A stroll through the loop-tree duality
arXiv:2104.14621
Abstract
The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over an Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.
arXiv comment45 pages, 20 figures. Contribution to the special issue of Symmetry on "Higher Order Radiative Corrections in QCD"
References in corpus (45)
- Asymptotic expansion of Feynman integrals near threshold
- Three-jet cross sections to next-to-leading order
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- Antenna Subtraction at NNLO
- An automatized algorithm to compute infrared divergent multi-loop integrals
- Higgs boson production in association with a jet at next-to-next-to-leading order
- One-Loop Splitting Amplitudes in Gauge Theory
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
- Two-loop Integrand Decomposition into Master Integrals and Surface Terms
- Integration-by-parts reductions from unitarity cuts and algebraic geometry
- Tops from Light Quarks: Full Mass Dependence at Two-Loops in QCD
- Explicit solutions of the 3--loop vacuum integral recurrence relations
- Vector Space of Feynman Integrals and Multivariate Intersection Numbers
- SecDec: A general program for sector decomposition
- To , or not to : Recent developments and comparisons of regularization schemes
- Geometric approach to asymptotic expansion of Feynman integrals
- Hepta-Cuts of Two-Loop Scattering Amplitudes
- Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
- Scattering Amplitudes from Multivariate Polynomial Division
- On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
- A first look at two-loop five-gluon scattering in QCD
- Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
- Loop Tree Duality for multi-loop numerical integration
- Four-dimensional unsubtraction with massive particles
- Towards gauge theories in four dimensions
- Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
- Four-dimensional unsubtraction from the loop-tree duality
- Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
- Adaptive Integrand Decomposition in parallel and orthogonal space
- Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
- On the computation of intersection numbers for twisted cocycles
- Universal four-dimensional representation of at two loops through the Loop-Tree Duality
- Tree-level splitting amplitudes for a quark into four collinear partons
- Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
- Causal representation of multi-loop Feynman integrands within the loop-tree duality
- Integrands of loop amplitudes within loop-tree duality
- Differential equations on unitarity cut surfaces
- Loop-tree duality from vertices and edges
- From multileg loops to trees (by-passing Feynman's Tree Theorem)
- in FDH
- Off-shell Currents and Color-Kinematics Duality
- BCJ Identities and -Dimensional Generalized Unitarity
- Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field Theories
- Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem