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Nonrenormalization Theorems without Supersymmetry.

Clifford Cheung1, Chia-Hsien Shen1

  • 1Walter Burke Institute for Theoretical Physics California Institute of Technology, Pasadena, California 91125, USA.

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Summary
This summary is machine-generated.

New nonrenormalization theorems constrain quantum field theory. Unitarity and helicity rules prevent divergences in operator running, explaining Standard Model cancellations.

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Area of Science:

  • Theoretical High Energy Physics
  • Quantum Field Theory (QFT)
  • Particle Physics

Background:

  • Higher dimension operators in quantum field theories can exhibit problematic running.
  • Renormalization of operators, particularly in the Standard Model, has shown unexplained cancellations.
  • Understanding operator evolution is crucial for predictive power in QFT.

Purpose of the Study:

  • To derive a new class of one-loop nonrenormalization theorems for general four-dimensional QFTs.
  • To strongly constrain the running of higher dimension operators.
  • To explain and generalize observed cancellations in operator renormalization.

Main Methods:

  • Utilizing unitarity: cuts of one-loop amplitudes are products of tree amplitudes.
  • Identifying selection rules based on helicity configurations that cause tree amplitudes to vanish.
  • Defining holomorphic and antiholomorphic weights (w, w[over ¯]) = (n-h, n+h) for operators.

Main Results:

  • Demonstrated that vanishing tree amplitudes lead to finite one-loop divergences.
  • Established a general condition for operator renormalization: Oᵢ can only be renormalized by Oⱼ if wᵢ ≥ wⱼ and w[over ¯]ᵢ ≥ w[over ¯]ⱼ (absent nonholomorphic Yukawa couplings).
  • Provided a theoretical framework explaining cancellations in the renormalization of dimension-six operators in the Standard Model.

Conclusions:

  • The derived nonrenormalization theorems offer strong constraints on operator running in QFT.
  • The results are general, relying on unitarity and helicity rather than specific symmetries.
  • This work provides a unified explanation for previously observed phenomena in operator renormalization.