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Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
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Complete Function Space for Planar Two-Loop Six-Particle Scattering Amplitudes.

Johannes Henn1, Antonela Matijašić1,2, Julian Miczajka1

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Summary
This summary is machine-generated.

We derived differential equations for two-loop massless six-particle master integrals, providing analytic solutions. This breakthrough enables future analytic evaluations of scattering amplitudes.

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Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • Mathematical Physics

Background:

  • Calculating scattering amplitudes in quantum field theory is crucial for understanding particle interactions.
  • Two-loop calculations, especially for multi-particle systems, present significant computational challenges.
  • Master integrals are fundamental building blocks for these calculations.

Purpose of the Study:

  • To derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals.
  • To analytically determine boundary conditions and specify the solutions.
  • To provide a framework for evaluating scattering amplitudes and their finite parts.

Main Methods:

  • Derivation of canonical differential equations for master integrals.
  • Analytical determination of boundary conditions.
  • Representation of solutions using Chen iterated integrals.
  • Reduction of integrals with Yang-Mills numerators.
  • Utilizing dihedral symmetry for solution space analysis.

Main Results:

  • Complete set of canonical differential equations for planar two-loop massless six-particle master integrals.
  • Analytically determined boundary conditions, fully specifying the solutions.
  • Solutions expressed as Chen iterated integrals.
  • Identification of the relevant function alphabet and independent iterated integrals up to weight four.
  • Numerical implementation and validation against Feynman integral evaluations.

Conclusions:

  • The derived solutions are sufficient for evaluating scattering amplitudes up to the finite part.
  • The results remove the bottleneck of Feynman integral evaluation.
  • This work paves the way for future analytic evaluations of six-particle scattering amplitudes.