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Disorder in field theories can create large hierarchies, analogous to electron localization in disordered wires. This mechanism explains phenomena like neutrino and quark masses, suggesting disorder, not order, may drive standard model hierarchies.

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Area of Science:

  • Theoretical Physics
  • High Energy Physics
  • Condensed Matter Physics

Background:

  • Exponential hierarchies in fundamental parameters are a key feature of the Standard Model.
  • The origin of these hierarchies, such as the smallness of neutrino masses and the ordering of quark masses, remains unexplained.
  • Anderson localization describes the confinement of electron wave functions in disordered materials.

Purpose of the Study:

  • To introduce a novel mechanism for generating exponential hierarchies in four-dimensional field theories.
  • To explore the analogy between Anderson localization and mass localization in a disordered 'theory space'.
  • To investigate the potential application of this mechanism to Standard Model parameter hierarchies and the electroweak hierarchy problem.

Main Methods:

  • Developed a theoretical framework inspired by Anderson localization in one-dimensional disordered systems.
  • Applied the concept of localized mass eigenstates in a 'theory space' with random mass parameters.
  • Investigated the localization of fields with arbitrary spin.

Main Results:

  • Demonstrated that mass eigenstates can be exponentially localized in theory space, even with weak disorder.
  • Showed that localized mass eigenstates lead to exponentially suppressed couplings.
  • Applied the mechanism to explain the smallness of neutrino masses and the ordering of quark masses.

Conclusions:

  • Disorder provides a viable mechanism for generating the large hierarchies observed in the Standard Model.
  • This framework offers a potential explanation for phenomena beyond the Standard Model, including the electroweak hierarchy problem.
  • The findings suggest that disorder, rather than fundamental order, may be responsible for some of the universe's most significant mass scales.