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Area of Science:

  • High-energy physics
  • Quantum field theory (QFT)
  • Scattering amplitudes

Background:

  • The elliptic double-box integral is crucial for understanding generic massless QFTs.
  • It represents a specific 10-point scattering amplitude in N=4 Super Yang-Mills (SYM) theory.

Purpose of the Study:

  • To express the elliptic double-box integral using elliptic polylogarithms.
  • To analyze the symbol of this integral and uncover its structure.
  • To compare its properties with non-elliptic integrals.

Main Methods:

  • Feynman parametrization was employed to represent the integral.
  • The study involved analyzing the symbol of the elliptic integral.
  • Comparison with known results for non-elliptic integrals was performed.

Main Results:

  • The elliptic double-box integral was successfully expressed in terms of elliptic polylogarithms.
  • Its symbol exhibits a rich structure with notable similarities to the non-elliptic case.
  • The first symbol entry relates to logarithms of dual-conformal cross ratios.

Conclusions:

  • The elliptic double-box integral shares structural similarities with non-elliptic integrals.
  • Elliptic letters appear only in the final two entries of the symbol.
  • This finding offers insights into the mathematical structures governing scattering amplitudes in N=4 SYM theory.