Related papers: Towards a Numerical Implementation of the Loop-Tre…
The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the…
We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the spinor helicity formalism, color decompositions,…
I discuss the recent advances in the computation of two-loop scattering amplitudes for five-particle processes. The latter are fundamental ingredients to obtain predictions at the next-to-next-to-leading order (NNLO) in QCD for many…
I discuss the state-of-the-art knowledge of long-distance singularities in multi-leg gauge-theory scattering amplitudes and report on an on-going calculation of the three-loop soft anomalous dimension through the renormalization of…
This thesis describes some of the recent (and some less recent) developments in calculational techniques for scattering amplitudes in quantum field theory. The focus is on on-shell recursion relations in complex momenta and on the use of…
We review generalized unitarity as a means for obtaining loop amplitudes from on-shell tree amplitudes. The method is generally applicable to both supersymmetric and non-supersymmetric amplitudes, including non-planar contributions. Here we…
We find that unitarity cuts and the duality between color and kinematics are sufficient constraints to bootstrap $D$-dimensional QCD scattering amplitudes starting from three-particle tree-level. Specifically, we calculate tree level…
We combine recent applications of the two-dimensional quantum inverse scattering method to the scattering amplitude problem in four-dimensional N=4 Super Yang-Mills theory. Integrability allows us to obtain a general, explicit method for…
We show how to apply the BCFW recursion relation to Feynman loop integrals with the help of the Feynman-tree theorem. We deconstruct in this way all Feynman diagrams in terms of on-shell subamplitudes. Every cut originating from the…
Numerical modelling of several coupled passive linear dynamical systems (LDS) is considered. Since such component systems may arise from partial differential equations, transfer function descriptions, lumped systems, measurement data, etc.,…
In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…
We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined,…
A precise understanding of LHC phenomenology requires the inclusion of one-loop corrections for multi-particle final states. In this talk we describe a semi-numerical method to compute one-loop amplitudes with many external particles and…
We introduce a new overlapping Domain Decomposition Method (DDM) to solve the fully nonlinear Monge-Amp\`ere equation. While DDMs have been extensively studied for linear problems, their application to fully nonlinear partial differential…
We introduce an algorithm that samples a set of loop momenta distributed as a given Feynman integrand. The algorithm uses the tropical sampling method and can be applied to evaluate phase-space-type integrals efficiently. We provide an…
We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently…
One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep…
We present a novel framework for computing differential cross-sections in quantum field theory using the optical theorem and loop amplitudes, circumventing the traditional method of squaring scattering amplitudes. This approach addresses…
We show how studying leading singularities of Feynman diagrams, when all momenta are complex, gives a simple way of writing multi-loop and multi-particle scattering amplitudes in N=4 super Yang-Mills. The simplicity of the method is…
We discuss recent progress towards extending the Helac framework to the calculation of two-loop amplitudes. A general algorithm for the automated computation of two-loop integrands is described. The algorithm covers all the steps of the…