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We introduce the symbol bootstrap method for elliptic Feynman integrals, a key tool in theoretical physics. This study bootstraps a complex integral, yielding a new formula for its components.

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Area of Science:

  • Theoretical Particle Physics
  • Quantum Field Theory
  • Mathematical Physics

Background:

  • Symbolic computation is crucial for Feynman integrals.
  • Elliptic Feynman integrals present significant computational challenges.
  • The symbol bootstrap has been successful for polylogarithmic integrals.

Purpose of the Study:

  • To initiate the symbol bootstrap method for elliptic Feynman integrals.
  • To compute the symbol of a specific twelve-point, two-loop double-box integral.
  • To generalize the Schubert-type analysis to the elliptic case.

Main Methods:

  • Symbol bootstrap technique
  • Schubert-type analysis generalized to elliptic functions
  • Calculation of dual-conformal cross ratios

Main Results:

  • The symbol alphabet for the target integral was determined.
  • The alphabet includes 100 logarithms and nine simple elliptic integrals.
  • A compact, one-line formula for the (2,2) coproduct was derived.

Conclusions:

  • The symbol bootstrap is applicable to elliptic Feynman integrals.
  • This work provides a new method for analyzing complex integrals.
  • The findings offer tools for future calculations in quantum field theory.