Related papers: Monte Carlo evaluation of divergent one-loop integ…
An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This…
We extend the four-dimensional unsubtraction method, which is based on the loop-tree duality (LTD), to deal with processes involving heavy particles. The method allows to perform the summation over degenerate IR configurations directly at…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…
Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The…
We present a new method for the numerical evaluation of loop integrals which is based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
In this paper we present a novel technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. In order to extract…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
We present a completely numerical method of calculating one-loop amplitudes. Our approach is built upon two different existing methods: the contour deformation and the extrapolation methods. Taking the best features of each of them, we…
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…
Contour integral methods for nonlinear eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algorithms, establishing a relationship to system realization…
We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
Mellin-Barnes integral representation of one-loop off-shell box massless diagram is five-fold by construction. On the other hand, it is known from the year 1992 that it may be reduced to certain two-fold Mellin-Barnes integral. We propose a…
Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the…
We review the basic outline of the highly successful diffusion Monte Carlo technique commonly used in contexts ranging from electronic structure calculations to rare event simulation and data assimilation, and propose a new class of…
We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1+1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its…
Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…
Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar…
We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the…