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Exact Off Shell Sudakov Form Factor in N=4 Supersymmetric Yang-Mills Theory.

A V Belitsky1, L V Bork2, A F Pikelner3

  • 1Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA.

Physical Review Letters
|March 17, 2023
PubMed
Summary
This summary is machine-generated.

We studied the Sudakov form factor in planar N=4 supersymmetric Yang-Mills theory. We found that terms exponentiate up to three loops, matching twice the logarithm of the null octagon.

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Area of Science:

  • High-energy physics
  • Quantum field theory
  • Supersymmetric gauge theories

Background:

  • The Sudakov form factor is crucial for understanding scattering amplitudes in quantum field theories.
  • Planar N=4 supersymmetric Yang-Mills theory provides a tractable framework for studying non-perturbative effects.
  • Investigating off-shell kinematics is essential for a complete description of physical processes.

Purpose of the Study:

  • To analyze the Sudakov form factor in planar N=4 supersymmetric Yang-Mills theory in the off-shell regime.
  • To investigate the exponentiation properties of both infrared-divergent and finite terms.
  • To compare the results with existing theoretical conjectures and introduce a new relationship.

Main Methods:

  • Consideration of the Coulomb branch to achieve off-shell kinematics.
  • Perturbative calculations up to three loops.
  • Comparison with the recently introduced null octagon within integrability-based approaches.

Main Results:

  • Demonstration of exponentiation for both infrared-divergent and finite terms up to three loops.
  • Identification of the octagon anomalous dimension (Γ_{oct}) as the coefficient of log^{2}(m^{2}).
  • Observation that the logarithm of the Sudakov form factor equals twice the logarithm of the null octagon (O_{0}) up to three loops.

Conclusions:

  • The exponentiation behavior observed contrasts with previous conjectures.
  • The established relationship between the Sudakov form factor and the null octagon suggests a deeper connection.
  • A conjecture is proposed for the all-loop order validity of this relationship, leveraging the known closed form of O_{0}.