Statistical Understanding of Quark and Lepton Masses in Gaussian Landscapes

Abstract

The fundamental theory of nature may allow a large landscape of vacua. Even if the theory contains a unified gauge symmetry, the 22 flavor parameters of the Standard Model, including neutrino masses, may be largely determined by the statistics of this landscape, and not by any symmetry. Then the measured values of the flavor parameters do not lead to any fundamental symmetries, but are statistical accidents; their precise values do not provide any insights into the fundamental theory, rather the overall pattern of flavor reflects the underlying landscape. We investigate whether random selection from the statistics of a simple landscape can explain the broad patterns of quark, charged lepton, and neutrino masses and mixings. We propose Gaussian landscapes as simplified models of landscapes where Yukawa couplings result from overlap integrals of zero-mode wavefunctions in higher-dimensional supersymmetric gauge theories. In terms of just five free parameters, such landscapes can account for all gross features of flavor, including: the hierarchy of quark and charged lepton masses; small quark mixing angles, with 13 mixing less than 12 and 23 mixing; very light Majorana neutrino masses, with the solar to atmospheric neutrino mass ratio consistent with data; distributions for leptonic 12 and 23 mixings that are peaked at large values, while the distribution for 13 mixing is peaked at low values; and order unity CP violating phases in both the quark and lepton sectors. While the statistical distributions for flavor parameters are broad, the distributions are robust to changes in the geometry of the extra dimensions. Constraining the distributions by loose cuts about observed values leads to narrower distributions for neutrino measurements of 13 mixing, CP violation, and neutrinoless double beta decay.

arXiv comment86 pages, 26 figures, 2 tables, and table of contents

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Cited by in corpus (23)

• Codimension-3 Singularities and Yukawa Couplings in F-theory
• Flavor Structure in F-theory Compactifications
• Life at the Interface of Particle Physics and String Theory
• Pieces of the Flavour Puzzle
• Right-handed Neutrinos in F-theory Compactifications
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• Boundary definition of a multiverse measure
• The Multiverse and Particle Physics
• Searching for the Standard Model in the String Landscape : SUSY GUTs
• Quark and Lepton Masses from Gaussian Landscapes
• Statistics of Flux Vacua for Particle Physics
• Statistical Predictions From Anarchic Field Theory Landscapes
• Neutrino mixing and mass hierarchy in Gaussian landscapes
• Neutrino Oscillation Observables from Mass Matrix Structure
• Large Mixing Angles From Many Right-Handed Neutrinos
• Flavor Beyond the Standard Universe
• Degenerate spectrum in the neutrino mass anarchy with Wishart matrices and implications for $0\nu \beta \beta$ and ${\delta }_{\mathrm{CP}}$
• Anthropic Origin of the Neutrino Mass from Cooling Failure
• Quark Masses: An Environmental Impact Statement
• Grand Unified Yukawa Matrix Ansatz: The Standard Model Fermion Mass, Quark Mixing and CP Violation Parameters
• The Concept of an Emergent Cosmographic Vacuum