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Automatic Fine-Tuning in the Two-Flavor Schwinger Model.

Howard Georgi1

  • 1Center for the Fundamental Laws of Nature, Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review Letters
|November 16, 2020
PubMed
Summary

Conformal coalescence in unparticle physics explains puzzling features in the two-flavor Schwinger model with fermion masses. Isospin-breaking effects are exponentially suppressed, appearing as fine-tuning but automatically handled by this phenomenon.

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Area of Science:

  • Theoretical High Energy Physics
  • Quantum Field Theory
  • Unparticle Physics

Background:

  • The two-flavor Schwinger model is a fundamental model in quantum field theory.
  • Understanding the behavior of fermion masses and their impact on model dynamics is crucial.
  • Puzzling features arise in models with small fermion masses, requiring theoretical explanation.

Purpose of the Study:

  • To analyze the two-flavor Schwinger model with and without fermion masses.
  • To explain puzzling features observed in the model with small fermion masses.
  • To investigate the role of conformal coalescence in simplifying complex theoretical behaviors.

Main Methods:

  • Analysis of the two-flavor Schwinger model.
  • Application of the concept of conformal coalescence from unparticle physics.
  • Examination of isospin-breaking effects in the low-energy theory.

Main Results:

  • Conformal coalescence provides an explanation for puzzling features in the Schwinger model with small fermion masses.
  • Isospin-breaking effects are found to be exponentially suppressed, with suppression factor exp[-(m/m_{f})^{2/3}].
  • This suppression occurs even when the mass difference is comparable to the average fermion mass, provided both are small compared to the dynamical gauge boson mass.

Conclusions:

  • Conformal coalescence automatically handles what appears as exponential fine-tuning in the low-energy theory.
  • The phenomenon simplifies the understanding of isospin-breaking effects in the two-flavor Schwinger model.
  • This work highlights the utility of unparticle physics concepts in resolving complexities in other quantum field theory models.