Related papers: Numerical Evaluation of Tensor Feynman Integrals i…
The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…
Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle…
A set of programs is presented for automatically generating and calculating Feynman diagrams. Diagrams are generated with FeynArts, then algebraically simplified using a combination of Mathematica and FORM implemented in the package…
Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and especially the definition and study of an…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
We present a method for the analysis of singularities of Feynman amplitudes based on the Speer sector decomposition of the Schwinger parametric integrals combined with the Mellin-Barnes transform. The sector decomposition method is…
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current…
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in $4+\ep$-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric…
We discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to…
The Feynman integral is one of the most accurate methods for calculating density operator dynamics in open quantum systems. However, the number of time steps that can realistically be used is always limited, therefore one often obtains an…
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
Collisions at the LHC produce many-particle final states, and for precise predictions the one-loop $N$-point corrections are needed. We study here the tensor reduction for Feynman integrals with $N \ge 6$. A general, recursive solution by…
We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to…
Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…
A framework to represent and compute two-loop $N$-point Feynman diagrams as double-integrals is discussed. The integrands are 'generalised one-loop type" multi-point functions multiplied by simple weighting factors. The final integrations…
A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for…
We identify cluster algebras for planar kinematics of conformal Feynman integrals in four dimensions, as sub-algebras of that for top-dimensional $G(4,n)$ corresponding to $n$-point massless kinematics. We provide evidence that they encode…