Abstract
The large N limit has been successfully applied to QCD, leading to qualitatively correct results even for N = 3. In this work, we propose to treat the number N = 3 of Standard Model generations as a large number. Specifically, we apply this idea to the neutrino anarchy scenario and study neutrino physics using Random Matrix Theory, finding new results in both areas. For neutrino physics, we obtain predictions for the masses and mixing angles as a function of the generation number N. The Seesaw mechanism produces a hierarchy of order 1/N 3 between the lightest and heaviest neutrino, and a θ 13 mixing angle of order 1/N, in parametric agreement with experimental data when N goes to 3. For Random Matrix Theory, this motivates the introduction of a new type of ensemble of random matrices, the “Seesaw ensemble.” Basic properties of such matrices are studied, including the eigenvalue density and the interpretation as a Coulomb gas system. Besides its mathematical interest, the Seesaw ensemble may be useful in random systems where two hierarchical scales exist.
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References
S. Coleman, Aspects of Symmetry, Cambridge University Press, Cambridge U.K. (1985).
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
A.V. Manohar, Large-N QCD, hep-ph/9802419 [INSPIRE].
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].
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].
A. de Gouvêa and H. Murayama, Statistical test of anarchy, Phys. Lett. B 573 (2003) 94 [hep-ph/0301050] [INSPIRE].
A. de Gouvêa and H. Murayama, Neutrino Mixing Anarchy: Alive and Kicking, arXiv:1204.1249 [INSPIRE].
M.L. Mehta, Random Matrices, Academic Press, New York U.S.A. (1991).
M. Stephanov, J. Verbaarschot and T. Wettig, Random matrices, hep-ph/0509286 [INSPIRE].
V. Dahirel et al., Coordinate linkage of HIV evolution reveals regions of immunological vulnerability, Proc. Nat. Acad. Sci. U.S.A. 108 (2011) 11530.
F. Denef and M.R. Douglas, Distributions of nonsupersymmetric flux vacua, JHEP 03 (2005) 061 [hep-th/0411183] [INSPIRE].
D. Marsh, L. McAllister and T. Wrase, The Wasteland of random supergravities, JHEP 03 (2012) 102 [arXiv:1112.3034] [INSPIRE].
X. Chen, G. Shiu, Y. Sumitomo and S.H. Tye, A global view on the search for de-Sitter vacua in (type IIA) string theory, JHEP 04 (2012) 026 [arXiv:1112.3338] [INSPIRE].
F. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3 (1962) 140 [INSPIRE].
A. Steiger, Poincaré-irreducible tensor operators for positive-mass one-particle states. 1., J. Math. Phys. 12 (1971) 1178 [INSPIRE].
A. Altland and M.R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55 (1997) 1142 [INSPIRE].
K. Slevin and T. Nagao, Nonuniversal correlations for random matrix ensembles, J. Math. Phys. 34 (1993) 2075.
K.A. Muttalib, Y. Chen and M.E.H. Ismail, q-Random Matrix Ensembles, cond-mat/0112386.
M. Gonzalez-Garcia, M. Maltoni, J. Salvado and T. Schwetz, Global fit to three neutrino mixing: critical look at present precision, arXiv:1209.3023 [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
S.A. Thomas, F.B. Abdalla and O. Lahav, Upper Bound of 0.28 eV on the Neutrino Masses from the Largest Photometric Redshift Survey, Phys. Rev. Lett. 105 (2010) 031301 [arXiv:0911.5291] [INSPIRE].
Troitsk collaboration, V. Aseev et al., An upper limit on electron antineutrino mass from Troitsk experiment, Phys. Rev. D 84 (2011) 112003 [arXiv:1108.5034] [INSPIRE].
C. Jarlskog, Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP-violation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].
J.D. Bjorken and I. Dunietz, Rephasing Invariant Parametrizations of Generalized Kobayashi-Maskawa Matrices, Phys. Rev. D 36 (1987) 2109 [INSPIRE].
J. Gluza and R. Szafron, Real and complex random neutrino mass matrices and θ 13, Phys. Rev. D 85 (2012) 047701 [arXiv:1111.7278] [INSPIRE].
G. Veneziano, Some aspects of a unified approach to gauge, dual and Gribov theories, Nucl. Phys. B 117 (1976) 519 [INSPIRE].
N. Arkani-Hamed and M. Schmaltz, Hierarchies without symmetries from extra dimensions, Phys. Rev. D 61 (2000) 033005 [hep-ph/9903417] [INSPIRE].
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ArXiv ePrint: 1210.2394
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Bai, Y., Torroba, G. Large N (=3) neutrinos and random matrix theory. J. High Energ. Phys. 2012, 26 (2012). https://doi.org/10.1007/JHEP12(2012)026
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DOI: https://doi.org/10.1007/JHEP12(2012)026