Related papers: Analytical Results for Dimensionally Regularized M…
Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to…
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…
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 a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without…
We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…
Diagrammatic rules are developed for simplifying two-loop QED diagrams with propagators in a constant self-dual background field. This diagrammatic analysis, using dimensional regularization, is used to explain how the fully renormalized…
The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of…
We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our…
In the monotone integer dualization problem, we are given two sets of vectors in an integer box such that no vector in the first set is dominated by a vector in the second. The question is to check if the two sets of vectors cover the…
We apply a recently suggested new strategy to solve differential equations for Feynman integrals. We develop this method further by analyzing asymptotic expansions of the integrals. We argue that this allows the systematic application of…
We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential…
We present a method to obtain analytic results in terms of multiple polylogarithms for one-loop triangle, box and pentagon integrals depending on an arbitrary number of scales and to any desired order in the Laurent expansion in the…
We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as…
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
We elaborate on the application of on-shell and unitarity-based methods for evaluating renormalization group coefficients, and generalize this framework to account for the mixing of operators with different dimensions and leading mass…
We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential…
The general structure of infrared divergences in the scattering of massive particles is captured by the soft anomalous dimension matrix. The latter can be computed from a correlation function of multiple Wilson lines. The state-of-the-art…
Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots in a fixed Region of Interest in the complex plane. The iterations can be applied to a black…
We initiate a systematic study of non-planar on-shell diagrams in N=4 SYM and develop powerful technology for doing so. We introduce canonical variables generalizing face variables, which make the dlog form of the on-shell form explicit. We…