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All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order.

D Chicherin1, T Gehrmann2, J M Henn1

  • 1Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München, Germany.

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|September 7, 2019
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Summary

We analytically solved unknown nonplanar master integrals for massless five-particle scattering at two loops. This breakthrough provides complete two-loop Feynman integrals for precision collider phenomenology.

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Area of Science:

  • High Energy Physics
  • Quantum Field Theory
  • Particle Physics

Background:

  • Calculating multi-loop Feynman integrals is crucial for precise predictions in particle physics.
  • Nonplanar integrals, particularly for multi-particle scattering, present significant analytical challenges.

Purpose of the Study:

  • To analytically evaluate previously unknown nonplanar master integrals for massless five-particle scattering at two loops.
  • To provide a complete set of integrals essential for advancing precision collider phenomenology.

Main Methods:

  • Utilized the differential equations method to analyze the integrals.
  • Obtained a canonical form of differential equations by identifying integrals with constant leading singularities in D space-time dimensions.

Main Results:

  • Successfully evaluated nonplanar master integrals, yielding Q-linear combinations of multiple polylogarithms.
  • Results are consistent with existing conjectures for nonplanar pentagon functions.
  • Provided the complete set of two-loop Feynman integrals for any massless 2→3 scattering process.

Conclusions:

  • The analytical evaluation of these integrals represents a significant advancement in theoretical particle physics.
  • Enables higher precision in theoretical predictions for collider experiments.
  • Opens new avenues for precision collider phenomenology and the study of fundamental interactions.