Related papers: p-adic reconstruction of rational functions in mul…
We perform an analytical four loop calculation of exponent $z$ in model A of critical dynamics in $d=4-2\varepsilon$ dimensions. This is the first time such a large order of perturbation theory has been calculated analytically for models of…
Massive field theory at fixed dimension d<4 is combined with the minimal subtraction scheme to calculate the amplitude functions of thermodynamic quantities for the O(n) symmetric phi^4 model below T_c in two-loop order. Goldstone…
We present the bare one-, two-, and three-loop form factors in massless Quantum Chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their $\epsilon$ expansions and thereby reproduce all…
In practice of acoustic tomography, for example, in medical applications and ocean tomography, the relative deviation of sound speed from its background value usually does not exceed 10-30%. At the same time, in electromagnetic…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
Renormalization of composite three-quark operators in dimensional regularization is complicated by the mixing of physical and unphysical (evanescent) operators. This mixing must be taken into account in a consistent subtraction scheme. In…
Some of the difficulties faced when calculating multi-loop amplitudes with several mass scales are reviewed. We then focus on one particular difficulty, the evaluation of the Feynman integrals, and introduce the program pySecDec which can…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
We propose a numerical spectral reconstruction workflow for high-temperature gauge theories that incorporates elements of semi-classical real-time evolution directly into standard lattice QCD simulations via high-temperature dimensional…
We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.
The advent of efficient numerical algorithms for the construction of one-loop amplitudes has played a crucial role in the automation of NLO calculations, and the development of similar algorithms at two loops is a natural strategy for NNLO…
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the…
We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue…
We study the number of real rational degree n functions (considered up to linear fractional transformations of the independent variable) with a given set of 2n-2 distinct real critical values. We present a combinatorial reformulation of…
The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with…
Multiresolution analysis of electronic structure affords the opportunity to capture the full physics of atomic cores in a systematically improvable manner. Applying new techniques, we demonstrate for the first time that multiresolution…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
In order to approximate transandental functions, several algorithms were proposed.Historically, polynomial interpolation, infinite series, $\cdots$ and other$+,\times, -$ and $/$ based algorithms were studied for this purpose.The CORDIC…