Anarchy and hierarchy

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We advocate a new approach to study models of fermion massesand mixings, namely anarchy proposed in hep-ph/9911341. In this approach,we scan the O(1) coefficients randomly. We argue that this is the correctapproach when the fundamental theory is sufficiently complicated.Assuming there is no physical distinction among three generations ofneutrinos, the probability distributions in MNS mixing angles can bepredicted independent of the choice of the measure. This is because themixing angles are distributed according to the Haar measure of the Liegroups whose elements diagonalize the mass matrices. The near-maximalmixings, as observed in the atmospheric neutrino data and as required inthe LMA solution ... continued below

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Haba, Naoyuki & Murayama, Hitoshi September 14, 2000.

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We advocate a new approach to study models of fermion massesand mixings, namely anarchy proposed in hep-ph/9911341. In this approach,we scan the O(1) coefficients randomly. We argue that this is the correctapproach when the fundamental theory is sufficiently complicated.Assuming there is no physical distinction among three generations ofneutrinos, the probability distributions in MNS mixing angles can bepredicted independent of the choice of the measure. This is because themixing angles are distributed according to the Haar measure of the Liegroups whose elements diagonalize the mass matrices. The near-maximalmixings, as observed in the atmospheric neutrino data and as required inthe LMA solution to the solar neutrino problem, are highly probable. Asmall hierarchy between the Delta m2 for the atmospheric and the solarneutrinos is obtained very easily; the complex seesaw case gives ahierarchy of a factor of 20 as the most probable one, even though thisconclusion is more measure-dependent. U_e3 has to be just below thecurrent limit from the CHOOZ experiment. The CP-violating parameter sindelta is preferred to be maximal. We present a simple SU(5)-likeextension of anarchy to the charged-lepton and quark sectors which workswell phenomenologically.

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  • Journal Name: Physical Review; Journal Volume: D63; Journal Issue: 5; Related Information: Journal Publication Date: 8 February2001

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  • Report No.: LBNL--46831
  • Report No.: UCB-PTH-00/29
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 908479
  • Archival Resource Key: ark:/67531/metadc885534

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  • September 14, 2000

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  • Sept. 22, 2016, 2:13 a.m.

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  • Sept. 29, 2016, 1:41 p.m.

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Haba, Naoyuki & Murayama, Hitoshi. Anarchy and hierarchy, article, September 14, 2000; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc885534/: accessed August 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.