Related papers: Methods to calculate scalar two-loop vertex diagra…
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…
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
We numerically integrate finite two- and three-loop scalar integrals using the threshold subtraction method. This represents a first step towards extending our calculation of the $N_f$-part to the full NNLO virtual corrections for the…
By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved…
We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given.…
We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the spectral representation to study some…
One and two loop self-energies are worked out explicitly for a heavy scalar field interacting weakly with a light self-interacting scalar field at finite temperature. The ring/daisy diagrams and a set of necklace diagrams can be summed…
Ab initio predictions of two-loop electroweak contributions to observables are increasingly essential for precision collider experiments, yet their evaluation remains very challenging. We connect recurrence techniques and dispersive method…
In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…
The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and…
We present a method for the integrand-level reduction of two-loop helicity amplitudes in both $d=4-2\epsilon$ and $d=4$ dimensions. The amplitude is expressed in terms of a set of Feynman integrals and their coefficients that depend on the…
We discuss the calculation of the nf-contributions to the two-loop amplitude for e+ e- -> q qbar g. The calculation uses an efficient method based on nested sums. The result is presented in terms of multiple polylogarithms with simple…
We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
This paper presents some relations for orthonormal bases in the Minkowski space and isotropic tetrads constructed from the vectors of these bases. As an example of an application of the obtained formulae, in particular recursion relations,…
We present an algorithm for the computation of period matrices and the Abel-Jacobi map of complex superelliptic curves given by an equation $y^m=f(x)$. It relies on rigorous numerical integration of differentials between Weierstrass points,…
We discuss recent progress in multi-loop integrand reduction methods. Motivated by the possibility of an automated construction of multi-loop amplitudes via generalized unitarity cuts we describe a procedure to obtain a general…
3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation…
We present the program SecDec 2.0 which contains various new features: First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities…