Related papers: Differential equations from unitarity cuts: nonpla…
A short review is given of the simplified differential equations approach to Master Integrals, which was recently proposed by one of the authors. We show its applicability by calculating some non-trivial two-loop planar Master Integrals,…
We review the current status of high-multiplicity double-virtual QCD corrections to processes relevant for LHC phenomenology. In particular, we discuss the recent full-color calculation of the five-parton process, whose two-loop amplitudes…
We give an algorithm to compute inhomogeneous differential equations for definite integrals with parameters. The algorithm is based on the integration algorithm for $D$-modules by Oaku. Main tool in the algorithm is the Gr\"obner basis…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
We develop a mixed-integer nonlinear programming (MINLP) approach for the classical Heilbronn triangle problem, demonstrating the capability of modern global optimization solvers to tackle challenging combinatorial geometry problems. A…
Conformal blocks are a central analytic tool for higher dimensional conformal field theory. We employ Harish-Chandra's radial component map to construct universal Casimir differential equations for spinning conformal blocks in any dimension…
In this paper, we focus on both analytical expressions of three and four point integrals for the case of small Gram determinant and numerical improvement of $n$-point integrals for $n\ge5$. Explicit expressions of three and four-point…
We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
The four-loop, two-point form factor contains the first non-planar correction to the lightlike cusp anomalous dimension. This anomalous dimension is a universal function which appears in many applications. Its planar part in N = 4 SYM is…
We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association with a jet at hadron colliders. We construct the system of…
We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…
We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by…
We discuss a numerical package, named ORTHOCUB, for the computation of linear functionals of both integral and differential type on multivariate polynomial spaces. The weighted sums corresponding to such integral and differential cubatures…
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…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…