Abstract
We show renormalization group invariants in neutrino sector. These are found from a simple analytical discussion of Majorana mass matrix for light neutrinos. There are four invariants, which are ratios among elements of the mass matrix. They are independent of neutrino mass ordering and a parameterization of mixing matrix for the lepton sector. We also investigate two running parameters of renormalization group equations, which can directly show neutrino mass matrix at the high energy scale.
Similar content being viewed by others
References
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
B. Pontecorvo, Neutrino experiments and the problem of conservation of leptonic charge, Sov. Phys. JETP 26 (1968) 984 [Zh. Eksp. Teor. Fiz. 53 (1967) 1717] [INSPIRE].
T2K collaboration, K. Abe et al., Indication of electron neutrino appearance from an accelerator-produced off-axis muon neutrino beam, Phys. Rev. Lett. 107 (2011) 041801 [arXiv:1106.2822] [INSPIRE].
MINOS collaboration, P. Adamson et al., Improved search for muon-neutrino to electron-neutrino oscillations in MINOS, Phys. Rev. Lett. 107 (2011) 181802 [arXiv:1108.0015] [INSPIRE].
DOUBLE-CHOOZ collaboration, Y. Abe et al., Indication for the disappearance of reactor electron antineutrinos in the Double CHOOZ experiment, Phys. Rev. Lett. 108 (2012) 131801 [arXiv:1112.6353] [INSPIRE].
DAYA-BAY collaboration, F. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
RENO collaboration, J. Ahn et al., Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
D. Forero, M. Tortola and J. Valle, Global status of neutrino oscillation parameters after Neutrino-2012, Phys. Rev. D 86 (2012) 073012 [arXiv:1205.4018] [INSPIRE].
G. Fogli et al., Global analysis of neutrino masses, mixings and phases: entering the era of leptonic CP-violation searches, Phys. Rev. D 86 (2012) 013012 [arXiv:1205.5254] [INSPIRE].
M. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, JHEP 12 (2012) 123 [arXiv:1209.3023] [INSPIRE].
P. Minkowski, μ → eγ at a rate of one out of 1-billion muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
T. Yanagida, Horizontal symmetry and masses of neutrinos, in Proceedings of the Workshop on Unified Theories and Baryon Number in the Universe, O. Sawada and A. Sugamoto eds., KEK report 79-18, Japan (1979) [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, in Supergravity, P. van Nieuwenhuizen and D.Z. Freedman eds., North Holland, Amsterdam The Netherlands (1979) [arXiv:1306.4669] [INSPIRE].
R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
J. Schechter and J. Valle, Neutrino masses in SU(2) × U(1) theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].
J. Schechter and J. Valle, Neutrino decay and spontaneous violation of lepton number, Phys. Rev. D 25 (1982) 774 [INSPIRE].
P.H. Chankowski and Z. Pluciennik, Renormalization group equations for seesaw neutrino masses, Phys. Lett. B 316 (1993) 312 [hep-ph/9306333] [INSPIRE].
K. Babu, C.N. Leung and J.T. Pantaleone, Renormalization of the neutrino mass operator, Phys. Lett. B 319 (1993) 191 [hep-ph/9309223] [INSPIRE].
J.R. Ellis and S. Lola, Can neutrinos be degenerate in mass?, Phys. Lett. B 458 (1999) 310 [hep-ph/9904279] [INSPIRE].
N. Haba, N. Okamura and M. Sugiura, The renormalization group analysis of the large lepton flavor mixing and the neutrino mass, Prog. Theor. Phys. 103 (2000) 367 [hep-ph/9810471] [INSPIRE].
N. Haba, Y. Matsui, N. Okamura and M. Sugiura, The effect of Majorana phase in degenerate neutrinos, Prog. Theor. Phys. 103 (2000) 145 [hep-ph/9908429] [INSPIRE].
N. Haba, Y. Matsui and N. Okamura, Analytic solutions to the RG equations of the neutrino physical parameters, Prog. Theor. Phys. 103 (2000) 807 [hep-ph/9911481] [INSPIRE].
N. Haba, Y. Matsui and N. Okamura, The effects of Majorana phases in three generation neutrinos, Eur. Phys. J. C 17 (2000) 513 [hep-ph/0005075] [INSPIRE].
N. Haba, Y. Matsui, N. Okamura and T. Suzuki, Are lepton flavor mixings in the democratic mass matrix stable against quantum corrections?, Phys. Lett. B 489 (2000) 184 [hep-ph/0005064] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner and M. Ratz, Running neutrino masses, mixings and CP phases: analytical results and phenomenological consequences, Nucl. Phys. B 674 (2003) 401 [hep-ph/0305273] [INSPIRE].
S. Antusch, J. Kersten, M. Lindner, M. Ratz and M.A. Schmidt, Running neutrino mass parameters in see-saw scenarios, JHEP 03 (2005) 024 [hep-ph/0501272] [INSPIRE].
J.-W. Mei, Running neutrino masses, leptonic mixing angles and CP-violating phases: from M Z to ΛGUT, Phys. Rev. D 71 (2005) 073012 [hep-ph/0502015] [INSPIRE].
J.-W. Mei and Z.-Z. Xing, Radiative corrections to democratic lepton mixing, Phys. Lett. B 623 (2005) 227 [hep-ph/0506304] [INSPIRE].
S. Luo, J.-W. Mei and Z.-Z. Xing, Radiative generation of leptonic CP-violation, Phys. Rev. D 72 (2005) 053014 [hep-ph/0507065] [INSPIRE].
S. Ray, W. Rodejohann and M.A. Schmidt, Lower bounds on the smallest lepton mixing angle, Phys. Rev. D 83 (2011) 033002 [arXiv:1010.1206] [INSPIRE].
S. Luo and Z.-Z. Xing, Impacts of the observed θ 13 on the running behaviors of Dirac and Majorana neutrino mixing angles and CP-violating phases, Phys. Rev. D 86 (2012) 073003 [arXiv:1203.3118] [INSPIRE].
N. Haba, Y. Matsui, N. Okamura and M. Sugiura, Energy scale dependence of the lepton flavor mixing matrix, Eur. Phys. J. C 10 (1999) 677 [hep-ph/9904292] [INSPIRE].
N. Haba and N. Okamura, Stability of the lepton-flavor mixing matrix against quantum corrections, Eur. Phys. J. C 14 (2000) 347 [hep-ph/9906481] [INSPIRE].
N. Haba and R. Takahashi, Grand unification of flavor mixings, Europhys. Lett. 100 (2012) 31001 [arXiv:1206.2793] [INSPIRE].
N. Haba, K. Kaneta and R. Takahashi, Stability of leptonic self-complementarity, Europhys. Lett. 101 (2013) 11001 [arXiv:1209.1522] [INSPIRE].
S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].
R. Mohapatra and W. Rodejohann, Scaling in the neutrino mass matrix, Phys. Lett. B 644 (2007) 59 [hep-ph/0608111] [INSPIRE].
Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].
WMAP collaboration, C. Bennett et al., Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: final maps and results, arXiv:1212.5225 [INSPIRE].
Planck collaboration, P. Ade et al., Planck 2013 results. XV. CMB power spectra and likelihood, arXiv:1303.5075 [INSPIRE].
N. Haba and R. Takahashi, Constraints on neutrino mass ordering and degeneracy from Planck and neutrino-less double beta decay, arXiv:1305.0147 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1306.1375
Rights and permissions
About this article
Cite this article
Haba, N., Takahashi, R. Renormalization group invariants in neutrino sector. J. High Energ. Phys. 2013, 123 (2013). https://doi.org/10.1007/JHEP08(2013)123
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2013)123