Abstract
We develop a formalism for constructing the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix and neutrino masses using an expansion that originates when a sequence of heavy right handed neutrinos are integrated out, assuming a seesaw mechanism for the origin of neutrino masses. The expansion establishes relationships between the structure of the PMNS matrix and the mass differences of neutrinos, and allows symmetry implications for measured deviations from tri-bimaximal form to be studied systematically. Our approach does not depend on choosing the rotation between the weak and mass eigenstates of the charged lepton fields to be diagonal. We comment on using this expansion to examine the symmetry implications of the recent results from the Daya-Bay collaboration reporting the discovery of a non zero value for θ 13, indicating a deviation from tri-bimaximal form, with a significance of 5.2 σ.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
B. Pontecorvo, Mesonium and anti-mesonium, Sov. Phys. JETP 6 (1957) 429 [INSPIRE].
Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].
G. Fogli, E. Lisi, A. Marrone, A. Palazzo and A. Rotunno, Evidence of θ 13 > 0 from global neutrino data analysis, Phys. Rev. D 84 (2011) 053007 [arXiv:1106.6028] [INSPIRE].
P. Harrison, D. Perkins and W. Scott, Tri-bimaximal mixing and the neutrino oscillation data, Phys. Lett. B 530 (2002) 167 [hep-ph/0202074] [INSPIRE].
G. Altarelli and F. Feruglio, Models of neutrino masses and mixings, New J. Phys. 6 (2004) 106 [hep-ph/0405048] [INSPIRE].
G. Altarelli and F. Feruglio, Discrete Flavor Symmetries and Models of Neutrino Mixing, Rev. Mod. Phys. 82 (2010) 2701 [arXiv:1002.0211] [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].
C. Csáki, C. Delaunay, C. Grojean and Y. Grossman, A Model of Lepton Masses from a Warped Extra Dimension, JHEP 10 (2008) 055 [arXiv:0806.0356] [INSPIRE].
S. Weinberg, The Problem Of Mass, Trans. New York Acad. Sci. 38 (1977) 185.
S. King, Atmospheric and solar neutrinos with a heavy singlet, Phys. Lett. B 439 (1998) 350 [hep-ph/9806440] [INSPIRE].
S. King, Atmospheric and solar neutrinos from single right-handed neutrino dominance and U(1) family symmetry, Nucl. Phys. B 562 (1999) 57 [hep-ph/9904210] [INSPIRE].
S. 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].
S. King, Constructing the large mixing angle MNS matrix in seesaw models with right-handed neutrino dominance, JHEP 09 (2002) 011 [hep-ph/0204360] [INSPIRE].
H. Fritzsch, Calculating the Cabibbo Angle, Phys. Lett. B 70 (1977) 436 [INSPIRE].
H. Harari and Y. Nir, \( B - \overline B \) Mixing and Relations Among Quark Masses, Angles and Phases, Phys. Lett. B 195 (1987) 586 [INSPIRE].
C. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
M. Gell-Mann, P. Ramond and R. Slansky, Supergravity, Amsterdam, North Holland (1979), pg. 315.
T. Yanagida, Horizontal Symmetry and Masses of Neutrinos, in Proc. of the workshop on the unified Theory and Baryon Number in the Universe, KEK, Tsukuba (1979) pg. 95.
R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].
A. Broncano, M. Gavela and E.E. Jenkins, The Effective Lagrangian for the seesaw model of neutrino mass and leptogenesis, Phys. Lett. B 552 (2003) 177 [Erratum ibid. B 636 (2006) 330] [hep-ph/0210271] [INSPIRE].
A. Broncano, M. Gavela and E.E. Jenkins, Neutrino physics in the seesaw model, Nucl. Phys. B 672 (2003) 163 [hep-ph/0307058] [INSPIRE].
E.E. Jenkins and A.V. Manohar, Tribimaximal Mixing, Leptogenesis and θ 13, Phys. Lett. B 668 (2008) 210 [arXiv:0807.4176] [INSPIRE].
S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].
S.A. Thomas, F.B. Abdalla and O. Lahav, Upper Bound of 0.28eV on the Neutrino Masses from the Largest Photometric Redshift Survey, Phys. Rev. Lett. 105 (2010) 031301 [arXiv:0911.5291] [INSPIRE].
E. Otten and C. Weinheimer, Neutrino mass limit from tritium beta decay, Rept. Prog. Phys. 71 (2008) 086201 [arXiv:0909.2104] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1203.4410
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Grinstein, B., Trott, M. An expansion for neutrino phenomenology. J. High Energ. Phys. 2012, 5 (2012). https://doi.org/10.1007/JHEP09(2012)005
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2012)005