Related papers: Scalar 1-loop Feynman integrals as meromorphic fun…
We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not…
We present an analytical method to calculate the three-loop massive Feynman integral in arbitrary dimensions. The method is based on the Mellin-Barnes representation of the Feynman integral. The Meijer theorem and its corollary are used to…
An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises…
We study the generalized hypergeometric systems, in the sense of Gel'fand, Kapranov, and Zelevinsky, associated with one-loop Feynman integrals, and determine when their rank is independent of space-time dimension and propagator powers.…
We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three…
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…
We propose a systematic approach to calculating $n$-point one-loop parametric conformal integrals in $D$ dimensions which we call the reconstruction procedure. It relies on decomposing a conformal integral over basis functions which are…
Feynman integrals appropriately generalized are $\mathsf A$-hypergeometric functions. Among the properties of $\mathsf A$-hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions…
Hypergeometric function method is proposed to calculate the scalar integrals of Feynman diagrams. For the scalar integral of three-loop vacuum diagram with four-propagator, we verify the equivalency of Feynman parametrization and the…
We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces - an algebraic invariant…
In this sequel calculation of the one-loop Feynman integral pertaining to a massive box diagram contributing to the photon-photon scattering amplitude in quantum electrodynamics, we present the six solutions as yet unknown in the…
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…