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Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms
Luise Adams1, Ekta Chaubey1, Stefan Weinzierl1
1PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany.
Physical Review Letters
|April 22, 2017
Summary
We developed a new algorithm using Picard-Fuchs operator factorization to simplify differential equations for multiscale Feynman integrals. This method efficiently decouples complex equations, aiding calculations in quantum field theory.
Area of Science:
- Theoretical Physics
- High Energy Physics
- Quantum Field Theory
Background:
- Multiscale Feynman integrals are crucial in quantum field theory calculations.
- Solving differential equations for these integrals is computationally challenging.
- Picard-Fuchs operators play a key role in analyzing these differential equations.
Purpose of the Study:
- To develop an efficient method for decoupling differential equations of multiscale Feynman integrals.
- To leverage the factorization properties of Picard-Fuchs operators for simplification.
- To provide a tool for converting differential equations into a more manageable 'epsilon form'.
Main Methods:
- Exploiting factorization properties of Picard-Fuchs operators.
- Developing an algorithm to decouple differential equations.
- Reducing differential equations to blocks based on irreducible factors.
Main Results:
- Successfully decoupled differential equations for multiscale Feynman integrals.
- The algorithm reduces complexity by factoring the Picard-Fuchs operator.
- Enabled straightforward conversion of Feynman integral differential equations to epsilon form.
Conclusions:
- The proposed method offers an efficient approach to solving complex Feynman integral equations.
- Factorization of Picard-Fuchs operators is a powerful technique for simplification.
- The developed algorithm facilitates calculations involving multiple polylogarithms.
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