptogenesis, Nucl. Phys. B 727 (2005) 318 [hep-ph/0502082] [INSPIRE].
M.-C. Chen and S.F. King, A4 See-Saw Models and Form Dominance, JHEP 06 (2009) 072 [arXiv:0903.0125] [INSPIRE].
E.E. Jenkins and A.V. Manohar, Tribimaximal Mixing, Leptogenesis and θ 13, Phys. Lett. B 668 (2008) 210 [arXiv:0807.4176] [INSPIRE].
E. Bertuzzo, P. Di Bari, F. Feruglio and E. Nardi, Flavor symmetries, leptogenesis and the absolute neutrino mass scale, JHEP 11 (2009) 036 [arXiv:0908.0161] [INSPIRE].
P.F. Harrison, D.H. Perkins and W.G. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].
S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
R.N. Mohapatra and W. Rodejohann, Scaling in the neutrino mass matrix, Phys. Lett. B 644 (2007) 59 [hep-ph/0608111] [INSPIRE].
R. Sinha, R. Samanta and A. Ghosal, Generalized ℤ2 × ℤ2 in scaling neutrino Majorana mass matrix and baryogenesis via flavored leptogenesis, JHEP 12 (2017) 030 [arXiv:1706.00946] [INSPIRE].
S.F. King, Large mixing angle MSW and atmospheric neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 576 (2000) 85 [hep-ph/9912492] [INSPIRE].
P.H. Frampton, S.L. Glashow and T. Yanagida, Cosmological sign of neutrino CP-violation, Phys. Lett. B 548 (2002) 119 [hep-ph/0208157] [INSPIRE].
P.H. Chankowski and K. Turzynski, Limits on T reh for thermal leptogenesis with hierarchical neutrino masses, Phys. Lett. B 570 (2003) 198 [hep-ph/0306059] [INSPIRE].
A. Ibarra and G.G. Ross, Neutrino phenomenology: The case of two right-handed neutrinos, Phys. Lett. B 591 (2004) 285 [hep-ph/0312138] [INSPIRE].
I. Esteban, M.C. Gonzalez-Garcia, A. Hernandez-Cabezudo, M. Maltoni and T. Schwetz, Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of θ 23 , δ CP and the mass ordering, JHEP 01 (2019) 106 [arXiv:1811.05487] [INSPIRE].
K. Harigaya, M. Ibe and T.T. Yanagida, Seesaw Mechanism with Occam’s Razor, Phys. Rev. D 86 (2012) 013002 [arXiv:1205.2198] [INSPIRE].
D.M. Barreiros, R.G. Felipe and F.R. Joaquim, Minimal type-I seesaw model with maximally restricted texture zeros, Phys. Rev. D 97 (2018) 115016 [arXiv:1802.04563] [INSPIRE].
K Zyczkowski and M Kus, Random unitary matrices, J. Phys. A 27 (1994) 4235.
L.J. Hall, H. Murayama and N. Weiner, Neutrino mass anarchy, Phys. Rev. Lett. 84 (2000) 2572 [hep-ph/9911341] [INSPIRE].
N. Haba and H. Murayama, Anarchy and hierarchy, Phys. Rev. D 63 (2001) 053010 [hep-ph/0009174] [INSPIRE].
E. Nardi, Y. Nir, E. Roulet and J. Racker, The importance of flavor in leptogenesis, JHEP 01 (2006) 164 [hep-ph/0601084] [INSPIRE].
S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP 03 (2007) 018 [hep-ph/0607330] [INSPIRE].
S. Pascoli, S.T. Petcov and A. Riotto, Connecting low energy leptonic CP-violation to leptogenesis, Phys. Rev. D 75 (2007) 083511 [hep-ph/0609125] [INSPIRE].
A. Anisimov, S. Blanchet and P. Di Bari, Viability of Dirac phase leptogenesis, JCAP 04 (2008) 033 [arXiv:0707.3024] [INSPIRE].
K. Moffat, S. Pascoli, S.T. Petcov and J. Turner, Leptogenesis from Low Energy CP Violation, JHEP 03 (2019) 034 [arXiv:1809.08251] [INSPIRE].
O. Vives, Flavor dependence of CP asymmetries and thermal leptogenesis with strong right-handed neutrino mass hierarchy, Phys. Rev. D 73 (2006) 073006 [hep-ph/0512160] [INSPIRE].
P. Di Bari and A. Riotto, Successful type-I Leptogenesis with SO(10)-inspired mass relations, Phys. Lett. B 671 (2009) 462 [arXiv:0809.2285] [INSPIRE].
P. Di Bari and A. Riotto, Testing SO(10)-inspired leptogenesis with low energy neutrino experiments, JCAP 04 (2011) 037 [arXiv:1012.2343] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1812.07720
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Di Bari, P., Re Fiorentin, M. & Samanta, R. Representing seesaw neutrino models and their motion in lepton flavour space. J. High Energ. Phys. 2019, 11 (2019). https://doi.org/10.1007/JHEP05(2019)011
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2019)011