Related papers: A numerical method for NNLO calculations
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular…
The possibility of production of pulses with scale-invariant properties at presence of fluctuations of parameters of self-oscillatory system with three-dimensional phase space is shown. The system of equations of inertial nonlinearity…
We present an analytic technique for evaluating single cuts for one-loop integrands, where exactly one propagator is taken to be on shell. Our method extends the double-cut integration formalism of one-loop amplitudes to the single-cut…
Some methods for the numerical computation of two-loop non-infrared vertices are reviewed. A new method is also proposed and compared to the old ones. Finally, some preliminary results are presented, concerning the evaluation of the…
We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no…
We show that a well-known simple formula for the explicit infrared poles of one-loop QCD amplitudes has a corresponding simple counterpart in unintegrated form. The unintegrated formula approximates the integrand of one-loop QCD amplitudes…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
NLO scattering amplitudes are provided by fully automated numerical tools, such as OpenLoops, for a very wide range of processes. In order to match the numerical precision of current and future collider experiments, the higher precision of…
In this paper we will present a mathematical description and analysis of a fractional-order regulated system in the state space and the state-space controller design based on placing the closed-loop poles on the complex plane. Presented are…
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…
Fully differential next-to-next-to-leading order calculations require a method to cancel infrared singularities. In a previous publication, I discussed the general setup for the subtraction method at NNLO. In this paper I give all…
We present a simple choice of integration variables that can be used to exploit the near-integrable character of problems in celestial mechanics. The approach is based on the well-known principle of variation of parameters: instead of…
We present a novel framework to streamline the calculation of jet and beam functions to next-to-next-to-leading order (NNLO) in perturbation theory. By exploiting the infrared behaviour of the collinear splitting functions, we factorise the…
SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present…
We uncover an unexpected connection between the physics of loop integrals and the mathematics of spline functions. One loop integrands are Laplace transforms of splines. This clarifies the geometry of the associated loop integrals, since a…