Matter Dependence of the Four-Loop Cusp Anomalous Dimension
J M Henn1, T Peraro2, M Stahlhofen3
1Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 Munich, Germany.
Physical Review Letters
|June 8, 2019
Summary
Researchers analytically computed matter-dependent contributions to the four-loop cusp anomalous dimension in Quantum Chromodynamics (QCD). This calculation advances understanding of fundamental particle interactions and high-energy physics phenomena.
Area of Science:
- High-Energy Physics
- Quantum Field Theory
- Particle Physics
Background:
- The cusp anomalous dimension is a crucial quantity in Quantum Chromodynamics (QCD), particularly in understanding scattering processes at high energies.
- Previous calculations have determined parts of the anomalous dimension, but a complete analytical result, especially concerning matter-dependent contributions, remained elusive.
Purpose of the Study:
- To analytically compute the matter-dependent contributions to the quartic Casimir term of the four-loop lightlike cusp anomalous dimension in QCD.
- To combine results with existing literature to achieve the complete fermion (n_f) and scalar (n_s) flavor dependence of this dimension.
- To provide an improved numerical prediction for the cusp anomalous dimension in N=4 super Yang-Mills theory.
Main Methods:
- Adopted a novel strategy for selecting master integrals with simplified analytic and infrared properties.
- Identified integrals with d-log forms, ensuring uniform transcendental weight.
- Systematically analyzed soft and collinear regions, constructing integral combinations with simpler infrared pole structures.
- Employed the method of differential equations with an auxiliary scale for integral computation.
Main Results:
- Successfully computed the matter-dependent contributions to the quartic Casimir term of the four-loop cusp anomalous dimension in QCD.
- The calculation required only integrals with ten or fewer propagators, demonstrating the efficiency of the new strategy.
- Combined with a parallel study, the complete n_f dependence of the four-loop cusp anomalous dimension in QCD was obtained.
Conclusions:
- The developed method significantly simplifies the calculation of the cusp anomalous dimension.
- The complete analytical result for the four-loop cusp anomalous dimension in QCD, including matter dependence, has been achieved.
- An improved numerical prediction for the cusp anomalous dimension in N=4 super Yang-Mills theory was derived.
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