Reduction to master integrals and transverse integration identities
arXiv:2409.04783 · doi:10.1007/JHEP03(2025)113
Abstract
The reduction of Feynman integrals to a basis of linearly independent master integrals is a pivotal step in loop calculations, but also one of the main bottlenecks. In this paper, we assess the impact of using transverse integration identities for the reduction to master integrals. Given an integral family, some of its sectors correspond to diagrams with fewer external legs or to diagrams that can be factorized as products of lower-loop integrals. Using transverse integration identities, i.e. a tensor decomposition in the subspace that is transverse to the external momenta of the diagrams, one can map integrals belonging to such sectors and their subsectors to (products of) integrals belonging to new and simpler integral families, characterized by either fewer generalized denominators, fewer external invariants, fewer loops or combinations thereof. Integral reduction is thus drastically simpler for these new families. We describe a proof-of-concept implementation of the application of transverse integration identities in the context of integral reduction. We include some applications to cutting-edge integral families, showing significant improvements over traditional algorithms.
44 pages, 13 figures, published version
References in corpus (22)
- Algorithm FIRE -- Feynman Integral REduction
- Kira - A Feynman Integral Reduction Program
- FIRE6: Feynman Integral REduction with Modular Arithmetic
- Integral Reduction with Kira 2.0 and Finite Field Methods
- A novel approach to integration by parts reduction
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
- Towards a Basis for Planar Two-Loop Integrals
- Two-loop Integrand Decomposition into Master Integrals and Surface Terms
- Integration-by-parts reductions from unitarity cuts and algebraic geometry
- Reconstructing Rational Functions with
- Vector Space of Feynman Integrals and Multivariate Intersection Numbers
- Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
- Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
- Decomposition of Feynman Integrals by Multivariate Intersection Numbers
- Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
- Adaptive Integrand Decomposition in parallel and orthogonal space
- Isolated photon production in association with a jet pair through next-to-next-to-leading order in QCD
- Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
- Caravel: A C++ Framework for the Computation of Multi-Loop Amplitudes with Numerical Unitarity
- Reduction to master integrals via intersection numbers and polynomial expansions
- Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices