Related papers: The Master Differential Equations for the 2-loop S…
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…
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…
The moments of the real eigenvalues of real Ginibre matrices are investigated from the viewpoint of explicit formulas, differential and difference equations, and large $N$ expansions. These topics are inter-related. For example, a third…
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
We present an efficient approach to evaluate two-center two-electron integrals with exponential functions and with an arbitrary polynomial in electron-nucleus and electron-electron distances. We show that the master integral with the single…
Recently several workers have attempted determinations of the so-called magnetic mass of d=3 non-Abelian gauge theories through a one-loop gap equation, using a free massive propagator as input. Self-consistency is attained only on-shell,…
We present a new method for the momentum expansion of Feynman integrals with arbitrary masses and any number of loops and external momenta. By using the parametric representation we derive a generating function for the coefficients of the…
We present the results for two-loop massive kite master integrals with elliptics in terms of iterated integrals with algebraic kernels. The key ingredients are new integral representations for sunset subgraphs in $d=4-2\epsilon$ and…
An algorithm to construct analytic approximations to two-loop diagrams describing their behaviour at small non-zero thresholds is discussed. For some special cases (involving two different-scale mass parameters), several terms of the…
In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.
A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram…
We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several…
Sunset integrals are among the simplest of two-loop integrals that appear in perturbative quantum field theories and possess up to four distinct mass scales. By means of integration by parts identities, they can be written in terms of four…
We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the…
We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the…
We compute one-loop matter amplitudes in homogeneous Maxwell-Einstein supergravities with N=2 supersymmetry using the double-copy construction. We start from amplitudes of N=2 super-Yang-Mills theory with matter that obey manifestly the…
We consider the two-loop amplitude of $gg\rightarrow HH$ mediated by bottom quarks, which provides a correction of percent level at leading order in the low invariant mass region. In order to compute the corresponding master integrals, we…
We review the main steps of the differential equation approach to the analytic evaluation of Feynman graphs, showing at the same time its application to the 3-loop sunrise graph in a particular kinematical configuration.
We discuss the calculation of two-point three-loop functions with an arbitrary number of massive propagators and one large external momentum. The relevant subdiagrams are generated automatically. The resulting massless two-point integrals…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…