Full Angle Dependence of the Four-Loop Cusp Anomalous Dimension in QED

Area of Science:

• High-energy physics
• Quantum field theory
• Particle physics

Background:

• The angle-dependent cusp anomalous dimension describes divergences from soft gluon exchanges between heavy particles, such as top quarks.
• Understanding these divergences is critical for precise predictions in quantum field theory.
• Previous calculations have focused on simpler cases, leaving nonplanar contributions less explored.

Purpose of the Study:

• To compute the first truly nonplanar contributions to the angle-dependent cusp anomalous dimension.
• To specialize the general gauge theory result to Quantum Electrodynamics (QED) and derive the full four-loop result.
• To analyze the analytic and numerical properties of these new terms and their implications for particle interactions.

Main Methods:

• Calculation of four-loop contributions to the cusp anomalous dimension in a general gauge theory.
• Identification of terms proportional to the quartic Casimir operator.
• Specialization to U(1) gauge theory (QED) and analysis of the resulting multiple polylogarithms.
• Evaluation of various kinematic limits and power-suppressed corrections.

Main Results:

• The first nonplanar terms are found to be proportional to a quartic Casimir operator.
• The full four-loop angle-dependent cusp anomalous dimension in QED is derived, expressed in terms of multiple polylogarithms.
• Numerically, the four-loop result closely approximates the rescaled one-loop formula over a wide kinematic range.
• The subleading power correction vanishes in the antiparallel lines limit (threshold production of two massive particles).

Conclusions:

• The complexity of the analytic result belies its simpler numerical behavior and connection to lower-loop orders.
• The derived results provide new insights into soft gluon exchange effects and corrections to particle potentials.
• This work lays the groundwork for understanding nonplanar effects in other supersymmetric gauge theories and QED.