Quark and lepton masses and mixing in the landscape

Abstract

Even if quark and lepton masses are not uniquely predicted by the fundamental theory, as may be the case in the string theory landscape, nevertheless their pattern may reveal features of the underlying theory. We use statistical techniques to show that the observed masses appear to be representative of a scale invariant distribution, rho(m) ~ 1/m. If we extend this distribution to include all the Yukawa couplings, we show that the resulting CKM matrix elements typically show a hierarchical pattern similar to observations. The Jarlskog invariant measuring the amount of CP violation is also well reproduced in magnitude. We also apply this framework to neutrinos using the seesaw mechanism. The neutrino results are ambiguous, with the observed pattern being statistically allowed even though the framework does not provide a natural explanation for the observed two large mixing angles. Our framework highly favors a normal hierarchy of neutrino masses. We also are able to make statistical predictions in the neutrino sector when we specialize to situations consistent with the known mass differences and two large mixing angles. Within our framework, we show that with 95% confidence the presently unmeasured MNS mixing angle sin theta_{13} is larger than 0.04 and typically of order 0.1. The leptonic Jarlskog invariant is found to be typically of order 10^{-2} and the magnitude of the effective Majorana mass m_{ee} is typically of order 0.001 eV.

32 pages, 17 figures, some references added

References in corpus (6)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• The Anthropic Landscape of String Theory
• Solar Neutrinos Before and After Neutrino 2004
• Towards a theory of quark masses, mixings and CP-violation
• Anarchy in the neutrino sector?
• Neutrinoless Double $\beta$-Decay: Status and Future

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• The Degree of Fine-Tuning in our Universe -- and Others
• Landscape Predictions for the Higgs Boson and Top Quark Masses
• Likely values of the Higgs vev
• Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes
• The Multiverse and Particle Physics
• Quark and Lepton Masses from Gaussian Landscapes
• Anarchy with Hierarchy: A Probabilistic Appraisal
• The fine-tuning problems of particle physics and anthropic mechanisms
• Measures on Mixing Angles
• Radiative natural supersymmetry emergent from the string landscape
• Neutrino mixing and mass hierarchy in Gaussian landscapes
• Neutrino Anarchy and Renormalization Group Evolution
• Multiverse Predictions for Habitability: The Number of Stars and their Properties
• Naturalness of CP Violation in the Standard Model
• Large Mixing Angles From Many Right-Handed Neutrinos
• Fine-tuned vs. natural supersymmetry: what does the string landscape predict?
• String Landscape and Fermion Masses
• Multiverse Predictions for Habitability: Planetary Characteristics
• Multiverse Predictions for Habitability: Origin of Life Scenarios
• String Theory Bounds on the Cosmological Constant, the Higgs mass, and the Quark and Lepton Masses
• Anthropic Origin of the Neutrino Mass from Cooling Failure
• Probing The Neutrino Sector via A Statistical Approach
• Quark Masses: An Environmental Impact Statement
• The Concept of an Emergent Cosmographic Vacuum