Related papers: Numerical evaluation of multi-loop integrals for a…
The calculation of exclusive observables beyond the one-loop level requires elaborate techniques for the computation of multi-leg two-loop integrals. We discuss how the large number of different integrals appearing in actual two-loop…
We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet…
We show that the integration-by-parts reductions of various two-loop integral topologies can be efficiently obtained by applying unitarity cuts to a specific set of subgraphs and solving associated polynomial (syzygy) equations.
We present a simple method which simplifies the evaluation of the on-shell multiple box diagrams reducing them to triangle type ones. For the $L$-loop diagram one gets the expression in terms of Feynman parameters with $2L$-fold…
We obtain a color-kinematics-dual representation of the two-loop four-vector amplitude a general renormalizable massless $\mathcal{N}=1$ SYM theory, including internal matter as chiral supermultiplets. The integrand is constructed to be…
Numerical reconstruction techniques are widely employed in the calculation of multi-loop scattering amplitudes. In recent years, it has been observed that the rational functions in multi-loop calculations greatly simplify under partial…
A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in details. The package includes the explicit expressions for relevant spectral functions calculated up to the…
Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers…
Numerical relativity simulations of merging black holes provide the most accurate description of the binary dynamics and the emitted gravitational wave signal. However, practical considerations such as imperfect initial data and initial…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
The calculation of interaction integrals is a bottleneck for the treatment of many-body quantum systems due to its high numerical cost. We conduct configuration interaction calculations of the few-electron states confined in III-V…
In this paper we introduce an efficient method to unwrap multi-frequency phase estimates for time-of-flight ranging. The algorithm generates multiple depth hypotheses and uses a spatial kernel density estimate (KDE) to rank them. The…
We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for…
A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
We develop an iterative method for constructing four-dimensional generalized unitarity cuts in $\mathcal{N} = 2$ supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets ($\mathcal{N} = 2$ SQCD). For iterated…
We present a semi-numerical method to compute one-loop corrections to processes involving many particles. We treat in detail cases with up to five external legs and massless internal propagators, although the method is more general.
New developments in CARLOMAT, a program for automatic computation of the lowest order cross sections, are presented. They include improvements of the phase integration routines and implementation of extensions of the standard model, such as…
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…