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Geometric Bookkeeping Guide to Feynman Integral Reduction and ϵ-Factorized Differential Equations.
Iris Bree1, Federico Gasparotto2, Antonela Matijašić1
1Johannes Gutenberg-Universität Mainz, PRISMA Cluster of Excellence, Institut für Physik, D-55099 Mainz, Germany.
We developed an efficient algorithm for Feynman integral reduction and epsilon-factorized differential equations. This method simplifies calculations by trivializing epsilon dependence and directly yielding master integrals.
Area of Science:
- Quantum Field Theory
- High-Energy Physics
- Mathematical Physics
Background:
- Feynman integral reduction is crucial for calculating scattering amplitudes in quantum field theory.
- Existing methods for Feynman integral reduction can be computationally intensive.
- Epsilon-factorized differential equations simplify the analysis of divergent integrals.
Purpose of the Study:
- To present a systematic and efficient algorithm for Feynman integral reduction.
- To obtain epsilon-factorized differential equations for Feynman integrals.
- To improve the efficiency of the Laporta algorithm.
Main Methods:
- Trivializing epsilon dependence in integration-by-parts identities using specific prefactors.
- Employing a specific order relation in the Laporta algorithm to directly obtain master integrals.
- Proving the transformation of differential equations to an epsilon-factorized form.
Main Results:
- A novel algorithm for Feynman integral reduction and epsilon-factorized differential equations.
- Demonstration of trivializing epsilon dependence in integration-by-parts identities.
- Direct derivation of master integrals with differential equations in Laurent polynomial form.
Conclusions:
- The proposed method provides a systematic approach to obtain epsilon-factorized differential equations.
- The improvements significantly enhance the efficiency of Feynman integral reduction.
- This work offers a powerful tool for theoretical physics calculations.
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