Related papers: On multi-propagator angular integrals
The perturbation technique within the framework of the asymptotic iteration method is used to obtain large-order shifted 1/N expansions, where N is the number of spatial dimensions. This method is contrary to the usual…
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to…
We present a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without…
In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three…
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field…
We present the integrand decomposition of multiloop scattering amplitudes in parallel and orthogonal space-time dimensions, $d=d_\parallel+d_\perp$, being $d_\parallel$ the dimension of the parallel space spanned by the legs of the…
We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in $d = 4 - 2\epsilon$ dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces,…
The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D…
A method for calculating phase-space master integrals for the decay process $1 \to n$ massless partons in QCD using integration-by-parts and differential equations techniques is discussed. The method is based on the appropriate choice of…
We apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. After a set of master integrals has been found using the integration-by-parts method, the crucial point of…
We proposed a recipe to systematically calculate Feynman integrals containing linear propagators using the auxiliary mass flow method. The key of the recipe is to introduce a quadratic term for each linear propagator and then using…
We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The…
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…
We find new representations for Itzykson-Zuber like angular integrals for arbitrary beta, in particular for the orthogonal group O(n), the unitary group U(n) and the symplectic group Sp(2n). We rewrite the Haar measure integral, as a flat…
We compute epsilon-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
In order to calculate cross sections with a large number of particles/jets in the final state at next-to-leading order, one has to reduce the occurring scalar and tensor one-loop integrals to a small set of known integrals. In massless…