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Three-Loop Corrections to the Soft Anomalous Dimension in Multileg Scattering
Øyvind Almelid1, Claude Duhr2,3, Einan Gardi1
1Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, Scotland, United Kingdom.
Physical Review Letters
|November 9, 2016
Summary
We calculated the three-loop soft anomalous dimension for gauge theory scattering amplitudes. Nondipole corrections appear for three or more partons, with kinematic dependence emerging for four or more.
Area of Science:
- High-energy particle physics
- Quantum field theory
- Scattering amplitudes
Background:
- Long-distance singularities in gauge theories complicate scattering amplitude calculations.
- The soft anomalous dimension governs these singularities.
- Previous calculations were limited to lower orders or simpler configurations.
Purpose of the Study:
- To compute the three-loop soft anomalous dimension for multileg scattering amplitudes of massless partons.
- To analyze the structure and emergence of nondipole corrections.
- To verify consistency with theoretical expectations.
Main Methods:
- Calculation of contributing webs involving semi-infinite Wilson lines at three loops.
- Obtaining the complete three-loop correction to the dipole formula.
- Analysis of nondipole corrections and their kinematic dependence.
Main Results:
- The complete three-loop soft anomalous dimension is derived.
- Nondipole corrections appear for three colored partons as a constant.
- Kinematic dependence, expressed via conformally invariant cross ratios, emerges for four or more partons.
- Results are expressed using single-valued harmonic polylogarithms of weight five.
Conclusions:
- The derived three-loop result provides a significant advancement in understanding scattering amplitudes.
- Nondipole corrections and their kinematic dependence are characterized.
- The results preserve strict collinear factorization properties and are consistent with the Regge limit.
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