Blade: A package for block-triangular form improved Feynman integrals decomposition

Blade: A package for block-triangular form improved Feynman integrals decomposition

23 May 2024 | Xin Guan, Xiao Liu, Yan-Qing Ma, Wen-Hao Wu
Blade is a package for block-triangular form improved Feynman integral decomposition. It is the first public implementation of the block-triangular form method for Feynman integral reduction. The block-triangular form significantly reduces the number of equations compared to traditional integration-by-parts (IBP) systems, allowing for efficient block-by-block solutions. This results in faster evaluations and reduced resource consumption. Blade introduces novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Benchmarks show that Blade is competitive with existing reduction tools. It supports complex kinematic variables, user-defined Feynman prescriptions, and general integrands. Blade provides a structured approach to reduce Feynman integrals by leveraging the block-triangular form, which allows for efficient reduction of complex integrals to master integrals. The package includes algorithms for determining master integrals, symmetry relations, and spanning-sector reduction. It also supports finite field techniques and syzygy equations to further improve the efficiency of the reduction process. Blade is designed to handle a wide range of Feynman integral problems, including those with massive external lines and internal particles. The package is implemented in a modular way, allowing for customization and extension to different types of Feynman integrals. The block-triangular form method is particularly effective for reducing integrals with high loop orders and complex structures. The package provides a systematic way to determine the canonical form of Feynman integrals and to identify symmetry relations between different sectors of the integral family. Blade is a powerful tool for high-energy physics calculations, enabling the efficient reduction of Feynman integrals to master integrals, which are then used to compute scattering amplitudes and other physical quantities.Blade is a package for block-triangular form improved Feynman integral decomposition. It is the first public implementation of the block-triangular form method for Feynman integral reduction. The block-triangular form significantly reduces the number of equations compared to traditional integration-by-parts (IBP) systems, allowing for efficient block-by-block solutions. This results in faster evaluations and reduced resource consumption. Blade introduces novel algorithms for finding the canonical form and symmetry relations of Feynman integrals, as well as for performing spanning-sector reduction. Benchmarks show that Blade is competitive with existing reduction tools. It supports complex kinematic variables, user-defined Feynman prescriptions, and general integrands. Blade provides a structured approach to reduce Feynman integrals by leveraging the block-triangular form, which allows for efficient reduction of complex integrals to master integrals. The package includes algorithms for determining master integrals, symmetry relations, and spanning-sector reduction. It also supports finite field techniques and syzygy equations to further improve the efficiency of the reduction process. Blade is designed to handle a wide range of Feynman integral problems, including those with massive external lines and internal particles. The package is implemented in a modular way, allowing for customization and extension to different types of Feynman integrals. The block-triangular form method is particularly effective for reducing integrals with high loop orders and complex structures. The package provides a systematic way to determine the canonical form of Feynman integrals and to identify symmetry relations between different sectors of the integral family. Blade is a powerful tool for high-energy physics calculations, enabling the efficient reduction of Feynman integrals to master integrals, which are then used to compute scattering amplitudes and other physical quantities.
Reach us at info@study.space
[slides and audio] Blade%3A A package for block-triangular form improved Feynman integrals decomposition